complex formation between the 'ferric ion and some...

COMPLEX FORMATION BETWEEN THE 'FERRIC ION AND SOME

HOMOLOGUES OF SALICYLIC ACID AND RELATED .COMPOUNDS

by

Edward Antoni Lipinski

A Thesis submitted to the University of London for the degree of Doctor of Philosophy

Department of Chemical Physics Battersea College of Technology London, S.W.li(now University of Surrey

Guildford, Surrey)March, 1971

tT 9 o Af-.o (c'6

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SUMMARY

A number of coloured 1:1 complexes formed by the Interaction of iron(lll) with ligands containing the phenolic hydroxyl group

of the complexes and the ionisation constants of the ligands were determined by spectrophotometric methods. These methods were devised in such a way that it was possible to calculate the equilibrium hydrogen ion concentrations of the experimental solutions by successive approximations procedures. The direct measurement of the pH's of the solutions was thus avoided, and the only physical quantity measured was the optical density at a selected wavelength. This proved to be particularly valuable in those cases in which complex formation was followed by a fairly rapid reduction-oxidation reaction (ligands I and II). Since a great deal of time and effort was devoted to the selection of the experimental conditions and to the treatment of data, the number of complexes studied was modest. The following ligands were used:

was studied in aqueous solutions at 25°C. The stability constants

I II

o-hydroxyphenylacetic Acid melilotic Acid

III^ Y C O c h 3

^ - O HIV

o-hydroxyacetophenone o-hydroxypropiophenon e

V VIOH

o-hydroxy-n-butyrophenone 3-hydroxycoumarin

Aqueous solutions of the ligands were found to be photochemically unstable in alkaline and, to a lesser extent, in acid media.

Four different variants of the spectrophotometric method for the determination of ionisation constants were used to determine the indicator constant of bromocresol green (B.C.G.) and their relative merits compared and discussed. The indicator constant of B.C.G. was used to determine the first ionisation constants of I and II which could not be determined by direct spectrophotometry. In order to assess the accuracy of the indicator method, the ionisation constants of acetic acid and propionic acid were determined with B.C.G. as the indicator.

It was shown that whereas o-hydroxyphenylacetic acid forms a chelate complex with iron(lll), coordinating through both the phenolic and the carboxyl oxygen atoms, melilotic acid acts as a monodentate ligand, coordinating through the phenolic oxygen only. The iron(lll) complex of 31 is thus a complex acid.

The spectrophotometric methods devised for the determination ofthe stability constants of the complexes formed by iron(111) withmonobasic phenols (ligands III to VI) took into account the dimer,

/ \ -+Fe^OH)^ , and allowed the use of excess of either the metal or the ligand. In comparison with existing methods, these methods are particularly advantageous when the solubility of the ligand is low or when the complex has low stability and/or a small extinction coefficient. When the range of concentrations selected for the determination of stability constants is such that only a small fraction of the constituent (metal or ligand) present at the lower concentration is com- plexed, considerable uncertainties in the determined constant arise, even though it is possible to determine the product: (stability constant) x (extinction coefficient of the complex), with reasonable accuracy. Under certain conditions, these uncertainties are further

A-+exacerbated by the neglect of the dimer Fe^OH)^The stability constants are discussed in relation to the ionisa

tion constants of the ligands and the stabilities of related complexes.

ACKNOWLEDGEMENTS

The work described in this thesis was carried out in theDepartment of Chemical Physics, Battersea College of Technology,now University of Surrey, under the direction of the Head ofDepartment, Professor V.S. Griffiths. It.was a pleasure towork in a department in which the Academic and the TechnicalStaff always had a sympathetic and helpful attitude to research

\

students.

I wish to express my gratitude to Professor Griffiths for his encouragement and help during the course of the work described here and for his patience during the long period of writing it up.

I thank Dr. Z.L. Ernst for a number of critical discussions.

The financial assistance of the Wilmot Breeden Company and of the Battersea College of Technology is gratefully acknowledged.

CONTENTS

Page

SUMMARY 2ACKNOWLEDGEMENTS k

CONTENTS 5LIST OF PRINCIPAL SYMBOLS • 8CHAPTER I INTRODUCTION 11CHAPTER II EXPERIMENTAL 20

Section 2.1 Materials 21Section 2.2 Preparations 2*fSection 2.3 Spectrophotometric Measurements 26Section Processing of Data 29

CHAPTER III SPECTROPHOTOMETRIC DETERMINATION OF THEIONISATION CONSTANTS OF THE LIGANDS 30

Section 3*1 Determination of the Indicator Constant 32of Bromocresol Green

Introduction 32Theoretical 3 *Results and Discussion 39

First Method kO

Second Method 72Third Method 7&Fourth Method 78

Conclusion 82Section 3*2 Determination of the Ionisation Constants

of Acetic Acid and Propionic Acid, using Bromocresol Green 83

Page

Section

Section

Section

CHAPTER IV

Section

Section

3»3 Determination of the First IonisationConstants of o-Hydroxyphenylacetic Acidand Melilotic Acid, using Bromocresol Green 96

3.4 Determination of the Second Ionisation Constants of o-Hydroxyphenylacetic Acidand Melilotic Acid 99

Introduction 99Theoretical 106Calculations and Results 109

3 .5 Determination of the Ionisation Constants of o-Hydroxy-acetophenone, -propiophenoneand -n-butyrophenone 114-

Calculations and Results 122

SPECTROPHOTOMETRIC DETERMINATION OF STABILITY CONSTANTS OF SOME IRON(ill) COMPLEXES 128

4.1 Determination of the Stability Constants of the Complexes Formed by Iron(lll) with o-Hydroxy-acetophenone, -propiophenone and -n-butyrophenone 129

Introduction 129Theoretical 131Results and Discussion 138

4.2 Determination of the Stability Constants of the Complexes formed by Iron(lll) with o-Hydroxyphenylacetic Acid and MeliloticAcid 147

Page

Introduction 14-7Theoretical 154Calculations and Results 158

Section 4.3 Determination-of the Formation Constant of the Complex Formed by Iron (111) v/ith 3-Hydroxycoumarin 184

CHAPTER V COLLATION OF RESULTS AND DISCUSSION 200Section 5*1 Ionisation Constants 200Section 5*2 Stability Constants 212

APPENDICES 220

REFERENCES 231

LIST OF PRINCIPAL SYMBOLS

A Constant of theHebye-Huckel equation for activitycoefficients

a Stoichiometric concentration of a phenola Ion-size parameter (in Angstroms)B Constant of the Debye-Huckel equation for activity

coefficientsb Stoichiometric concentration of sodium hydroxideCT Stoichiometric concentration of bromocresol greenInc Stoichiometric concentration of buffering acidc Concentration of a complexD Optical density (absorbance)d Stoichiometric concentration of perchloric acidE Molar extinction coefficient (molar absorptivity)e Electronic chargeF Faradayfz Activity coefficient of a z-valent ionG Gibbs free energyAG°(g) Standard free energy change of a gas phase reaction at 0°KAG°(g) Standard free energy change of a gas phase reaction at T°KAG°(aq) Standard free energy change of a chemical reaction in water

at T°KG r ? ( S ) Standard free energy of solvation at T°K .H EnthalpyAH°(g), AH°(g), AH°(aq), Standard enthalpy changes defined

analogously to the corresponding free energy changesh Hydrogen-ion concentrationI Ionic strengthK^ Ionisation constant of the complex FeHL^+EL Ionisation constant of a monobasic acid

CL

K ,, K-~ First and second ionisation constant of a dibasic acidal ’ a2

Dimerisation constant of Fe(OH)^4/ 3 2 4* \Formation constant of a complex (Fe + HL ~ FeL + H )

First hydrolysis constant of the ferric ionThermodynamic and classical indicator constant of bromocresol green

3 4" ** p >|>Stability constant of a complex (Fe + L = FeL' )Ionic product of waterSecond ionisation constant of carbonic acid

Kon, Kco Equilibrium constants defined in section k.2ol Ot* ^al». *a2 Microscopic ionisation constants defined in

section 5 «1Path length of a cellStoichiometric concentration of ferric perchlorateArogadros numberNumber of points in a runPressureHydrogen-ion exponent -log KaPartition function Gas constant Radius of an ion Entropy

AsJ(g), AS°(aq), Standard entropy changes definedanalogously to the corresponding free energy changesAbsolute temperatureInternal energy

AU°(g), AU^(aq) Standard internal energy changes defined analogously to the corresponding free energy changesVolumeIndependent variable in a linear relation Dependent variable in a linear relation

Valency of an ion

Intercept of a linear plot Slope of a linear plotResidual Y = Y(observed) - Y(calculated) Residual D = D(observed) - D(calculated) Dielectric constant WavelengthStandard chemical potential Standard deviation

CHAPTER I

INTRODUCTION

The quality of an electrodeposit is often improved by the addition of a selected organic compound to the electroplating solution [l, 2], Thus coumarin is included in the Watts nickel plating solutions because of its action as a brightener and leveller f3» 4-1 • The disadvantage of coumarin as an additive is that its breakdown products, formed at the electrodes and accumulating in the electro-plating solution, have a detrimental effect on the quality of the nickel deposit • Melilotic acid and several hydroxycoumarins havebeen identified as the main breakdown products of coumarin.It was suggested that a possible method of effectively removing these products from the electroplating solution would be to complex them with the ferric ion, which is known [*0 to have a strong affinity for the phenolic hydroxyl group. In order to estimate the extent to which such a reactionvould proceed, the knowledge of the stability constant of the complex is required. The present investigation was started with this end in view; however, as the work proceeded the "centre of gravity” of the study shifted and it was decided to investigate several related systems. The rest of this section will therefore be devoted to a brief review of the previous work on the iron(lll)-phenol complexes.

The colour reaction of ferric chloride with phenols and enols is a well-known test for the phenolic hydroxyl group.Hantzsch and Desch [6] have shown that the presence of a free hydroxyl group in the aromatic ring is essential for the production of colours in this reaction, and that a considerable amount of hydrochloric acid has to be added to destroy these colours. .Weinland and Binder £7] have suggested that the colours are due to the formation of compounds with the general formula C^-Fe-O-C^H^R. V/esp and Brode [8] have shown that the absorption spectra of the solutions produced by mixing

different ferric salts with the same phenol are identical, while*v/hen ferric chloride is mixed with different phenols the spectra,

although of the same shape, occur in different positions. Notingthe similarity of the band shapes of these spectra to that of thecomplex formed by the ferric ion with the thiocyanate anion, at

3—that time thought to have the structure Fe(CNS)^ , they suggested an analogous structure for the iron(lll)-phenol complexes : Fe(ArO)^The increase in the intensity of the colour around the anode during the electrolysis of a mixture of phenol and ferric chloride was regarded by them as confirmation of their proposed formula.However, further investigations [9, 10., 11, 12j have shown that the red ferric thiocyanate complex formed at low concentrations of SON is predominantly Fe(SCN)

Using Job's method of continuous variations, Broumand and Smith [l3] have investigated spectrophotometrically the coloured complexes which iron(lll) forms with phenols, naphthols and enols at low pH values. They have found that monohydric phenols (3-nitrophenol, nitrophenol, salicylaidehyde, salicylic acid), ethyl salicylate and 2-naphthol-3-6-disulphonic acid form 1:1 complexes with the ferric ion. Migration studies Q-3J have shown that the complexes carry a positive charge. The data obtained with resorcinol indicated a 2:1 as well as a 1:1 complex, and with phloroglucinol as many as three ferric ions appear to combine with one molecule of the phenol [13] *

A large number of investigations [lA- to 39] have been devoted to the study of the nature and stability of the complexes formed by the ferric ion with salicylic acid and its derivatives in aqueous solutions. Most of the studies have been carried out using either potentiometry or spectrophotometry and pH measurements.

The complexes of salicylic acid [l4 to 29] itself and its 3-sulpho [19, 20, 22, 24, 30 to 36] and 4 -amino [1 7 , 19, 20, 2k, 37] aeri- vatives have been particularly extensively studied. The consensus of opinion is that substituted salicylic acids react with iron(lll) according to the equation:

1/ X'CCUH

+ Fe3+ • =O H

/

X o.

+

ox H I j. c 3'1' c l (3_2n)+n H 2 L + Fe Fe Ln 4- 2nH Cm )where n = 1, 2 or 3i and x is a substituent in the benzene ring.

Which of these three complexes will be present at a predominant concentration in a given solution is dictated to a large degree by the pH value of the solution; there is general agreement that at low pH values (pH<3) only the 1:1 complex is formed.

Park [29] used potentiometry to determine the stepv/ise equilibrium constants for reaction (1.1) with seven substituted salicylic acids. He found some evidence for the formation of

2 - fprotonated complexes of the type FeLH . .Ernst and Menashi [2 7 , 3 9] ,' in a careful and detailed study, have used spectrophotometry to measure with high precision the stability constants of the 1:1 complexes and the absorption spectra of several (X=H, 3-Me,3-N02, 5-C1, 3-Br and substituted salicylic acids. They havefound no evidence for the formation of either hydroxy or protonated complexes. These authors have obtained [39] an excellent correlation (correlation coefficient = 0.996) betY/een the logarithm of the stability constant of the complex and the negative logarithm of the product of the two ionisation constants of the ligand. The value ofthe slope ( <1) of their correlation plot led them to the conclusionthat the ferric ion acts as a TT-electron donor.

However, they also observed that as the TT-donor tendency of the ligand increases, the characteristic band of the complex shifts to longer wavelengths, suggesting that the ferric ion acts as a

II- electron acceptor. They concluded that the dilemma could be resolved "if in ferric salicylate complexes the ferric ion behaves as'a U-donor in the ground state and a ti- electron acceptor in the excited state".

At low pH values, simple monohydric phenols form 1:1 complexes with the ferric ion, according to the equation [13* 1^» ^0, 41, 42, 43] :

OFe2+0-2)

where x is a substituent in the benzene ring.

If a formyl, acetyl, ester or an amido group is present in the orthoposition to the hydroxyl group, then it is generally assumed [Mf, 4-5»46, 47] that a chelate is formed, i.e.

O H= < 2 + H+ O'3)

v ywhere y = H, NH^, R, COR j R being an alkyl group.

Chelate complexes of the type shown in reaction (1.3) have higher thermodynamic stabilities than those in which the phenol acts as a monodentate ligand. By using chelating ligands it appears possible in some favourable cases to obtain high enough concentrations of the 1:2 complex for the measurement of its stability constant [VO • With most simple phenols, however, it is only possible to measure the stability constant of the 1:1 complex.'

Babko (V)"] has reported an equilibrium constant for reaction (1.2) with X ~ H, and found that it is impossible to produce conditions under which this reaction goes to completion. He neglected iron(lll) removed by hydrolysis, the temperature was not controlled, no attempt was made to keep the ionic strength constant or to take activity coefficients into account, and measurements were not made until the initially changing optical densities had become steady (See section 2.3, p. 2S ).

Jatkar and Mattoo [4 7] have studied this reaction with X = 2-CH^, 2-CHO and 2-COCH^. They also disregarded temperature control, ionic strength and changing optical densities, as well as the competing hydrolysis reactions and the formation of iron(111) - chloride complexes. More important, they neglected to control or to have knowledge of the hydrogen ion concentrations, and identified the phenolate ion concentrations with the total phenol introduced into the solutions.

The first systematic and reliable study of reaction (1.2) was made by Milburn [41] who measured spectrophotometrically the thermodynamic equilibrium constants for reaction (1.2) with X = H, 4-CH,,34-Br, 4-NC>2 and He drew attention to the photochemicalinstability of these complexes and allowed for its effects by devising a method which is also used in the present v/ork, (see section 2.3, p» 26 )• By means of the Sarmousakis equation [48 [] , Milburn calculated the equilibrium constants for the exchange reaction:

X C ^ O F e 2+ C ^ c T = XC6H/fO“ 4- C ^ O F e 2+ (1.4)

Since the values computed in this way differed markedly from the experimental values, he concluded that, the simple electrostatic model with localised charges is inadequate for the explanation of the bonding in these complexes.

Ernst and Hearing have extended Milburn1 s work bymeasuring spectrophotometrically the stability constants of 15

mono substituted phenols. They found that their own data and Milburn'sdata conform roughly to the linear relation

log10 Kg = - a log10 + b (1.5)where K is the ionisation constant of the phenol and KP the ecuili-a “ obrium constant for the reaction

Fe3* +, XCgH^O ~ — XC^OFe 2+ (1.6)

The values of the empirical constants a and b were found to be0.8 - 0.3 and 0,3 i'2.8 respectively. Basing their interpretationon Williams* suggestion [%-9 ] that the slope of such a correlationplot is a measure of TT-bonding, Ernst and Hejnring concluded that inferric phenolate complexes the ferric ion behaves as a {1-electrondonor. It has to be pointed out, however, that the experimentalconditions used by Ernst and Kefcring in some instances did not justify

*f+the neglect of the concentration of the dimer Fe2 (cH)2 ; as a result of this approximation, some of the stability constants reported by them could be in error by as much as 100 - 200 % I

A recent potentiometric redetermination by Jabarpurv/ala and Milburn of the stability constants of some Ik ferric phenolatesshows that the values obtained by this method are consistently larger (by about 300%) than the values determined spectrophotometrically. Furthermore, when the potentiometric results were fitted to equation (1.5)» a- value of b = 1.01 - 0.04 was obtained, suggesting that N- bonding is unimportant in these complexes.

This conclusion is supported by Milburn's [_30] latest work, in which he reports A H values for reaction (1.2) (X=H, f-Cl, 4-NO2

and 3-N02). The enthalpy changes are expressed as the sumA H = AH(int) + A H (ext) (1.7)

where A H (int) is attributed to the internal contributions within the reactant species, and AH(ext)as the contribution due to the solvent- solute interactions; and the values of A H (int) are estimated for reaction (1.6). A plot of these values against the values of (-AH(int)) for the ionisation of the corresponding substituted phenols was found to be linear, with a slope of unity.

The absorption band which the iron(111)-phenol complexes exhibit in the visible region of the spectrum, and which is responsible for their characteristic colouration, has been interpreted as being due to charge transfer. According to Williams [51, 52] it arises as a result of a transition of an electron from the ligand into one of the t2g orbitals of the ferric ion, vacated by a previous d-d transition within the metal ion.

One object of the-present work was to determine the effect of the alkyl group R ( = Me, Et, n-Pr) on the ionisation constants of the phenols of the type HO-C^H^’COR, and to see how far such effects are reflected in the stability constants of the 1:1 complexes formed by these phenols with the ferric ion. The complexes of the ferric ion with o-hydroxyphenyl^acetie acid and melilotic acid were studied in order to determine whether these ligands react with the ferric ion in the same manner as salicylic acid or whether they act as monodentate ligands, co-ordinating to the metal through the phenolic oxygen atom only. The formation constant of the iron(ill)-3-hydroxy-coumarin complex was also studied.

Due to a large number of factors (such as purity of materials, control of temperature, ionic strength and pH, accuracy of physical measurements, range of metal and ligand concentrations, allowance for side reactions and the quality of the constants used for this purpose, method of calculation) which have a bearing on the accuracy with which stability constants can be determined, and since the study of the

literature [53] shows that carelessly obtained results often lead to contradictory conclusions, it was felt desirable to devote much care and attention to the experimental determination of the various equilibrium constants and the estimation of the reliability of the methods used, even if it meant that the number of complexes studied was less than had been initially hoped for.

CHAPTER II

EXPERIMENTAL

SECTION 2.1 MATERIALS Purification of Materials

Acetic acid, sodium carbonate, perchloric acid and sodium hydroxide were all "AnalaR" grade (B.D.H.) and were used without further purification.

Bromocresol green was recrystallised three times from glacial acetic acid, and dried at 110°C for 3 hours before use.

Propionic acid was redistilled tv/ice, the middle fraction being collected each time.

o-Hydroxyphenylacetic acid and o-hydroxyphenylproplonic acid were purified by repeated recrystallisation from aqueous ethanol and from conductivity water respectively and dried over phosphorus pentoxide for two weeks. The purity of these acids, as well as that of acetic acid and propionic acid, was checked by titration against standard alkali.

o-Hydroxyacetophenone, o-hydroxypropiophenone and o-hydroxy-n- butyrophenone were purified by distillation under reduced pressure in an atmosphere of nitrogen. The distillations were repeated until the refractive indices of two, successive fractions were within 0.1% of each other. The extrapolated boiling points of these three compounds were in reasonable agreement with literature values.

The melting points or the boiling points of the organic materials used in this work are listed in table 2.1.

Bromocresol GreenStock solutions of bromocresol green were prepared by dissolving

a weighed amount of the indicator in dilute sodium hydroxide or sodium carbonate of a known concentration.

TABLE 2.1

Compound

Bromocresol greeno-Hydroxyaceto-

phenoneo-Hydroxybutyro-

phenone3-Hydroxy-

coumarino-Hydroxyphenyl- acetic acido-Hydroxypropio-phenone

Melilotic acidPropionic acid

Origin of Sample

B.D.H.Light and CoLtd

Light and CoLtd

Synthesised

light and CoLtd

SynthesisedB.D.H.

Melting Point (°C)

Observed Literature

217-219 218-219

152 153

87-88 86

Boiling Point (°C)

Observed literature

214-216 217.3

124 12 4 -126(l4mzn%) (l4nmHg)

148 150(SOmmHg) (80mm%)

141-142 l4l

Light and CoLtd 147-148 147-149

Reference

3435

56

56

56

56

456

Ferric perchlorateFerric hydroxide was prepared ["57] by precipitation from a

hot solution of ferric chloride with a slight excess of ammonia. The precipitate was washed with water until it gave a negative test for chloride ions and then dissolved in 72% perchloric acid. Crystals of hydrated ferric perchlorate obtained from this solution.were filtered through a sintered glass funnel and some of the excess perchloric acid was washed away with water.

Stock solutions of ferric perchlorate were prepared by dissolving crystalline ferric perchlorate in perchloric acid, and were analysed for iron(ill) both gravimetrically [58] (as Fe20^) and volumetrically [58]. The perchloric acid content was determined by titrating these solutions with standard sodium hydroxide to a phenolphthalein end-point [59]• Towards the end of the titration, after each addition of alkali, the precipitated iron(111) hydroxide was allowed to settle and the colour of the supernatant liquid was observed. The excess perchloric acid was calculated from the total alkali required and the known iron (111) concentration. The following three stock solutions of ferric perchlorate were used :

a) 0.1042 M in ferric perchlorate and 0.0190M in perchloric acidb) 0.1052 M in ferric perchlorate and 0.01880 M in perchloric acidc) 0.1102 M in ferric perchlora.te and 0.0627 M in perchloric acid.

Perchloric AcidStandard solutions of perchloric acid were prepared from

HAnalaR,f 72% perchloric acid and were standardised against both sodium carbonate and borax.

Sodium HydroxideStandard solutions were prepared by transferring a filtered,

approximately 50%, sodium hydroxide solution into either a nickel or

a polythene bottle ["6o] fitted with a soda lime guard tube and containing the requisite amount of carbon dioxide-free conductivity water. The resulting solution was standardised against potassium hydrogen phthalate and standard perchloric acid. In experiments in which either sodium hydroxide or sodium carbonate was used, all solutions were made up with cahbon dioxide-free conductivity water.

Na~.CC).. /-NaHCO, buffer solutions 2 _____________These solutions were prepared by adding a standard perchloric

acid solution to a solution of sodium carbonate. In order to prevent loss of carbon dioxide, the acid was added below the surface of the sodium carbonate solution.

SECTION 2.2 .PREPARATIONS

Melilotic acidThe reduction of orthocoumaric acid with 1% sodium amalgam by

the standard procedure [6l] was initially used for the preparation of melilotic acid. Subsequently it was obtained more conveniently [3] from commercial dihydrocoumarin. A mixture of dihydrocoumarin (l6g) and dilute sulphuric acid (50 ml.) was shaken in a mechanical shaker until a white precipitate was formed and the supernatant liquid lost its initial turbidity. The product (17g) was recrystallised from aqueous ethanol.3-Hydroscycoumarin •

3-Hydroxycoumarin was prepared [62] »by hydrolysis of 3-acetamidocoumarin, v/hich was obtained by the condensation of salicylaldehyde with acetylglycine:

/NtfCOCHs| f * Y CH0 + f H* .(ch,cq)zO ; | P ^ Y M H C 0 CH5 | ^ V ^ f 0H

CH3CO2.A/0L k v; ^k.o / C O H a

(i) Ace-tyl glycineAcetic anhydride (358g.) was added in one portion to a

solution of glycine (123g. ) in water(300ml.) and the mixture stirred for 20 minutes. Acetylglycine, which crystallised out on cooling, was filtered off and washed with ice-cold water. Yield 130g;M.Pt. 206-208°C*

(ii) 3-AcetamidocouraarinA mixture of S&licylaldehyde (122g.), acetylglycine (117g.),

anhydrous sodium acetate (82g.) and acetic anhydride (300g.) was rapidly heated to 100°C and maintained at this temperature for 2 hours. After cooling and filtering, the crystal mass was warmed with benzene (1 litre) and filtered; this was repeated with two further portions of benzene (500 ml.). The storage of these benzene extracts in a refrigerator overnight led to extensive crystal!sation of 3-acetamiaocoumarin which was filtered off and used in the next stage without further purification. Yield: 46g. ; M.Pt.: 20*f-203°C.

(iii) 3-Hydroxycoumarin3-Acetamidocoumarin (40g.) was refluxed with 3N hydrochloric

acid (600 ml.) for two hours under an atmosphere of nitrogen and then the hot reaction mixture was filtered. On chilling the filtrate in an ice-salt mixture, 3-kydroxycoumarin (23g») crystallised out. The product was recrystallised from water as white needles.

SECTION 2.3 SPECTPOPHOTOMETBIC MEASUREMENTS

The SpectrophotometerSpectrophotometric measurements were made by means of a Unicam

S.P.300 spectrophotometer. It is a manual instrument and consists of: a deuterium lamp for the 200-330 mp range and a tungsten lamp for the 350 -1000 mp range, a quartz prism monochromator and interchangeable blue and red photocells for the ranges 200-623 mp and 623-IOOO mp respectively. The photocell output current is measured by balancing the drop across a load resistance of 2000 megohms with a slide wire potentiometer calibrated in both percentage transmittance and optical density. The sensitivity control varies the electrical sensitivity by approximately 10 to 1, allowing the user to set the slit width and operate at predetermined widths. A switch which increases the scale sensitivity by a factor of 10 and permits greater accuracy of reading when the transmittance value is below 10% is also provided.

The instrument was fitted with a Unicam S.P.370 Constant Temperature Cell housing, through which water (thermostated at 25°C)was circulated by means of a "Circotherm” Unit (supplied by Shandon and Co.). All optical density measurements were made at a temperature cf 23°C - 0.1°C.

Calibration of the SpectrophotometerOccasional checks of both the wavelength scale and the optical

density calibration were made throughout the course cf this work.For the optical density calibrations, an aqueous solution of potassium chromate [*63] in 0.03K KOH was used as a standard. The wavelength scale was checked by means of the hydrogen lines at 6563 2 and 4861 2 . Treatment of Cells and Optical Density Measurements

Matched silica cells (of either 1cm. or 4cm. path length) were used in all spectrophotometric measurements. Concentrated nitric acid,

diluted with water in the ratio 1:1, was used for cleaning the cells; when not in use, the cells were stored in this solution. To measure the optical density of a solution, the following procedure was followed first the cell correction was obtained by filling both cells with the solvent and measuring the optical density of the lfsample cell", with the other cell as reference; then the "sample cell" was filled with the solution, placed in the instrument in exactly the same position as before and its optical density measured; the difference between these two readings gave the corrected optical density. In measurements where sodium hydroxide was employed, the dry "sample cell" was quickly filled with the solution and stoppered. A quick and efficient method of obtaining a clean dry cell consists of washing the cell with water followed by alcohol, acetone and ether.

As far as possible, the concentrations of the absorbing species were adjusted to give optical density readings within the range 0.2 to 0.8. When measurements were made at a fixed wavelength, the specified wavelength was always approached from one direction, in order to prevent back-lash; the slit width was then set and all measurements made using this fixed slit width.

Optical density measurements made with bromocresol green were all obtained on single solutions; in all other experiments the optical densities used for calculation purposes were averages of the readings obtained with duplicate solutions.

The solutions which were found to be stable over a period of oneday or longer were placed in a thermostat at 25°C and allowed to reachthermal equilibrium. Then a portion of the solution under study was transferred to an optical cell and placed in a thermostated cell holderof the spectrophotometer, where the solution remained until itsoptical density attained a steady value, indicating the establishment

of thermal equilibrium. In most cases the difference between.the optical density measured immediately after the transfer of the solution to the cell holder and after a period of 5 - 15 minutes was insignificant. The optical density of a solution was taken as an average of at least five successive readings.

The solutions of the complexes formed between iron(lll) and phenols are photochemically unstable [4l]. As a result of this instability, the colour of the solutions fades with time and a brownish precipitate is produced in some cases. The processes which take place involve a reduction of the ferric ion (the production of the ferrous ion may be demonstrated by the development of a characteristic red colouration on addition of o-phenanthreline) and an oxidation and polymerisation of the phenols [64^ * The rates at which these processes take place change from one ligand to the next. For example, when melilotic acid is mixed with the ferric ion, within minutes the initial blue colour changes to green and then to yellow, and a brownish precipitate is produced. In contrast, with o-hydroxyacetophenone the initial violet colour persists for months. For the measurement of the optical densities of these unstable solutions the method developed by Milburn [4l] was used. The solution containing all the required constituents except the ferric perchlorate was equilibrated in a thermostat at 23°C. Then the required amount of ferric perchlorate (also equilibrated at 25°C) was pipetted into the above solution, a sample of this mixture quickly transferred into an optical cell and placed in a spectrophotometer. Readings of optical density were taken at intervals for about 10 minutes - the time interval between mixing and the first measurement rarely exceeding 60 seconds. These readings were then plotted against time and the graph extrapolated to zero time. In the calculation of stability constants, these extrapolated values were used. The validity of this procedure rests on the assumption that

the complexation equilibria are established within the time of mixing and that the drift in optical densities is due to a subsequent, slower, oxidation - reduction reaction.

SECTION 2.4 PROCESSING OF DATAMost of the calculations required in the course of this work

were carried out on the I.C.L. Sirius and Elliott 803 computers. Programmes were written by the author in either the Sirius Autocode or the Elliott A103 Autocode.

CHAPTER III

SPECTROPHOTOMETRIC DETERMINATION OF THE IONISATION CONSTANTS OF THE LIGANDS

INTRODUCTIONr

Accurate determinations of ionisation constants of weak acids have depended in large part on conductometric and electrometric methods. A third method, that of spectrophotometry, has been increasingly used [6 5, 66]] since the war, when photoelectric spectrophotometers became commercially available. The main advantages of this method lie in its versatility. Due to the large variations in molar extinction coefficients and the possibility of varying cell lengths, optical densities may be measured with equal accuracy over a wide range of concentrations. Consequently, ionisation constants may be determined even at very low concentrations [6 7] and acids of . low solubility may be investigated. Spectrophotometry has also been used to measure the ionisation constants of some very weak £68}. an

strong [6 9] acids with considerable precision; it is difficult to see how these ionisation constants could have been determined in any other way.

Even if an acid and its conjugate base do not absorb light, or if their spectra are identical, the ionisation constant can still be determined spectrophotometrically by using suitable indicators. This method is variously described as the indicator method £70}, the colorimetric method £71] » or the spectrophotometric comparison method. The accurate determination of an acid ionisation constant by this method requires an indicator with a known ionisation constant of comparable magnitude.

SECTION 5*1, DETERMINATION OF THE INDICATOR CONSTANT OF BROMOCRESOL-GREEN

INTRODUCTION

The spectra of both o-hydroxyphenyl^acetic acid and melilotic acid are identical with their respective singly-ionised anions (see p. and figures 3«1^ and 3*13)» Clearly their first ionisation constants cannot be determined by direct spectrophotometry; consequently it was decided to use the indicator method. Approximate determination of the first ionisation constants of these acids by pH measurement, and a brief scan through the literature, indicated that the necessary conditions are satisfied by the indicator bromocresol green.

The indicator constant of bromocresol green was determined in both acetic acid/acetate buffer^ and propionic acid/propionate buffers. These values were then used to calculate the ionisation constants of acetic acid and propionic acid, both of which have been determined in the past with exceptionally high accuracy. Thus the accuracy of the indicator method could be assessed.

Mechanism of the colour change in bromocresol greenSulphophthaleins, to which bromocresol green [7 2] (21,2n-dimethyl

3 1, 3', 3n» 5U ” tetrabromosulphophthalein) belongs, have two colour transformations. In strong acid solutions they are believed to exist as the hybrid ions (I).

These dissociate into the yellow form (II), which bears one extra negative charge, and finally into the blue alkaline form (III), with

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an excess of two negative charges. Kolthoff and Guss [733 showedthat at low ionic strengths the hybrid ions (I), (II) and (III) behave, as far as salt effects are concerned, as uncharged, singly, charged and doubly charged species respectively. The labelling of species (II) and (III) as HIn and In" respectively is probably justified in the present work, since fairly low ionic strengths were used (less than G.03& mole/1).

The spectra of bromocresol green, in aqueous solutions of various pH values, are shown in figure 3«1» As the pH of the solutions is increased, the peak at 617 mji increases from zero absorption at low pH.values to a constant value above a pH of about 7*3* This peak is assigned to the species In". The peak at 450 mji decreases v/ith decreasing acidity and is assigned to the anion HIn~» The intersection of the spectra at a common isosbestic point indicates that in the pH range under consideration only a single equilibrium need be considered. For this reason, in the treatment which follows it will be assumed that the total concentration of the indicator,

At low ionic strengths, the activity coefficients of all ions of the same valence type may be assumed equal. Thus the thermo-

CIn, is given by

THEORETICAL

dynamic indicator constant of bromocresol green, Kjn i which controls the colour change from yellow to blue, may be defined as

(3.1)Y/here h is the hydrogen ion coneentration and f^ is the activity coefficient of the doubly charged ion.

species HI and In'" respectively. If these species absorb light independently and if the Beer-Lambert Law is obeyed by each, then the optical density D (at a wavelength 7\ ), of a solution of the indicator of concentration Cjn » 3-n a cell of pathlength 1, may be expressed by

D = Eht 1 [HIn-] + EInl [ln=] (3-2)“n

The equation ’= [HIn-] +• [ln=] (3.3) '

combined with equations (3»l) and (3»2) may be shown to lead to theexpression

KIn = hf2/(D2-D)

where and are defined by the equations

* (BHIn-)1Ctn

Da = ( Em = ) lcin

Since the indicator constant of bromocresol green is of the “5order of 10 mole/1, the indicator equilibrium may be forced suffi

ciently in favour of either In'" or HIn to make a direct measurement of and possible. Equation (3-^0 may then be used to obtain

by measuring optical densities of indicator solutions at various hydrogen ion concentrations, coupled with some estimate of the activity coefficient f2*

Recently, Ernst and Menashi [7 -1 have shown that equation (3*^0 may be expressed in two alternative ways:-

l A D - D p = 1/(D2-D1 ) * hf2/KIn(D2 -D1 ) (3 .7 )and

1/(D2-D) = l / ^ - D p + KIn/hf2(D2-D1 ) (3.8)

(3.*0

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(3.6)

Equation (3*7) predicts that if is measured directly, a. plot of 1/(D-D^) against hih, should be a straight line whose slope and intercept may be used to calculate not only IC but also . Thus a direct measurement of is not required.. On the other hand, if equation (3*8) is used, a direct determination of D~, is necessary while a linear plot of l/XD^-D) against 1/hf^ leads to both and

Calculation of_ equilibrium hydrogen ion concentrationsFor the determination of the indicator constant of bromocresol

green, partly neutralised solutions of acetic acid (or propionic acid) were used as buffers.

Solutions were made up by adding various quantities of a standard solution of sodium hydroxide (or sodium carbonate) to fixed amounts of standard acetic acid, followed by fixed amounts of standard indicator solution (see p. 2,1 ). Finally, each mixture was made upv/ith water to a constant volume (100ml.), so that the total concentrations of both indicator and acetic acid (or propionic acid) remained constant. In some experiments the ionic strength was maintained constant by adding predetermined quantities of standard NaClO^ solution to the test solutions, prior to the addition of water.

Since accurate values for the dissociation constants K of theb.

buffering acids a.re available and are of the same order of magnitudeas the equilibrium hydrogen ion concentrations of the testsolutions used could be obtained by calculation.

Let c be the stoichiometric concentration of a buffering acidwith an ionisation constant K , thena

C = [ l “3 + [H L] (3. 9 )

andK& = hf^ [l~] /[HLj (3-10)

where HL and L stand for the buffering acid and its conjugate base

respectively, and f^ is the activity coefficient of a monovalent ion.

The condition of electroneutrality requires that:

[H+] + [Na+] = [OH"] + [Li + 2 [ln=] + [kIiT] t [ciO ] (3 .1 1)Denoting by b the stoichiometric concentration of sodium

hydroxide (assumed to be completely ionised) and making use of equation (3 *3 )» equation (3 *1 1 ) may be simplified to

h 4r b = [0H~] + [if] +- C + [ln=] (3*12)

Combination of equations (3*9) and (3*10) leads to

[if] = Kac/(Ka + hfp2) (3 *1 3 )Similarly, equations (3*1) and (3*3) give

[ln=] = KInCIn/(KIn + hf2 ) (3 .1^)

An alternative expression for [ln~]raay be obtained by combining equations (3 *2 ) and (3 *3 ) with equations (3 *3 ) and (3 *6 ):

[ln=] =- (3*13)

Finally, the ionic product of v/ater,Kw = [0H_]hf^ (3 -1 6)

may be used to express [OH ] in terms of h:

[oh"] =- KwAf-f (3 .1 7 )

Substituting for [l ] , fin-] and [OH ] from equations (3-13)>(3 *1 3) and (3 *1 7 ) respectively into equation (3 *1 2 ) ana rearranging,the cubic equation in h is obtained

2 ?. h + b = Kw/hfi + (d^-D)C^ii/(Di-D2 ) +- Kac/(Ka + h f p (3*18

This equation may be solved for h by using Newton-Faphson method ’(see appendix A2, p. 2ZI ) and thus the equilibrium hydrogen ion concentration determined.

For experimental solutions which contained a stoichiometric concentration [NadO^*] of sodium perchlorate (assumed to be completely ionised), the ionic strength, I, is given by

I = + [ha*] + [0H~]a+ [HIn*”] 4- [ln=]'h[ciO^”]. | (3*19)

which may be simplified to

I = h + [Na+] 4- [ln=] (3*20)

Noting that in this case

[n&+] = [NaClO^] 4- band making use of (3*13)* the required expression for I is obtained:

I =• h 4v [NaClO^] 4- b 4- C (D-D )/(D2-Di ) (3*21)

The ionic strength of the solutions to which [NaClO^jv/as not added may also be obtained from equation (3*21), by putting [NaCloJ .= 0*

In some experiments, NaOH was replaced by Na^CQ^* The condition of electroneutrality in this case takes the form

h 4- [Na+]= [oH~] +[HIn“] +• 2 [ln=] 4- [if] 4- [HCO-"] £[c 0 = ] (3*22Hov/ever, in the pH region employed (pH^(3**0, the concentrations of the ions HCO^" and C0^“ may be neglected [75]*Hence, putting

2 [Na2C0^] = b (3*23)where [Na^CO^] is the stoichiometric concentration of sodium carbonate, leads to

h 4- b ~ [OH"] 4- [if] 4- C -h [ln=] (3*2*0Equations (3*2*f-)and (3*12) are algebraically identical, but whereas in the former b donotes the stoichiometric concentration cf sodium hydroxide, in the latter it represents tv/ice the stoichiometric concentration of sodium carbonate. Bearing this distinction in mind, it may be shown that equations (such as (3*18) and (3*21) ), derived on

the basis of equation (3*12). for experiments in which NaOH was em-

justified. However, since calculations were carried out on a computer, it was thought better to write a more general programme, allowing for

value in future work.N.B. In appendix A 1 (p. 2.2.0) the pH values of three acetic

acid/sodium acetate buffers, recommended by the N.B.S. as secondary standards for the calibration of glass electrodes, are compared with the pH values calculated for the same buffers by a procedure similar to the one given above.

Eight separate experiments (runs) were done; three in acetate and five in propionate buffers. Although the absorption spectrum of bromocresol green in alkaline solutions has a maximum at 6l7m}i, optical densities of the indicator solutions were measured at in ailexperiments (runs), because this wavelength could be set more conveniently on the wavelength drum of the instrument used. The test solutions used for the determination of the indicator constant of bromocresol green were chosen so that the percentage ionisation of the indicator and the buffering acid were both within the 20-80;s range. In runs at constant ionic strength NaClO^ was used not only because it is completely dissociated but also because it exhibits no specific effects on the indicator equilibrium [78]. Since bromocresol. green was shown to be the only constituent of the test solutions absorbing light in the visible region, optical densities of the test solutions were measured against water as reference.

ployed, are equally applicable to experiments in which Ha^CO^ was used It is realised that under the conditions used in the present

work, the neglect of [OH ] in equations (3*12) and (3*19) would be

(3 *1 2) and (3 «1 9)» as such a programme could be of

RESULTS AND DISCUSSION

Acetic acid and propionic acid are known to be selfassociated in aqueous solutions [70]; the dimerisation constants of these acids ( K — [m] [H A-,] ), determined by conductometricmeasurements, are l$)mole/l and 20mole/l respectively [77] • On the basis of these figures, calculation shows that no more than 0.2% of either acid would be dimerised in the solutions of highest acidity employed in the present work. In less acid solutions, the amount would be less. The neglect of dimerisation in this work was therefore considered justified.

In all calculations described in this section, the values adopted for the ionisation constants of acetic acid, propionic acid and the ionic product of water were 1.75^ x 10 ^mole/1 [78],1 .3 3 6 x 10'5mole/l [79] and 1 .0 0 8 x l O ^ m o l e 2/!2 £80] respectively♦

Several alternative methods of treating the experimental data presented themselves and are discussed below:First Method

This method is based on that of Ernst and Menashi [7^J •Dn obtained by direct measurement v/as used, while and YL- were 1 2 Inobtained by the method of successive approximations as follows:

(i) The first estimate of the ionic strength, I, v/as obtained for each solution from equation (3 *2 1), by neglecting h and assuming a reasonable value for D^.

(ii) The activity coefficients were then estimated from the Davies eau. in its recently modified form: [bl] :

- log fz =-0.5z2[i}7(1 + 1^) - 0 .31} (3 .2 5)where z is the ionic charge and f^ is the activity coefficient.

(iii) The first estimate of the equilibrium hydrogen ion concentration could be then obtained by solving equation (3 »l8 ) for h, using the Nev/ton-Raphson procedure (see appendix A2. p. 25L1 ).

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(iv) The method of least squares (see appendix A3«l p. 2.2.2) was applied to equation (3*7) in the form

Yx = °C +f>Xx (3‘26)where = l/(D-D^) and = hf2 (3*27)leading to an estimate of the intercept, qC > anc* the slope^y3 * where

o( - 1/(D2-D1) and £=: l/Kj^D^D^- (3-28)‘and hence to the first estimates of D_ and K_ . The relevant stan-2 Indard deviations were also computed (see appendix A3*l and A f, p.2.2.6).

The values of h obtained in (iii), in combination with thefirst estimate of from (iv), were used to obtain improved valuesof the ionic strength I from equation (3*21) and hence improvedvalues of the activity coefficients from the Davies Equation. Thesein turn were used to obtain the second estimate of the hydrogen ionconcentrations (as in (iii) ) and a second estimate of D^ (as in (iv)This procedure was repeated until the hydrogen ion concentrations,calculated in two successive cycles, agreed to six significant figuresAt this stage, the agreement between the values of both K_ and D_In ^obtained in the last two cycles v/as better than 0.001%.

Detailed results of the calculations described above foreach run are given in the first eight columns of tables 3«1 to 3»&iand illustrated graphically in figures 3«2 to 3*9* The finalresults for all the runs are collected together in table 3»9 •Examination of coliimns 7, 8 and 9 in table 3*9 reveals that:

(a) For each run, the standard deviations in both K_ and the±nextrapolated D^ values are less than l.*f%.

(b) The values of D^ obtained by the two methods - directmeasurement and extrapolation - are in some cases in close agreement (runs 2 and b) whilst in others differences of up to 3% are found.

(c) The determined value of the indicator constant K_ variesIn

from run to run - the difference between the two extremes is of the order of 10% !

(d) The extinction coefficient (E_ =) of the alkaline formInof the indicator In~ (column 1 6), computed from the directly measured values of (column 10), show’s very little variation (maximum deviation from the mean 0.6%).

The observations summarised above indicate the presence of systematic errors. Such errors may arise as a result of a flaw in either the theoretical treatment or the experimental procedure, or as a result of the combined effect of. these two factors.

Initial attempts were directed at improving the precision of the various measurements involved in the experimental procedure. This, incidentally, is the reason why such a large number of determinations was made. Great care was taken in the standardisation of stock solutions, temperature control, measurements of volumes, etc.The chemical or the photochemical instability of the indicator solutions could be a source of serious error, if not allowed for. The colour^ of the alkaline solutions of sulphophthaleins is knov/n to fade [82, 83, Bk] ; the rate of fading increases with increasing hydroxyl ion concentrations. Storage of solutions in the darknessseems to inhibit this reaction. In the present work, it was found

-3that solutions of bromocresol green in 1 x 10 M sodium hydroxide -3or in 1 x 10 M sodium carbonate showed no change in colour or

optical densities after storage in the dark for t¥/o weeks. In another test, optical densities at 6l5mp of a number of indicator solutions of various pH values between 2 and 3 were measured immediately after preparation and after storage in. the dark for three days. The difference between the two measurements in no case exceeded 1%, which is probably within the limits of experimental accuracy. In all

OP

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experiments* freshly prepared stock solutions of the indicator were used for the preparation of the test solutions. Optical densities of these test solutions were usually measured within 2k hours of their preparation* and in no case did this period exceed tv/o days. Between measurements, the solutions were always stored in the dark. Thus the errors, if any* due to the instability of the indicator solutions could be neglected. (An additional fact in support of this conclusion is the constancy of the extinction coefficient of the alkaline form of the indicator (see (d) on p. 60).

The theoretical treatment on which the present method is based requires the two extinction coefficients and Sjn= to betrue constants, independent of the nature of the ions added to the indicator solution and independent of the ionic strength. The effect of ionic strength on the absorption of both the acid and the alkaline forms of the indicator was investigated as follows. Tv/o series of solutions were prepared. In the “alkaline series" the concentrations of both the indicator and the sodium hydroxide were constant* while the ionic strength v/as altered by the addition of varying amounts of sodium perchlorate. The “acid series" contained a constant concentration of perchloric acid in place of sodium hydroxide - in every other respect it v/as identical with the “alkaline series". Figure 3*10 shows a plot of the optical densities of these solutions against the ionic strength* at the wavelengths indicated. Up to the ionic strength of 0.1* the optical densities of the acid and the alkaline forms of the indicator (D^ and respectively) are independent ofthe ionic strength (I) at the three wavelengths studied; at higherionic strenghts, only at 613 mp shows a slight dependence on I.In the experimental determination of the indicator constant ofbromocresol green the highest ionic strength used was 0.036 mole/1.Hence for the purpose of this work, both and D- (and also S -

JL d. in n

and ST =) may be taken as independent of ionic strength, in accordXXIwith the assumptions of the theoretical treatment.

The evaluation of activity coefficients is next considered.In the procedure described above (p.40 ), the Davies equation was employed to estimate activity coefficients. Presently the Debye- Huckel [70] equation will be used: -

-log f Az2 / T / U -h-Bayf) (3.29)z

where A and B are constants for a given temperature and dielectric constant (for water at 25°C they are 0.3092 and O .3286 respectively [70] ) and a (measured in Angstroms) is the"ion-size parameter". Sometimes a reasonable but arbitrary value is assigned to the ion- size parameter* more often it is fitted to the experimental data.A commonly used extended form of the Debye-Huckel equation [70* 83] contains a second adjustable parameter C. (The Davies equation is a special case of this* v/ith aB = 1 and C = 0.13z2)»

-log fz = As2 V T /(1 + Ba/I) - Cl (3*30)

To a first approximation* over a narrow range of ionic strengths, increasing the ion-size parameter in equation (3 .2 9) is equivalent to subtracting a linear term in I, as in equation (3*30).

The procedure of successive approximations, described on page 4-0 , was repeated for each run, except that now equation (3 .2 9) was used for evaluation of the activity coefficients. A range of values of the icn-size parameter between 0 and OO was used. Putting a = 0 is equivalent to the Debye-Huckel limiting law

O M M .- log fz = Az JT'while putting a — oO is equivalent to neglecting activity coefficients altogether* i.e. fz = 1. Clearly* the activity coefficients evaluated with any finite (positive) value of the ion-size parameter will lie between these two limits.

In tables 3*10 and 3*11 detailed results of the calculations described above are given for two runs: one at constant (run.2), and

TABLE 3.10 INDICATOR CONSTANT OF BROMOCRESOL GREEN. RUN 2 (CONSTANT IONIC STRENGTH). DATA TREATED BY THE FIRST METHOD USING THE DEBYE - HUCKEL 'EQUATION WITH DIFFERENT VALUES OF THE ION - SIZE PARAMETER a .

INTERCEPT SLOPE

0a 10^ 10 lO-2^ * ^ )1/mole

10 8(kt *cn: )mole^ Kln

103 (D2 ±C7^2)

0 124 1161 * 6 1095 - 3 1061 - 5 861 * 53 123 11*62 ±- 6 1039.**■ 3 1118 * 6 861 * 34 123 1162 1 6 1024 * 3 1134 * 6 861 ± 35 123 1162 - 5 1011 * 3 1149 ± 6 860 1 56 123 1162 1 3 999-0*3 1163 * 6 860 ± 37 122 1162 * 3 987.9*3 1177 * 6 860 * 58 122 1162 * 3 977-8*3 1189 * 7 860 * 39 122 1163 * 5 968.4*3 1200 * 7 860 * 5

10 122 1163 * 3 939.8*3 1211 * 7 860 ± 320 121 1163 * 5 900.4*2 1292 * 7 860 * 400 120 II63 * 3 748.2*2 1537 * 8 859 * 4« 123 1162 * 6 1014 * 3 1146 * 6 860 ± 5

Measured D^ - 0.860’Results obtained using Davies Equation

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TABLE 3.11 INDICATOR CONSTANT OF BROMOCRESOL GREEN. RUN 5 (VARIABLE IONIC STRENGTH). DATA TREATED BY THE FIRST METHOD USING THE DEBYE - HUCKEL EQUATION WITH DIFFERENT VALUES OF THE ION - SIZE PARAMETER a .

INTERCEPT SLOPE0a 1 0 ^ 10^ (0( ±C£) lO^C/S )

1/mole 1° In*mole/Li o^Cd .> *<

0 262 1227 + 10 9839 ± 33 124? + 13 815 ± 73 2k0 1203 ± 10 9706 ± 30 1242 ± 12 830 ± 74 233 1199 10 9666 ± 49 1241 + 12 834 ± 73 231 1194 ± 9 9627 ± 48 1240 ± 12 838 ± 76 229 1189 9 9390 - 47 1240 ± 11 841 ± 77 22? 1184 ± 9 9334 * 46 1239 ± 11 844 ± 78 223 1180 ± 9 9320 ± 46 1239 ± 11 847 ± 79 22k 1176 + 9 9488 ± 46 1240 ± 11 . 830 ± 710 22k 1173 ± 9 9437 ± 46 1240 ± 11 853 ± 711 22k 1170 J-mU 9 - 9428 * 46 1240 ± 11 836 ± 720 231 1148 ±- 10 9203 ± ^3 1248 ± 12 871 ± 800 281 1109 ± 12 8093 * 49 1370 ± 17 902 -i. 9

* 233 1193 4- 9 9631 1 48 1241 ± 10 837 ± 7

Measured D^ = O .856

* Results obtained using Davies Equation

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the other a.t variable (run 5) ionic strength. Some of the leastsquares lines obtained with the designated values of the ion-sizeparameter a (in equation (3 *2 9)) for runs 2 and 3 ane shown infigures 3*11 and 3*12; the lines obtained with the Davies equation(3*23) are included for comparison. For the sake of clarity, theexperimental points in each figure are shown only on the two extremelines. The arrows on the ordinates indicate the value of 1/(D^-Dn )c lcalculated from directly measured values of and

/

The outstanding feature of figure 3*11 (run at constant I) is that the lines, though obtained with different values of the ion- size parameter, all converge to the ss.me intercept on the ordinate; their slopes, .however, depend on a* This implies that dependson the parameter a chosen, while the extrapolated is independent of it. In contrast, for the run at variableionic strength (figure 3*12 and table 3*11)» the values of both and D^ are dependenton the choice of the ion-size parameter. That this difference in behaviour between the runs at constant and at variable ionic strength is quite general may be seen by examining table 3*12. In appendix A5 (p.2.2-7) it is shown that this behaviour is an inevitable consequence of the method of calculation.

For all‘runs the goodness of fit (measured by (Typ) is almost the same for all positive values of the parameter a, and therefore cannot be used to decide the most probable value of a.

For each of the five runs at variable ionic strength it is possible to select a value of the ion-size parameter which leads to an extrapolated value of D2 in accord v/ith obtained by directmeasurement. The values of a, extracted in this way from tables 3*11 and 3*12, are presented in table 3*13* This table also includes the values of for the runs at constant ionic strength.

TABLE 3.13 VALUES OF THE ION-SIZE PARAMETER AHICH LEAD TO D2

(EXTRAPOLATED) IN AGREEMENT WITH D '(MEASURED DIRECTLY)

Number of runsL in angstroms

310 (extrapolated)Z10 Dp (measured

directly)

Runs at variable ionic Runs at constantstrength ionic strength

3 k ' 5 ■ 6 7 1 2 8

11 6 11 14 20 Independent of a891 922 836 944 896 823 860 946892 920 836 943 898 860 860 963

Ideally, one would expect the parameter a derived from different runs to be the same in each case and hence determined unequivocally. Although the agreement between the various a ’s in the second row of table 3*13 is not very good, the values are of the same order of magnitude, and, considering the physical significance of a, they are also reasonable. It is somewhat perturbing, however, that for two out of the three runs at constant ionic strength, (last three columns of table 3*13)? an appreciable discrepancy exists between the extrapolated and the measured ( -.3% for run 1 and 2.0% for run 8). As pointed out previously, for these runs the extrapolated is independent of the ion-size parameter used in the calculations; clearly, then, the estimation of activity coefficients cannot explain this discrepancy; therefore errors of other origin are present in these runs. This may possibly also hold true for some of the runs at variable ionic strength, which would explain the variations of the parameter a in the second row of table 3*13* In other words, if in a given run at variable ionic strength a systematic error exists, a biased estimate of parameter £ will be obtained, because it is selected so as to make extrapolated coincide with measured, whether any initial difference between the two D^'s is explicable by activity estimates alone, or not.

In spite of the fact that this method of selecting the ion- size parameter is not very successful with the data obtained in this work, it holds promise for the treatment of more accurate results.

Second MethodIn this method, which is also based on the method of Ernst

and Menashi, [7 -J , use is made of D^ obtained by direct measurement, while and are calculated by a series of successive approximations, very similar to those used in the first method. Briefly,

the steps required are:(i) By assuming a reasonable value of D^ and putting h = 0,

calculate the preliminary values of the ionic strength from equation (3«2l).

(ii) Estimate activity coefficients from the Davies equation

(3 .2 5)(iii) Solve equation (3>l8) for h (see appendix AZ, p. 2X1) to

obtain the first estimates of the equilibrium hydrogen ion concentrations.

(iv) The method of least squares (see appendix A3*l, p«-2.2.2) applied to equation ( 3 « 8 ) j which for this purpose is written

?2 = o'.1 + f t 1 (3-31)where

Y2 = 1/(D2-D) and = lAf2 (3.32)./ /gives the intercept, CL , and the slope, j*, , where' /

0C= 1/(0 ^ ) ft = k^/Cc^-d^ (3 .3 3 )

,1 /Once (X and <3 are known, the first estimates of D^ and may becomputed. The standard deviations are also found (see appendix A3»l and A4, p.2^2-and p .12,6).

(v) from (iv), and the values of h from (iii), are usedto obtain improved values of the ionic strengths and the activity coefficients. Then recalculated values of h (as in (iii), lead to improved values of D^ and (as in (iv)).

This procedure of successive approximations was stopped YJhen the hydrogen ion concentrations obtained in two successive cycles agreed to six significant figures. The values of both and

obtained in the penultimate cycle agreed to better than C.OlX' with those obtained in the last cycle. The detailed results of these calculations for all the runs are given in tables 3*1 to 3*8 and

illustrated graphically in figures 3*2 to 3*9* Incidentally, inthese tables only one value of b and I is given for each point, asthese are identical (to four figures), as for the First Method. Thefinal results are collected together in table 3*9*

An examination of this last table shows trends parallel tothe trends observed in the results obtained by the First Method.For example, the differences (up to 30%) between the values'of K_inderived from different runs are many times larger than the standard deviation in for any single run (maximum of 3%)» Most of the points made about the First Method are therefore also valid here. ’

There are, however, some differences between the First and the Second Method. For instance, the range of values of (First Method) and Y2 (Second Method) is by and large the same, but the standard deviations in Y^ ( Gy" ) are Y;ith one exception only (run 3)? much smaller than the standard deviations in Y2 (^Y?)• Hence for a given set of data, the plot of Y^ versus usually gives a muchbetter straight line than a plot of Y2 versus X2 (see figures 3«2to 3*9) • Moreover, for some runs a slight departure from linearity is noticeable when the data are treated by the Second Method - e.g.a pronounced upward curvature is found for run 8 (see fig. 3*9 or thetrend in table 3*8). It is concluded that when systematic errors are present, the First Method is much better at '’concealing'1 them, by giving a good straight line, than the Second Method.

A different value of was obtained for each run, dependingon whether the First or Second Method of calculation/^ was used,(table 3*9)* The origin of these differences vd.ll now be discussed.- Following Ernst and Co-workers [68, yW 86J , the "unv/eighted” least squares procedure was used in both methods. By way of illustration, consider the First Method. It is supposed that the values of L are

known accurately and the va3.ues of Y^ are liable to random errors of measurement. An equal weight is attached to all points and the parameters d (intercept) and p> (slope) are selected so that the sum of the squares of the residuals is a minimum. (A residual is the difference between an observed value of X and its true value as given by the "best11 straight line for the same value of X (see appendix A3? p.ZU).

Wow, Y^ = l/(D~D^), or in practice Y^ = l/D since the measured value of D- — 0. For a small error, Dx>, in D, the error to be- feared in Y^ depends on the value of D, namely

~c)Y1 = Dd/D2For example, when D = 0.1, ^Y^ = lOQ^D, but when D — 1.0, c)Y = *c)D.The experimental conditions in all runs were such that the measured optical densities fell, roughly, within the limits: 0.2 to 0.8.Within this range of optical densities (for the instrument used) it is more correct to suppose that the absolute error " D is independent of, rather than proportional to, the optical densities, (i.e. absolute

*\)Derrors ( c)D) as opposed to the relative errors ( /D) are assumed tobe normally distributed). Thus within the range stipulated, optical densities should have equal weight. However, by using the "unweighted" least squares procedure, the values of Y^ (i.e. 1/D) were given equal

, L lweight, which is equivalent to giving a weight of 1/D to the optical densities [l^6]. Clearly, then, the First Method is erroneous in this respect. (Multiplication of each observation equation

2by D before forming the normal equations, would restore equal weight to the values of D. In the remaining sections of this thesis, due attention has been given to the weighting of data - observation equations were always reduced to linear form of equal weight before the required parameters were determined by the method of least squares). An 3.naiagous argument indicates that appropriate weighting factors

should have also been used in the treatment of data by the SecondMethod. The lack of agreement, (for a given run) between the valuesof K_ obtained by the First and the Second Method is attributed to Inthe different weighting of data in each of these methods - had appropriate weighting been applied, the result obtained would have been identical. (This discrepancy in could also be explicable interms of errors in either (measured) or (measured). This is not the case here, however, because it is known that both and have been determined to a high degree of accuracy - see point (d), page GO and column 3.6 of table 3«9)* If all the data for a given run were exact, then both the First and the Second Method would lead to a concurrent value of KTn, whether or not appropriate weighting was applied. Conversely, the runs for which the two methods, in their present form, give values of in close agreement, are more accurate than those for which such agreement is lacking. According to this criterion, runs 2 and k are the most, and run 8 the least, accurate (table 3*9)•

It is significant that for the former an excellent agreement exists, on the one hand between (extrapolated) and (measured.), and on the other betv/een (extrapolated) and IL, (measured), and that run 8 is the one for which a slight upward curvature in the plot of Y^ against was found.

Third MethodThe previous two methods were extrapolation methods in the

sense that only one of the two quantities measured directly, or was used; the other one was obtained from the data by extrapo

lation. The method to be described now is a direct one, and probably the most commonly used spectrophotometric method of determining ionisation constants when both and are accessible to direct measurement. Equation (3«^)» which is used here, shows that the data

necessary to determine the indicator constant, in addition to D^ andare: the optical density (D) of the indicator solution (measured

at the same concentration as used to determine D^ and ), the equilibrium hydrogen ion concentration h, and the activity coefficient f~.The values of h are normally obtained from pH measurements, but in this case they were calculated by a short series of successive approximations :

(i) Puth ~ 0, and calculate the approximate ionic strength I from equation (3*21).

(ii) Estimate fz 1s from the Davies equation.(iii) Solve equation (3«l8) for h (see appendix A2, p. 5-2.1).(iv) Using h obtained in (iii), recalculate I from equation (3*2-1)

and fz from the Davies equation, and hence obtain an improved value of h from equation (3*18). Repeat this procedure until the values of h obtained in two successive cycles agree to six significant figures.

Since I is now known, the Davies equation yields f , which together with the value of h obtained in the last cycle and the correspond! optical density, allows to be found from equation (3*^)* In thisway, for each optical density in a run a value of K . was obtained.From these, the average Kja > and its standard deviation, were calculated.

For each test solution, the value of h calculated by the presentmethod agreed to 0.1% with the values obtained by the preceding twomethods; the agreement in the values of I was even closer. For thisreason, for each test solution only one value of I and one.of h isrecorded in tables 3*1 to 3*8* The individual K_ values are recordedInin column 12 of these tables and the average values for each run in column 13 of table 3*9*

The most gratifying feature of the results obtained by the Third Method (table 3*9) is that although the average value of Kj

varies from run to run, the differences between these average valuesare of the same magnitude as the standard deviations associated withthem. Within the standard deviations, K^n is in fact reproducible fromrun to run, in striking contrast to the values of obtained bythe two extrapolation methods. For some runs (e.g. run 3). the indi-vidual values ox show a trend - the presence of systematic errorsis thus made immediately apparent. Presumably, these errors are notvery large, since the values of 'K. derived from runs suspected of"harbouring" such errors (e.g. run 3) agree,.within the standarddeviations, with K_ values of other runs. Out of the three methods ’ Inconsidered so far, the Third Method appears to secure the most reliable value of for a given set of data.

The results in table 3*9 show that for every run the value ofK_ obtained by means'of the Third Method lies between the values of InKj (First Method) and (Second Method). This is thought to bedue to the different weighting of optical densities (D) in each of the three methods: First Method - the weighting factor increaseswith increasing D; Second 2*!ethod - the weighting factor decreaseswith increasing D; Third Method - all values of D axe given an equalv; eight.

Fourth Method

In this method, the thermodynamic indicator constant K_ isInobtained by extrapolating the stoichiometric (classical) indicatorconstant determined at various ionic strengths, to infinite Indilution by means of the Debye-Huckel equation. For the purpose ox determining the stoichiometric indicator constant, the hydrogen ion concentration and the ionic strength were calculated for each test solution exactly as in the Third Method, and then was obtained

from equation (3*3^)

= (D-D1)h /(D2-D) (3.3'0

which in fact is a suitably modified form of equation (3*^)* Thelast column of tables 3*1 "to 3*8 shows the values of obtainedInin this way.

The stoichiometric and the thermodynamic indicator constants are related by

f In=• fH+--------- (3-35)

fHIn"

or

pKIn ~ pKIn + log fIn= * log " log (3-36)

where f denotes the activity coefficient of the species shown in the subscript, and pK^n =wlog • Assuming that the activity coefficients of all ions may be expressed in terms of the activity coefficient f^ of a "typical" univalent ion [72J , equation (3*3*6) may be written

pK*n = pKIn - m log (3-37)

where m is a constant, the meaning of v/hich v/ill be explained below.The species HI if and In= are hybrid ions. At low ionic strengths,such ions (bearing n unit charges and a net charge z) behave likesimple ions of charge z, and their activity coefficient f may bezexpressed in terms of f^ in the usual v/ay:

log fz =- z2log fx (3*38)

As the ionic strength increases, the behaviour of a hybrid ion approximates more closely to that of n independent univalent ions [?2J, and its activity coefficient is then given by:

log fz - n log ^ (3*39)

KIn = TC In

Fig.

3-1

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Kjn

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TABLE 3.14 INDICATOR CONSTANT OF 3ROMOCRESOL GREEN. PARAMETERS OBTAINED BY THE FOURTH METHOD USING DIFFERENT VALUES OF THE ION - SIZE PARAMETER a .

Va10 ^ I n pKIn

0 97 4.8571 97 4.8642 96 4.8705 96 4.8774 96 4.8835 95 4 .8 8 96 95 4.8967 95 4.9028 95 4.9089 95 4 .9 1 5

10 9k 4.92111 9k 4.92712 9k 4.93313 9k 4.93914 9k 4.94615 9k 4.952

-2.120 71 1.390-2.315 77 1.369-2 .5 1 9 83 1.348-2 .73I 90 1.328-2.953 96 1.309-3.179 104 I .2 9 0

-3.416 111 1.271-3.654 118 1.253-3.905 126 1.235-4 .I63 134 1.217-4.431 143 1.199-4.695 151 1.184-4.982 160 1 .1 6 6

-5*266 169 1.150-5.570 179 1.135-5.874 188 1.117

10

52545657596163656769717274767880

For HIn“, n = 3 and z = 1, for In“, n ~ k and z = 2 (see page 32L ).If equation (3«38}is used to calculate the activity coefficients of the species HIn“ and In= , then in equation (3*37) m — on the other hand, if equation (3«39) is used, then m = -2.

Equation (3*36), on substitution for f^ from equation (3*29) becomes :

pK^n =- pKIn -h-mAI^/d +. Bal1/i) (3*^0)

This equation predicts a linear plot of pKjn against AV?/(l+BaV?), provided that a correct value of the ion-size parameter is used.The slope and intercept of such a plot gives m and pKjn respectively, and hence Kjn *

The experimental data from all 8 runs were fitted simultaneously to equation (3*^0) for values of a ranging from 0 to 15&(for runs at constant I, the average values of IC?! were used - eachInwas given a weight - equal to the number of points in the run). Such

O oa fit, with a - o, is shown in figure 3*13* The values of m andpKT obtained by the method of least squares for each chosen a- J.I1parameter together with the requisite standard deviations, are shown in table 3.1^. The variation in (used as a criterion of fit)is so small that a choice of a single set of parameters a and m cannot be made with certainty. It is better, therefore, to regard each

3-Vf*value of given in tableAas having a well-defined significance only in relation to a specified set of parameters a and m.

CONCLUSIONFour methods of calculating the indicator constant from the

experimental data have been discussed. The First and Second methods (extrapolation methods). were found to be very sensitive to small

systematic errors and. the value of could not be reproduced fromrun to run, although the standard deviations in indicated a highprecision for each run. In contrast, values calculated by theThird Method were found to be reproducible within their standarddeviations. Furthermore, a reliable value of IC_ , with a realisticInestimate of errors, could be obtained by this method even when small systematic errors were known to be present. Finally, the Fourth Method has shown very clearly that values are meaningful onlywith reference to a specified equation for activity coefficients.

Although the indicator constant of bromocresol green has been determined many times [87 to 9?] since its preparation by Cohen [87] in 19231 only three determinations of the thermodynamic constant in v/ater at 25°C have been reported. In chronological order these are:

_ tzGuggenheim and Schindler [93] ^jn = 1*^3 x 10 mol e/i.Minnick and Kilpatrick [9*f] Kjn = I.O69 xlO-^ mole/lKilpatrick [95] = 1.11 x 10 ^ mole/1.

Using the Third Method, the average value obtained in the present~5work, = 1.146 x 10 mole/l, is in excellent agreement with

Kilpatrick's result and in reasonable agreement with the two older values.

SECTION 3.2 DETERMINATION OF THE IONISATIOK CONSTANTS OF ACETIC ACID AND PROPIONIC ACID USING BR0M0CH5S0L GREEN

The calculation of the ionisation constants of acetic acid and propionic acid by the indicator method with now be described, using the data contained in the previous section. In principle, this method depends on the measurement of the hydrogen ion coneentration

by means of an indicator with a known value. The relevantequations are the same as those derived in section 3*1; however, since the unknown quantities are now different, these equations are first suitably transposed:

h = (D-D..) f^KT /(D-D0) (3.^1)1 In d.

Ka = hf^A /(c-A) (3*^2)

where A =■- h +- b - Kw/hf^ - Cj (D-D^ / ( D ^ D ^ (3*^3)

and X = h + [NaClOjJ + b - Cin(D“Di ) ( 3 * W

Before h may be obtained from equation (3*^1), a series of successive approximations is necessary, because h is required to calculate I :

(i) Calculate I from equation (3*^*0 by putting h = 0, andhence f2 from the Davies equation (3* 23).

(ii) Obtain the first estimate of h from equation (3*^1)(iii) Recalculate X from equation (3*^), using the h obtained

in (ii) and hence obtain the second estimate of h from equation (3*^1(iv) Repeat this procedure until the values of h obtained in two

successive cycles agree to 0.01%.Ka is obtained from equation (3*^2) using the final value of

h, and calculated from the Davies equation (3*235*The ionisation constant of acetic acid was calculated from the

data of runs 1, 2 and 3 » the value of used in these calculations~3was 1.13*f x 10 mole/l (i.e. the average value of determined by

the Third Method, from runs in which propionate buffers were used).Detailed results are shown in tables 3*13 to 3-17* The ionisationconstant of propionic acid was calculated similarly, using =

-51.133 x 10 mole/l - the results are shown in tables 3»lS to 3*22.The final results for both acids are collected together in

TABLE 3.15 IONISATION CONSTANT OF ACETIC ACID. DATA FROM RUN 1.ft = 615 mp. ; c = 2 0955 x 10 ^ mole/l. ; C ^ = 1.88 x 10"* mole/l.

1 - 1 cm. ; D1 = 0.000 ± 0.001. ; Vg = 0 .8 6 0 i 0.002 ;Kln = ^ x 10“5 mole/l •5 b — [NaOH]

103moble/l 103 [InsCIQl] mole/l

D 105hmole/l 103Imole/l 105Ka mole/ 1

6.716 18.905 0 .1 8 1 7.894 25.70 1.7447 .^ 1 6 1 8 .2 1 5 0 .1 9 8 7.036 25.71 1.7678 .1 1 6 17.525 0.217 6 .2 3 6 25.71 1.7668 .8 1 6 16.830 0.235 5.597 25.71 1.7779.316 16.140 0.255 4.993 25.71 1 .7 6 8

10.216 15.440 0 .2 7 2 4.549 25.71 1.79110.916 14.750 0.291 4.115 25.71 1.79412.316 13.355 0.326 3.447 25.71 1.83113.716 1 1 .9 6 0 0.366 2.841 25.71 1.8271 5 .1 1 6 IO .565 0.407 2.342 25.71 1.82016.516 9.250 0.448 1.937 25.79 1.81917.916 7.770 0.488 1.604 25.71 1.83119.316 6.375 O .528 1.323 25.72 1 .8 5 0

20.716 4.975 O .569 1.076 25.71 1.8692 2 .116 3.575 0.609 0.8674 25.71 1.90923.316 2 .1 8 0 0.648 0.6886 25.72 1.98424.916 0 .7 8 0 0.694 0.5034 25.72 1.999

(Ka ± <OrKa) = (1.832 ± 0.073) x 1®"5 mole/l

TABLE 3,16 IONISATION- CONSTANT OF ACETIC ACID. DATA FROM RUN 2ft s= 615 mji. ; c = 2 .9 5 5 x 1 0”^ mole/l. ; C ^ = 1.88 x 10~^ mole/l. ; 1= 1 cm. ; D1 = 0.000 ± 0 .0 0 1 ; D2 = 0 .8 6 0 ± 0 .0 0 2 ;KIn = 1.154 x 10”5 mole/l. ; b = 2 Qta^CO^]

lO^b 10* &aOQ. ] D 105h 310^1 105Kamol © A moleA moleA moleA mole/l

6 .7 1 6 18.905 0.179 8 .0 0 6 25.70 1.7698 .1 1 6 17.525 0.217 6 .2 3 6 25.71 1 .7 6 6

9.516 16.140 0.257 4.938 2 5 .71 1.74910.916 14.750 0 .2 9 6 4.010 25.71 1.7481 2 .3 1 6 13.355 0.332 3.347 25.71 1.77813.716 1 1 .9 6 0 0.371 2.774 25.71 1.7841 5 .1 6 6 IO .565 0.414 2.269 25.76 1.7741 6 .516 9.170 0 .4 5 4 1 .8 8 2 25.71 1 .7 6 8

17.916 7*770 0.493 1.567 25.71 1 .7 8 8

19.316 6.375 0.539 1.253 25.72 1.7522 0 .7 1 6 4.975 0 .5 8 0 1 .0 1 6 25.71 1.76322 .116 3.575 0 .6 2 6 0.7867 25.71 1.73123 .5 1 6 2 .1 8 0 O .669 0 .6 0 0 9 25.72 1.73124.916 0 .7 8 0 0.710 0.4446 25.72 1.765

(Ka + = (1 .7 6 2 ± 0.018) X 10 ^mole/l

TABLE'3.17 IONISATION CONSTANT OF ACETIC ACID. DATA FROM RUN 3-—2 —B<\ = 615 mji. ; c = 3*94 x 10 mole/l. ; ^in= ■*■•97 x 10 mole/l.

1 = 1 cm. ; D = 0.000 ± 0.001 ; Dp =. O .892 ± 0.002 ;t

= 1 .1 5 4 x 10“^ mole/l. ; b = [NaOH]

103b D ' 105h 10^1 105Kamole/l . mole/l mole/l mole/l

7 .8 8 9 0.150 8.236 7.975 I .7389.328 0 .1 8 2 6 .6 7 6 9.399 1.716

10.829 0.214- 5.565 ‘ 10.89 1.72112.393 0.24-9 4.650 12.45 1.716 .14-. 020 0.284 3*948 14.07 1.73213.709 0 .3 2 1 3.357 15.75 1.74517*148 0.353 2.934 , 17.19 1.75618.387 0.386 2.563 18.62 1.76220.214 0.4-21 2 .2 2 8 2 0 .2 5 1.78921 .132 0.4-4-5 2.021 2 1 .1 8 1.77623.092 0.4-89 1 .6 9 2 23 .1 2 1.79723.094- 0.537 1.384 2 5 .1 2 1.80327 .0 9 6 O .587 1 .1 0 8 27 .1 2 1.79429.098 0 .6 3 2 0 .8923 2 9 .1 2 1.83731.100 0.684 O .6706 31.12 1.81532.727 0 .7 2 2 0.5259 32.75 1.850

(Ka ± ^ Ka) — (1,772 * 0.04-3) x 10”^ mole/l

TABLE 5.18 IONISATION CONSTANT OF PROPIONIC ACID. DATA FROM RUN 47\ - 615 mp. » c = 4.82 x 10 ^ mole/l. ; C ^ = 2.02 x 10~^ mole/l1 = 1 cm. ; D1 = 0.000 ± 0.001 ; D2 = 0.920 ± 0.002 ;

In * 1-*155 x 10~5 mole/l. ;

1—1

« 0Ii&

105b D 105h l(Pl 105Ka .mole/l mole/l mole/l mole/l9*700 0.197 6 .207 9.766 1.290

IO .815 0.219 5.519 1 0 .8 8 I .302

12.004 0.244 4.869 1 2 .0 6 1.3031 3 .2 6 8 0.271 4.290 13.32 1 .3 0 114.606 0 .3 0 1 3.754 14.65 1 .2 9 0

1 6 .0 1 8 O .333 3.279 1 6 .0 6 1.27717*305 O.36I 2.934 17.5^ 1 .2 9 619 .0 6 6 0.390 2 .6 23 1 9 .1 0 I .3172 0 .7 0 1 0.425 2.289 20.73 1 .3 1 0

2 1 .518 0 .4 5 0 2.071 21.55 1.26422.410 0.462 1.984 22.44 1 .2 9 8

2 5 .3 0 2 0.480 1.851 23.33 1.29924.194 0.495 1.749 24.22 1.31527.985 0.575 1 .2 6 6 2 8 .0 1 1.28429.935 0.604 1 .1 2 2 29.98 1.33932.073 0.646 0.9255 3 2 .1 0 1 .3 2 6

34.229 0.687 0.7523. 34.25 1.31636.459 0 .7 2 8 0.5946 36.48 1.307

(Ka ± ^ICa) = (1*302 ^ 0.018) x 10~^ mole/l

TABLE.-350.9. ■ IONISATION CONSTANT OF PROPIONIC ACID. DATA FROM RUN 5.A = 615 mji. ; c = 3*8^6 x 10~2 mole/l. ; CIn = 1.88 x 10*" mole/l.

1 = 1 cm. ; Dx =- 0.000 * 0.001 ; D£ = O.856 ± 0.002 ;a = 1-133 x lO”5 mole/l. ; b = [NaOH]'

105b D 105h 10^1 105Kamole/l mole/l mole/l mole/!

7.7 67 0 .1 8 6 3.871 7.830 1.2468.734 O .208 5.173 8.790 1.2609-774 0 .2 3 3 4.527 9.824 1.264

10.889 O.26O 3.956 10.93 1.26712.079 0.289 3.^51 12.12 1.26813-342 0 .3 2 0 3.003 13.38 1.26714.680 0.354 2.591 14.71 1.25716.092 0.385 2.277 16.12 1.2741 6 .8 3 6 0.404 2.103 16.87 1.2671 7 .379 0.416 2 .0 0 6 17.61 1.3011 8 .3 2 2 0.441 1 .8 0 1 18.35 1.25519*140 0.444 1.793 19.17 1.35419.938 0.484 1.498 19.98 1.2262 0 .773 0.491 1.462 2 0 .8 0 1.29722.485 0.524 1.269 22.51 1.33524.269 0.577 O .9857 2 4 .2 9 1.24826.127 0.605 0.8607 26.15 1.33628.059 0.645 O .6905 28.08 1.35030.066 0.695 0.4973 30.09 1.277

(Ka ± C K& ) = (1*281 ± O.O37) x 10“5 mole/l

TABLE 3.20 IONISATION CONSTANT OF PROPIONIC ACID. DATA FROM HUN 6

£ = 615 mjw ; c = 3*856 x 10 ^mole/l. ; C. ■ = 2 ,0 9 x 10 ^ mole/l. ;1 = 1 cm. ; D1 = 0 .0 0 0 ± 0 .0 0 1 ; D£ = 0.945 ± 0 .0 0 2 ;KJ n = 1 .1 3 3 x IQ"5 mole/l. ; b = 2 [Na^CO^]

105bmole/l

D 1 05hmole/l

103Imole/l

lC^Kamole/l

7.767 • 0 .1 9 8 6.149 7.83 1.3058.733 0 .2 2 6 3.287 8 .8 1 1.2919.773 0 .2 3 1 4.682 9.83 1 .3 0 8

1 0 .9 0 6 0.283 4.038 10.95 1 .2 9 6

1 2 .078 0.313 3.332 12 .1 2 1.30512.877 0.332 3*288 12.92 1.31914.683 0.379 2.729 14.72 1.32416.094 0.414 2 .3 8 8 16.13 1.3371 6 .8 3 6 0.432 2 .2 3 2 16.87 1.34517 .377 0.453 2 .0 6 0 1 7 .6 1 1.33518*324 0.472 1.918 18.35 1.33719*139 0.492 1.779 19.17 1.34319 .939 0 .5 0 8 1.677 19.99 1.37320.773 0.531 1.534 2 0 .8 0 1.36022.483 0.573 1 .3 0 0 22.51 1 .3 6 8

24.270 0 .6 1 8 1.079 24.29 1.36526.127 O .676 O .8256 26.15 1 .2 8 1

28.037 0.709 0 .7026 2 8 .0 8 1.37330.417 0.734 0.5454 30.44 1.475

(Ka ± (7Ka) = (1.339 * 0.044) x 10“5 mole/l

TABLE 3.21 IONISATION'CONSTANT OF PROPIONIC ACID. DATA FROM RUN 7A = 615 mp. ; c = 4.82 x 10"^ m oleA * » = 1 .9 9 x 10~^ m oleA *

1 = 1 cm. ; D1 = 0 . 00 0 ± 0 .0 0 1 ; D2 = O.898 ± 0 .0 0 2 ;

,133 x 10“5 m oleA * i b = 2 [Na2C0^]

l o V D 105h 10^1 105Kam oleA m oleA m oleA mole/.

9.697 0.193 6 .1 7 8 9.76 1.28310.849 0.217 5*414 10.91 1 .2 8 2

12.039 0.241 4.794 12.09 1.28713-267 0 .2 6 6 4.256 13.32 1 .2 9 0

14.602 0.294 3.750 14.65 1 .2 8 8

16.013 0 .3 2 1 3.343 16.05 1.30117.500 O.35O 2 .9 6 7 1 7 .5 4 1.31019.064 0 .3 8 1 2.619 1 9 .1 0 1.31520.734 0.411 2.330 20.77 1.3372 1 .520 0.428 2 .1 7 8 2 1 .5 5 1.32922.412 0.444 2.04 7 22.44 1.33923.305 0.463 1.897 23.33 1.33124.190 0.480 1.774 24.22 1.33426.051 0.514 1-549 2 6 .0 8 1.34728.019 0.550 1.335 28.04 I .358

2 9 .987 O .582 I.I65 3 0 .0 1 1.39432.069 0 .6 2 0 O .9783 32.09 ■1.40134.151 0.657 0 .8132 34.17 1.41236 .455 0.689 0.6839 36.48 1.503

(Ka * ^Ka) = (1*339 * O.O56) x lO"5 moleA

TABLE 3*22 IONISATION CONSTANT.OF PROPIONIC ACID. DATA FROM RUN 8

^ = 615 ; c = 2.448 x 10"" m oleA * » C jn = 2 .1 3 1 x 10 m oleA1 = 1 cm. ; D1 = 0 .0 0 0 ± 0 .0 0 1 ; D^ = O .965 - 0 .0 0 2 ;

K j = 1 .1 3 3 x 1 0 -5 m o le A . ; b = 2 [j^C O ^]

i o \m oleA

103 [NaC l0 jm oleA

D 10 5hm oleA

103Im oleA

105Kam o leA

4.6C9 15 .319 0 .2 0 5 7 .230 2 0 .0 0 1 .3 0 1

4.801 15 .123 '0 .2 1 4 6.843 2 0 .0 0 1 .2 9 4

4.993 14.927 0.224 6 .4 5 0 19.99 1 .2795.185 14.731 0 .234 6 .0 9 0 19.98 1 .2655*601 14.336 0 .2 5 2 5.517 2 0 .0 0 1 .2 6 2

5.793 14.136 0 .2 6 0 5.287 I 9 .9 9 1.2636.209 13.741 0 .2 7 6 4.868 2 0 .0 0 1.2736.593 13 .345 0 .2 9 2 4 .494 19.99 1 .2737.009 12.950 0.309 4 .140 2 0 .0 1 1 .275

7.585 12.355 0.334 3.683 19 .98 1 .2 6 8

8 .0 0 1 11.956 0 .350 3 .426 2 0 .0 0 1.274

8 .8 0 1 11 .1 6 1 O.38O 3 .0 0 2 2 0 .0 0 1 .2899 .6 0 1 10.363 0.411 2 .6 2 8 2 0 .0 0 1 .297

10.401 9.569 0.443 2 .2 9 8 2 0 .0 0 1 .297I I .585 8.372 0.490 1 .8 9 0 19.99 1 .2 9 6

1 2 .8 0 1 7.175 0.537 1 .5 5 4 2 0 .0 0 1 .2 9 914.593 5.376 0 .6 0 0 1 .1 8 6 19.99 1 .3 3416 .8 0 1 3 .1 8 1 0 .6 8 0 0.8173 2 0 .0 1 1 .361

19 .809 O .I82 0.772 0.4876 2 0 .0 1 1 .57 1

(Ka ± ^ a ) = (1.304 ± O.O69) x 10“5 moleA

TABLE 3*23 • THERMODYNAMIC IONISATION CONSTANTS OF ACETIC ACID ANDPROPIONIC ACID IN WATER AT 25°C.

Present Work10°(Ka * Ks)mole/l

Data from run 1 1832 £ 73Acetic _ , «, . , Data from run Acid 2 1762 18

Data from run 3 1772 ± A3

Average 1789 ± 61

Data from run 4- 1302 ± 18

_ . Data from run Propionic 5 1281 ± 37

Acid Data from run 6 1339 ± aaData from run 7 1339 t 36

Data from run 8 130^ * 69Average 1313 ± 5a

Previous WorkAuthors Method lO^Ka mol?l Reference

Earned and Ehlers emf 1.754- 78Earned and Ehlers emf 1.754- 98

Earned and Owen emf 1.73 99Grunvvald emf 1.73 100

Bates emf 1.732 101Acetic Ives Conductance 1.739 102Acid MacInnes and Shedlovsky Conductance 1.733 103

Dippy and Williams Conductance 1 .7 6 104-Jeffery and Vogel Conductance 1.764- 105Darken Conductance 1.785 106

MacInnes Conductance 1.765 107Saxton and Danger Conductance 1.759 108

Kilpatrick Chase and Riesch Indicator 1 .8 109Kinnick and Kilpatrick Indicator 1 .7 0 6 94-

Eropioub Earned and Ehlers emf 1.336 79Acid Belcher Conductance 1.34-3 110

TABLE 3.2k IONISATION-CONSTANT-OF ACETIC ACID. DETERMINED. BY THE MODIFIED PROCEDURE.

Data from Data from Data fromRun 1 Run 2 Run 3

a 108KIn 108(Ka ± CKa) 108 (Ka ± 108(Ka ±c7Ka)mole/l mole/l mole/l mole/l

0 1390 1803 ±- 72 1733 ± 17 1772 + 191 1369 1802 ±- 72 1733 ±- 17 1771 18

2 134.8 1801 + 72 1732 + 17 1770 ± 181328 1802 + 72 1732 + 17 1770 + 17

4 1309 1802 ± 72 1733 ± 17 1771 ± 16

5 1290 1802 ± 72 1733 ± 17 1771 ± 16

6 12?1 1802 ± 72 1733 ± 1? 1771 ± 16

7 1253 1802 + 72 1733 ± - 17 1770 158 1235 1802 ±- 72 1733 ± 17 1770 ± 159 1217 1801 ± 72 1732 ± 17 1770 ± 15

10 1199 1801 ± 72 1732 ± 17 1769 ± 14* 1154 1832 i r 73 1762 ± 18 1772 ± 4 3

* Results obtained using Davies Equation

TABL

E 3.2

5 IONISATION CO

NSTA

NT OF

PROPIONIC

ACID,

DETE

RMIN

ED BY

THE

MODI

FIED

PR

OCED

UR:

oog3aoJ-Hmoj4->(tiQ

+id

oo

o o o o o O o o o o O ONIs- Is- r- •t- r- f*— Is- r- r- f- VO+ 1 +» -H -fi +•, + 1 + i + i + i +1 +1

r-H r H r-H • rH CO CO co CO(NJ (NJ (NJ (NJ (NJ (NJ (NJ (NJ (NJ (NJ (NJ oCO CO CO CO CO CO CO CO CO CO CO COi—1 r H r H r H r H r H r H r-H r-H r H r-H r-H

PS

Ph

oPi

d+jctiQ

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o

ON oo Is- vO v£> m m CO NOCO CO co CO cO CO cO CO co CO CO m

+ l -H + +i +1 + i +1 •h +i +i +iIs- vO vQ vO vO vO vO vO m m ON

in tn m in m m m m m m in COco CO CO co CO CO co CO cO cO co cof-H r-H r-H r H r H r H r H r-H ^ H • H r-H • r H

vOrtpsPhOPiH(ti+JdQ

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CO (NJ (NJ (NJ (NJ (NJ (NJ (NJ (NJ (NJ (NJCO CO CO CO CO CO CO CO CO CO CO

+ 1 +1 + -H +1 + 1 -H + 1 +1 +1 +1 +1

o ON On ON O n ON ON o ON ON oo ONr - vO vO vO vO vO NO vO NO vO COcO CO CO CO cO CO CO cO CO CO CO COr-H r-H • H r H r-H r H r H r H r-H r-H r H r H

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CO CO CO CO CO CO CO CO co CO cocO CO CO CO cO CO CO cO co CO CO I’ 1

+1 +1 + + + l + i + l +1 -H +1 +1 + i

r Hi H

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i Hr H

r Hr H

r Hr H

or H

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Or H

t-HooA l

CO CO CO CO cO CO CO CO CO CO cO INIr H r H r-H H r H r H r H r H r H r H

NF(NJ (NJ (NJ (NJ CNJ

+ 1 +1 4 i -H +1

r-H r-H o O N o(NJ (NJ (NJ i H (NJCO co CO CO cOr-H r-H r-H H r-H

m m m(NJ (N) (NJ (NJ (NJ

+ 1 + 1 + i + i +1o o o o ON(NJ (NJ (NJ (NJ i-H

CO CO CO CO CO» H r-H r-H r H r-H

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o CO CO CO CO cO (NJ CO (NJ (NJ (NJ r H r Hr H • H r-H r H r H r H r H r H i—H »—i r H r H r H

) aJ o r-H (NJ CO in vO Is- oo ON o •JC-

table 3 *2 3 * some literature values are also included for comparison. The agreement is indeed excellent, and there is little doubt that the method is a reliable one, though less precise than the conductiometric and electrometric methods.

A modified method of calculating the hydrogen ion concentrations, prior to the evaluation of Ka from equation (3*42) .was also used. *'Modified Procedure

The stoichiometric indicator constant at any desiredIn Jionic strength may be calculated by means of equation (3*40), usingany one consistent set of parameters , a end m, given in table3.14. Once IC_ is found at the reouired ionic strength, h follows In * ■immediately from

h ■= ( D - D p K ^ /(D2-D1 ) (3.^5)

and Ka is then evaluated from equation (3 -^2)exactly as describedabove. It must be stressed that in this case, for each value of theion-size parameter a, a corresponding value of is used. Theresults are presented in tables 3-24 and 3*25. It is clear fromthese tables that Ka is independent of the parameters employed in

1evaluating K_ . This result underlines the importance of using the ° In -same equation for calculating activity coefficients as is used in the evaluation of the indicator constant, when hydrogen ion concentrations are measured by means of indicators. By complying with thisrequirement, it is possible to determine h reliably even when an unambiguous value of cannot be obtained.

SECTION 3 .3 _DETERMINATION, 0F_THE FIHST IONISATION CONSTANTS,OF o - HYDROXY PH MNY LA C ETIC ACID AND MELII.OTIC ACID USING BN CKO CN ES CL G5ZEK

It has already been mentioned (see also figures 3*14 and 3*15 and p.|05) that the spectra of o-hydroxyphenylacetic acid and meli-

TABLE 3.26 THE FIRST IONISATION CONSTANT.OF 0-HYDROXYRHSNYLACETIC ACID.

—3 —5^ = 613 mp.. ; c ~ 3 * 00 x 10 m o leA * J — 2 .5 0 x 10 m o leA * »

1 = 1 cm. ; D1 — 0 .0 0 0 * 0 .0 0 1 ; D2 = 1 . 12V ± 0 .0 0 3 5

KIn = 1.144 x 1 0 m oleA * *, b = [NaOH]

105bm oleA

D 105hm oleA

103 Im o leA

105Ka,m oleA

1 .00 0.102 13*30 1.135 3 .6081 .2 0 0 .124 1 0 .8 2 1 .311 3 .5 3 0

1 .40 0.146 9*077 1 .4 9 4 3 .5321 .6 0 0 .1 6 8 7.787 1 .682 3 .5 8 41 .8 0 0 .1 9 2 6.704 1.871 3 .6232 .00 0.221 5.693 2 .062 3 .5912 .20 0 .2 5 0 4 .9 1 3 2.255 3 .6 0 8

2 .4 0 0 .2 8 0 4 .270 2 .449 3.6472 .6 0 0.315 3.667 2 .644 3 .641

2 .8 0 0.35^ 3.129 2 .839 3 .6 20

3*00 0.396 2 .664 3 .035 3 .6033*20 0.436 . 2 .302 3 .233 3.6673*40 0.486 1.928 3 .430 3 .645

3*60 0.543 1.582 3 .628 3 .5923*80 0.603 1 .2 8 6 3 .8 26 3 .568

4 .0 0 0.663 1.041 4 .025 3 .621

(Kal±- ^Kai ) = (3*605 * 0.039) x 10”5 moleA

•TABLE 3.2? THE FIRST IONISATION CONSTANT OF MELILOTIC ACID.= 615 mji* ; c = 3 x 1 0*^ mole/l. ; C^n = 1 .5 5 x 1 0~^ mole/l.

1 ~ 1 cm. ; D ± = 0.000 ± 0.001 ; D£ -- 0.710 ± 0.002 ;

KIn = 1,144 x 10“5 mole/l. ; b = [NaOH]

10 Vmole/l

103 [NaCiq^ mole/l

D lO^hmole/l

105ImoleA

105Kaimole/l

7*849 17 .0 7 7 0.165 6.845 2 5 .0 0 1.8229.306 15.633 0.195 5.473 2 5 .0 0 1.84310.756 14.193 0.226 4.438 2 5 .0 0 1.85412.198 12.759 0 .2 5 5 3 .6 9 8 2 5 .0 0 1.89113.632 11.330 0.285 3.090 2 5 .0 0 1.9191 5 .058 9.908 0 .3 1 8 2.555 2 5 .0 0 1.91716.476 8.494 0.353 2 .0 9 6 2 5 .0 0 1 .9 0 0

17*886 7 .O86 0 .3 8 8 1 .7 2 0 2 5 .0 0 1.88919.289 5.685 0.423 1 .4o6 2 5 .0 0 1.88320.684 4.292 0.460 1 .1 2 6 2 5.OO 1 .8 5 8

2 2 .0 7 2 3 .0 6 0 0.493 0.9135 25.15 1 .8 8 8

23*950 1 .5 2 6 0.540 0.6555 25.49 1.92124.825 0.154 O .568 O .5181 2 5 .0 0 1.843

(Ka| i ^ a i ) ^ (1*879 * 0 .0 3 2 ) x 10“5 moleA

lotic acid are identical with their respective singly-ionised anions. Since this rules out the use of direct spectrophotometry, the indicator method was used to determine their first ionisation constants. Bromocresol green was used for this purpose.

Although both acids are dibasic, the ionisation of their carboxylic protons is virtually complete before the phenolic hydroxyl'groups begin to ionise (for o-hydroxyphenylacetic acid the ratio.-

6 6 Kai / Ka2 is 4-#7 x 10 , and for melilotic acid it is 1 .3 x 10 Yjconsequently, in the pH range (3*8 to 5*^) used for determining theirfirst ionisation constants, the acids may be regarded as monobasic.

The experimental solutions were prepared in exactly the sameway as described in section 3 *1 (p. 3 6 ), and the data were treatedby the method described in section 3*2 (p.$4-). The values adoptedfor Kt and K were l.l*f x 10 ^mole/l (p.5"B ) and 1.008 x 10 ^mole^/l^ In w t v

rso] respectively. The solutions of these acids undergo chemical changes on aging and particularly so when exposed to daylight (see figures 3*16 and 3 *1 7)* In order to minimise errors from this source, stock solutions of the acids, as well as the experimental solutions, were stored in the dark, and optical densitj' measurements were usually completed within a day of preparation.

The results are shown in tables 3*26 and 3*2?. The standard deviations indicate that a satisfactory precision has been attained. Neither of these constants has been previously reported.

SECTION 5. A ^DETEHMINATION^OF^ THiI_ SECOND IONISATION CONSTANTS OF O-HYDROXYPHENYLACETIC ACID AND MELILOTIC ACID

INTRODUCTIONThe spectra of o~hydroxyphenylacetic acid and melilotic acid

were recorded at various pH values, immediately after the solutions

LEGEND TO FIGURE 3*14: o-H YD3RQXYPHENY LAC ETIC ACID(conc. = 2 .3 x 10 mole/l)

0 .0 5 M HCIO^A spectrum identical with (l) was obtained in acetic acid/acetate buffers, of pH = 4*50 and pH = 5*86

carbonate/bicarbonate buffer, pH = 10.47// - ., pH = 10.88// - , pH = 11.30

1.0 M NaOH

LEGEND TO FIGURE 3.13 : MELILQTIC ACID-4(conc. = 2 .6 * 10 mole/1 )

(1) 0.03 M HCIO^A spectrum identical with (1) was obtained in acetic acid/acetate buffers, of pH = 4.30 and pH = 5*86

(2) carbonate/bicarbonate buffer, pH = 10.20

(3) - // - , pH =10.74(4) - // - , pH = 11.00(3) 1.0 M NaOH

(1)

(2)(3)(4)

(5)

OP

TIC

AL

DE

NS

ITY

Fig.3-14 Absorption S p e c tra o f o-Hydroxyphenyl- acetic Acid in Aqueous Solution.

0-9 r

0-8

0*7

0-6

0-5

0-4

0-3

0-2

310 3203 0 02 80 290250 260 270WAVELENGTH m f J

OP

TIC

AL

DE

NS

ITY

Fig.3*15 Absorption Spectra of Melilotic Acidin Aqueous Solution•o

0-9

0*8

0-6

0-5

0-3

0*2

250 260 270 320280 290WAVELENGTH TT1/J

310300

OP

TIC

AL

D

EN

SIT

YFig.3*16 E ffec t o f Aging on th e S p e c t r a of

o-H yd roxphenylacetic Acid in Aqueous So lu tion .

( conc..= 2 * 4 x I O ~ 4 -mole/I. )

•o-

0-8

0-6

0*4

0-2

2 7 02 3 0 2 5 0 3 5 02 90 310 3 3 0WAVELENGTH m yU

Acid Solutions ( 0 * 0 5 N H C I O 4 ) — -------------

A lk a l in e S o l u t i o n s ( 0*3 N N a O H ) ..................

© a nd @ immediately a f t e r p re p a ra t io n

© a n d © a f t e r six weeks in the d a r k

© a n d © a f t e r six weeks in daylight

OP

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Y

Fig. 3-17 E ffec t of Aging on the S p e c tra of

M eliio t ic Acid in Aqueous Solution.( c o n c .= 2 * 3 x 1 0 . 4 mole/l. )

1-4

•2-

•0 -

0-8

0-6

0*4

0-2

3303102 3 0 2 5 0 2 7 0 2 9 0W A V E L E N G T H m ju .

Acid S o lu t io ns ( 0 - 0 5 N HCIO4 ) — — ---------

Alkaline Solutions ( 0 * 3 N N a O H ) • .............

(T) and @ immediately a f t e r preparat ion(2 ) a nd (5) a f t e r six weeks in the d a r k

© a n d © a f t e r six w e e k s in d a y l ig h t

had been prepared. These spectra, which are shown in figures and 3 »15i are very similar to each other, and, as expected, to the spectrum of o-methylphenol [ill] . It is clear that the spectra of the unionised acids and their respective monoanions are identical, within the experimental accuracy, and that in each spectrum the band at the high wavelengths corresponds to the doubly-ionised species. Since the effect of pH on the absorption spectra of o-hydroxyphenylacetic acid and melilotic acid is most pronounced at the long wavelength peaks at 29 0 .5 and 291*5 ^ respectively, these wavelengths were selected for the determination of the second ionisation constants of the two acids.

Prior to the determination of the ionisation constants of these acids, their chemical stability was investigated. The results of these studies, presented in figures ^,16 and show that boththe acidic and the alkaline solutions of these'acids, on exposure to daylight, undergo profound chemical changes. When the solutions are stored in the dark, their stability is greatly enhanced. It would therefore appear that the processes which take place are, in part at least, photochemical in nature. During the determination of the ionisation constants of these acids, the effects described above, whatever their natiire, must be allowed for by taking suitable precautions .

In studies of solution aging over a period of several days, it was found that the solutions of o-hydroxyphenylacetic acid and melilotic acid, in both acidic and alkaline media, if stored in the dark immediately after preparation, did not show any detectable drift in optical densities at 2 9 0 .5 s.ud 291*5 nJl respectively.At the same wavelengths, the optical densities of solutions exposed to daylight for four days were found to increase by 5-6^ for the

alkaline solutions, and by 150-200% for the acid solutions. Consequently, during the determination of the ionisation constants, stock solutions of these acids, and the test solutions prepared from them, were stored in the dark and, invariably, the optical densities of the latter were measured within 36 hours of their preparation.

Preliminary determinations have shown that the second ioni--11 /sation constants of these acids were about 10 mole/litre or less.

To obtain the extinction coefficient, , of the doubly-c-harged anion L~ would therefore require measurements on solutions at least molar with respect to sodium hydroxide. The use of such high concentrations could, however, introduce a medium effect; so it was decided to determine the ionisation constants by an extrapolation method - this does not require a direct measurement of E^ - despite the reservations made about such methods in section 3 »1 « quantity = ^l~a (see telow) was obtained from measurements on solu-

-2tions which were 5 x 10 M in perchloric acid; this was possiblebecause the unionised acids E^L and their respective monoanionsHL~ happen to have identical extinction coefficients, i.e. ^ =^0~-B la, Y/here E is the extinction coefficient of the species H~L. o o 2

THEORETICALIf it is assumed that ftt4. = fT-T~ > the second ionisationxi ilLi

constant of a dibasic acid H^L may be defined byKaP - J k l hf (3 -^6 )[HIT] 2

where h is the hydrogen'ion concentration and f^ is the activity coefficient of the species L~. At high pH values, when pHj^pKap the concentration of the undissociated acid H^L may be neglected, and the stoichiometric, concentration, a, of the acid is given by

a = [Hi"] +.-[L=] (3^7)

Under these conditions, and in accordance with the Beer-Lambert Law, the optical density, D, of a solution of the acid at a selected wavelength may be expressed ss

D E1l[HL“] + E l [L=] ( 3 * Wwhere E^, are the extinction coefficients of the species KL- and L= respective^', end 1 is the path-length. Using equations (3.^7) and (3»^S), and introducing- the definitions

andDx = E p a (3*^9)

D2 = E2la (3-50)equation (3 A 6 ) ra&y be transformed into

Ka2 = (D-Dx)hf2 /(D2-D) (3.51)which on further transformation becomes

l A D - D p = l / ^ - D p + hf2 /(Dg-Dj^) ICa2 (3-52)

and finally substituting for h fromKy, =■- h[0H-]fi2 (3.53)

we havel/CD-D^ = 1 ■/(-D2r D 1 ) +• Kwf2/[CH-] (3-3^)

The use of this equation for the determination of Ka2 involves a measurement of and the optical densities at a number of hydroxyl ion concentrations. A plot of 1/(D-D^) versus

Ky/f 2/ [0H]f- should be a straight line with a slope of l/Ka2 (J>2 ** l and an intercept of l/CD^-D.^). Evaluation of the last two quantities, either graphically or by the method of least squares, (seeappendix A3 .2 p.2.^)allows D2 and Ka£ ‘to De calculated.

Calculation of the equilibrium hydrogen ion concentrationsSince the second ionisation constant of carbonic acid is of

the same order of magnitude as the second ionisation constants of the two acids under discussion, optical densities (D) were measured for

a series of test solutions containing carbonate/bicarbonate buffers. In the preparation of these test solutions, standard solutions of the acid under study and of sodium carbonate were mixed (25 ml* of each), the requisite volume of a standard solution of either sodium hydroxide or perchloric, acid was added and, finally, each solution was made up with water to a constant volume (100 ml.). Hence the stoichiometric concentrations of both the acid under study and the sodium carbonate remained constant throughout the series, while the concentration of either sodium hydroxide or perchloric acid varied from one test solution to the next in such a way that the degree of ionisation of the acid studied (for the second stage, i.e. from HIT to L“) remained within the range 20 - 80%,

The condition of electroneutrality requires that:[Hi + 0 a +] = [OH’] + [HCOr ] + 2[C03=] + [ciog) + 2 [L=] (3-55)The experimental conditions, (pH of all solutions ^10), justify two further approximations in addition to the one already made (equation 3*4-7 )• Firstly, the stoichiometric concentration, c, of sodium carbonate may be expressed as

c = [ccy] + [HCO^-j (3 .5 6 )( [H^CO^] is negligible since for carbonic acid pKap = 6.35 [112] .) and secondly, the hydrogen ion concentration may be neglected. With these approximations, equation (3*33) becomes

c + b = [0H”J + d + a +• [C0^=] +■ [l=] (3*37)where b and d are the stoichiometric concentrations of sodium hydroxide and perchloric acid respectively.

The defining equation for the second ionisation constant of carbonic acid,

K* = hf2 [C03=] / [hco -] (3.58)

together with equations (3*53) and (3*56) gives

[CO =] = cK2/(hf2 + K2 ) = cK2 [0H"]f2 /(f2Kv, + K2 [OH~] ) (3-59)

whereas combination of equations (3*47), (3*48), (3*49) and (3*30) yields

[IT] =.-■ a(D-D1 /(D2-D1) (3.60)Elimination [l-] and [cOT=] from (3*5?) v;ith the aid of the last tivo

Jequations, the following expression is obtained:

c b — [OH”] + d + a [1+(D-D1)/(D2~D1 )] +■ cK^ [pH”] f^/Cf^+K^ [oH“]f^,)

(3*61)Further rearrangement of(3«6l) gives the quadratic equation

K 2 f^[oir]2 +.[OH-]j|d-b+s.(l+ jp^/] 4 fl + f2Kw[ + Kv;f2 [d-c-b+a(l+£±i)] = 02 1 2 1

(3.62)which may be solved for [pH ] by the standard method.

The ionic strength I,I [oh”] + [h+] a [hit] +4 [it] + [Hcoy] +4 [co^=] + [Na+J + [ciO^-jJ, (3* 63 )in view of the stipulated approximations, may be reduced to the form:

I =- 3c +- 2b - d - a - [oh” ] (3.64)

CALCULATIONS AND RESULTS The first cycle in the adopted computational routine

required the following steps:(i) Calculation of approximate ionic strength from equation

(3*64)^ putting [oh ] = 0.(ii) Estimation of activity coefficients by means of the

Davies equation, (3*25)*(iii) Solution of equation (3«o2) for [OH ] using a reasonable,

TABLE 3 •■2.8 THE SECOND IONISATION CONSTANT OF o-HYDROXYFHENYLACETIC ACID.A - 290.5 mp. ; c ~ 1 x 10“ 2 m ole/1 . ; a = 2 .430 x 10 ^ m o le /l .

1 = 1 cm. ; D1 = 0 ,.011 0 . 001

105b lO^d 103D io V d 10^ [OH"]1 /f io 12R,f 103I

m o le /l m o le /l m o le /l ' (D -3 ^ ) m o le /l m o le /l

3.2735 ■ — 663 -31 3.289 1 .5 3 4 2 .2 0 1 3 3 .0 2

2 .8807 - 648 -45 2 .950 1 .570 2 .458 32 .572.4224 - 621 4 2 .570 1 .639 2.827 3 2 .0 31.964-1 - 598 -28 2.207 1 .704 3 .2 9 9 3 1 .4 8

1.5713 - 566 36 1.917 1 .8 0 2 3 .8 0 6 30 .98

1.1785 - 539 14 1 .646 1 .894 4 .441 30 .47

0.8511 - 510 38 1.441 2 .004 5 .0 8 4 3 0 .0 2

O.5238 • - 481 43 1.253 2 .1 2 8 5 .855 29.550.2619 - 457 45 1 .1 1 8 2 .242 6 .574 2 9 .1 6

- - 432 51 0.9960 2 .375 7 .39 3 2 8 .7 6

- 0 .212 421 -41 0.9048 2.439 8.143 2 8 .6 4- 0.4-24 394 33 0.8237 2 .6 1 1 8 .949 28.51- 0 .6 3 6 376 16 0.7493 2 .740 9.843 28.37- O .9OI 356 -24 0.6663 2 .899 1 1 .0 8 2 8 .1 9

1 .1 6 6 330 5 0.5940 3 . I 35 12 .44 2 8 .0 0- 1.4-31 311 -27 0.5303 3 .333 13 .94 2 7 .8 0- 1.749 283 3 0.4646 3 .676 15 .93 27 ,5 4- 2.067 266 . -6 2 0.4079 3.922 18.17 2 7 .2 8

- 2.385 239 - 8 0.3598 4 .386 20.62 2 7 .0 1- 2 .6 5 0 226 -46 0.3245 4 .651 2 2 .8 9 2 6 .78

Gp = 0 .0036 (D2 ±€rD2) = 0.84-5 ± 0.004-5

(Ka2 ± crKa2) = (7 .7 2 8 ± 0.073) x 1 0 -12 mole/ 1 .

Fig.

3*18

Seco

nd

Ioni

satio

n C

onst

ant

of

o-H

ydro

xyph

enyl

acet

ic

Aci

d. CM

CM

CO CM

( ' a - a ) / i

TABLE 3 .2 9 THE SECOND IONISATION CONSTANT OF MELILOTIC ACID^ 1

2 9 1 .3 c = 1 x 10 m o le /l . ; a = 2 .290 x l O ~ f m o le /l .

1 = 1 cm. ; D^ V o . 010 t o .001

103b 103d lO^D

V~'Q-tf-OH 105 [0H~]

mole/l1 lO12^ 10^1

mole/l mole/l (D - Dx ) mole/l mole/l

1.3713 - 669 -2 1 I .913 I .517 3 .8 1 4 3 1 .0 0

1.3094 - 636 -3 7 1.729 1.548 4 .225 3 0 .6 6

1.04?3 - 638 -17 1.556 1.592 4 .700 30 .310.7836 ■ - 613 38 1.396 1.653 5 .247 29 .950 .3 2 3 8 - 397 26 1.248 1 .7 0 4 5 .8 8 2 29.570.2619 - 376 31 ' 1 .1 1 2 1.767 6 .609 2 9 .1 8

359 -17 0.9894 1 .8 2 1 7.442 2 8 .7 8- 0.263 532 26 O.8788 1 .9 1 6 8 .384 28.63- 0.330 511 1 0 .7 8 0 2 1.996 9 .450 28 .46- 0.793 488 - 8 0.6935 2.092 10 .64 2 8 .2 8

- 1 .0 6 0 463 3 0 .6 1 7 7 2 .2 0 8 11.96 28 .09- 1.484 424 15 0.5155 2.413 14.35 27.77- 1.908 389 - 1 0.4326 2.639 17.12 27.43- 2.332 356 -20 0.3653 2.890 20 .31 27-07

2.736 322 - 8 0.3101 3.203 23 .96 26 .70- 3 .1 8 0 292 -1 6 0.2644 3.5^6 2 8 .1 5 26.33- 3 .7 10 256 -10 O.2173 4.063 34 .30 25 .8 4

- 4 .240 224 -1 4 0.1792 4.673 41 .71 25 .35- 4 .770 190 31 0.1477 5.556 50 .73 24 .85

(jp = 0.0022 (D2 .+ ) = 0 .842 ± Q. 0027

Ka2 ± C ^ 2 = (1 .4 31 * 0 .0 0 8 ) x lO -11 m o le / l

Fig.

3-19

Se

cond

Io

nisa

tion

C

onst

ant

ot M

elilo

tic

Aci

d.

in

O

mm

Oro

cm nJ

('a-a)/i

assumed, value of (e.g. = lOOO)(iv) Application of the method of least squares to equation

(3*5^)» yielding D2 an< &Q.2 % anc* calculation of the relevant standard deviations; (see appendix A3*2 and A*f, p.22^ and p.2.2,0

In subsequent cycles, the same routine was'followed, except that in steps (i) and (iii) the values of [OH J and from the preceding cycle were employed. This procedure of successive approximations was terminated when the hydrogen ion concentrations calculated in tv/o consecutive cycles agreed to 6 significant figures. In these calculations, the values used for and Kw wereA . 69 x 10*”i:Lmole/l [113] and 1 .008mole2/ ! 2 [86] .

The results are shown in tables 3*28 and 3*29 and illustrated graphically in figures 3*18 and 3 *1 9 * The standard deviations in Ka2 (less than 1%), indicate that the precision attained is high. However, in view of the fact that an extrapolation method has been used, it is very improbable that an equally high accuracy has been achieved

SECTION 3.3 DETERMINATION OF THE IONISATION CONSTANTS OF o-HYDBOXY-

ACETOPHBNOKB, - P50PI0PHSNCN3 AND -n-BUTYROPHENONSThe effect of pH on the spectra of freshly prepared solu

tions of o-hydroxyacetophenone, -propiophenone and -n-butyrophenone is shov/n in figures 3*20, 3*21 and 3*22. By applying the usual criteria [ll ] , the wavelengths chosen for the determination of the ionisation constants of these three phenols were; 358^ 355^ 35 7 respectively. It is interesting to note that the replacement of one alkyl group, attached to the carbonyl group, by another, does not evoke any prominent changes in the spectra of the compounds in

OPT

ICAL

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Fig. 3*20 Absorption Spectra of o.-'Hydroxyacetophenonein Aqueous Solution

conc. = ! * 8 x IO 4 mole/l .0-9

0-8

0-7

0 -6

0-5

0-4

0-3

0-2

4 2 02 8 0 3 0 0 3 2 0 3 4 0 3 8 0 4 0 03 6 0w a v e l e n g t h rnyu

<j> 0-02 M HC!04© 0-2 M NaOH

(2 ) pH = 9-83 ^ c a rb o n a te

© p H - | 0 -2 l - bicarbonate

@ p H = IO * 6 8 buffers

OP

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ITY

Fig.3-2i Absorption Spectra of cHHydroxypropiophenoriein Aqueous Solution.

conc. = 2 x IO 4- mo!e/l.j0-9

0 -8

0-7

0-6

0-4

0-3

0-2

2 7 0 4102 9 0 310 3 3 0 3 5 0 3 9 03 7 0

WAVELENGTH m f J

© 0-02 M HC104© 0-2 M NaOH

© p H = 9 - 8 0 ^ carbonate/

© pH= 10*26 — bjcarbonate

@ pH = 10-72 buffers

OP

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Fig.3-22 Absorption Spectra of srHydroxybutyrophenonein Aqueous Solution.

mole/I. jconc.^ 2 x IO *40-9

0-8

0*7

0-6

0-5

0 -4

0-3

0-2

4103 9 03 5 0 3 7 03 3 02 7 0 3102 9 0

WAVELENGTH m J J

<D 0-02 M HCIO4© 0-2 M NaOH

(D pH“ 9*93 carbonate/

(3) p H - 10*30 - bicarbonate

@ p H - 1 0 * 6 8 J buffers

OP

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AL

DE

NS

ITY

F i g . 3 - 2 3 E ffec t o f Aging on the S p e c t r a o f

q -H ydroxyaceto pheno ne in Aqueous Solution.

( conc. = l ' 8 x IO ^ mole/1. )

• o

0-8

0-6

0 -4

0*2

3 9 03703 5 0310 3 3 02 70 2 9 0WAVELENGTH myU.

Acid Solutions ( 0 * 0 2 N H C IO 4 ) ------------------

Alkaline Solutions ( 0 - 2 5 N N a O H ) ......

(T) and @ immediately a f t e r preparation,

© a n d © a f te r six weete in the dark,

© a n d @ a f t e r six weeks in daylight.

OP

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YFig.3-24 Effect of Aging on the Spectra of

o-Hydroxpropiophenone in Aqueous Solution.

( conc. = 2 ’2 x IO ^ mole/l. )

0-8

0*4

0-2

3 9 03 7 03 5 03 3 02 9 0 3102 7 0W A V E L E N G T H m^U-

Acid Solut ions ( 0 - 0 2 N H C I O ^ ) -----------------------

Alkaline Solutions ( 0 - 2 5 N N a O H ) ....... ••••■

@ immediately a f te r preparation.© a f t e r six weeks in the dark.

© a f t e r six weeks in daylight.

©©©

OP

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F ig .3-25 Effect o f Aging on th e S p e c t ra o f

orHydroxybutyrophenone in Aqueous Solution.

( conc. = 2 '2 x \ Q ~ 4 mol e/I . )

0-8

0-6

0*4

0-2

3903 7 03 5 03303102 7 0 2 9 0W A V E L E N G T H n\jU.

Acid Solut ions ( 0 * 0 2 N H CIO 4 ) --------

A lk a l in e Solut ions ( 0 - 2 5 N N a O H ) -

(T) and (4) immediately a f t e r p repara t ion -

(2 ) and (5 ) a f t e r six weeks in the dark.( 3 ) and (6 ) a f t e r six w e e k s in daylight.

this homologous series. This is consistent v.ith the view that the bands in this spectral range arise from the TT-kTT transitions.

The spectra of the alkaline solutions (0.23N NaOH) of the phenols undergo drastic changes on exposure to daylight (see figures p.2 3, 3*24 and 3*2 3) although solutions of the same composition, which have been stored in the dark for the same period of time, show no change in their spectra. The behavious exhibited by the acid so3.utions (0.02N HCIO^) is quite different: firstly, the changes in the spectra brought out by exposing the solutions to daylight for several weeks are not very pronounced, and, secondly, storage of the solutions in the dark inhibits these changes, but does not eliminate them. Also short term aging studies were carried out on solutions which were stored in the dark immediately after preparation. Within a period of 3 days, neither acidic nor alkaline solutions of these phenols showed any deterctable drift in optical densities at the wavelengths selected for the determination of the ionisation constants. The accuracy with which the ionisation constants were determined suffered little - if at all - from the instability of the solutions, since effective precautions, based on the above observations, were taken.

In preliminary runs, the ionisation constants of these acids were found to be sufficiently large (pK 10.4) to allow a reliable direct measurement of = Ef la (see below) in sodium hydroxide solutions of a concentration (0.2N) which did not raise anxieties about .the introduction of a medium effect. Since D = E la (see below) iso oalso readily accessible to direct measurement (solutions 0.02M in HCIO^ were used for this purpose), a direct method, in principle identical with Third Method of section 3*1 was employed for the accurate determination of these ionisation constants. Accordingly,

optical densities were measured for a series of solutions in which the degree of ionisation of the phenol under study ranged from 20% to 80%. These test solutions were prepared by mixing a fixed volume (23 ml.) of a standard phenol solution with an equal volume of a standard solution of sodium carbonate., adding a predetermined quantity of a standard perchloric acid solution and, finally, making up each solution with water to a fixed volume (100 ml.^so that the stoichi- metric concentrations of both sodium carbonate (c) and the phenol (a) were maintained constant throughout the series. In the case of o- hydroxy-n-butyrophenone - the least soluble of these phenols - the stock solution contained a small, known concentration of sodium carbonate; this was expedient because it raised the solubility of the phenol.

CALCULATIONS AND HESULTS On the basis of the principles enunciated in the previous

section, and employing an analogous notation, the'following* expression for the icnisation constant of a monoprotic acid may be derived:

Ka= [L"hff /[HLJ = (D-DQ)hf^ /(Dn -D) ^ (D-Dq )K„/(D1-D) [oh"J (2 .6 5)

where D, and are defined by the equationsD = E p [L-J + B l[HL] (3.66)

Dq= EQla (3.67)Dx=-. Epa (3-68)

in which E , S.. are the extinction coefficients of HL and L~ res-o 1pectively, at the same wavelength.

The ionic strength and the equilibrium hydroxyl ion concentrations were calculated by an iterative procedure which involved the • use of the equations:

[Off]2 .,.[0H-]|f-b+a ~ g - ] K ^ 2 * f2K ^ +. K,,f2 [d-c-b+a I L s ] = 0

(3-69)and

I = 3c +■ 2b - a - a P-~Do - [0H~] (3.?0)Di-Do

These equations are similar to the corresrjonding equations of • the previous section because in both cases the same buffer system was used; the values adopted for and Kw were, naturally, also the same *

The steps required in the computation - after the first estimate of the ionic strength has been obtained from equation (3.70) by putting {OH"”] = 0 are set out below:

(i) Calculation of the activity coefficients f^, f^ by means of the Davies equation (3*23)

(ii) Solution of equation (3*69) for .(iii) Recalculation of I using equation (3*70) and [OH ] obtained

in step (ii).(iv) Repetition of steps (i), (ii) and (iii) until self-

consistent (to 6 significant figures) results are obtained.(v) Calculation of Ka from equation (3*&3) using the value

of [pH ] obtained in the last cycle of step (iv).In tables 3*30, 3*31 and 3*32 the results of these calculations are shown.

Judging by the standard deviations (about 2%), the precision with which the ionisation constants have been determined is satisfactory; furthermore, since a direct method has been used, there is every reason to suppose that a comparable accuracy has been attained.

Only one of these ionisation constants.has been previously

TABLE 3.30 IOHISATION CONSTANT OF o-HYDKOXYACETOPHENONEO 1

Jl = 358 rop. ; c = 1 x IO" mole/l. ; a = 1.810 x 10 ~ mole/l. ;1 = 1 cm. ; Dq = 0 .1 0 9 - 0 .001 ; = 0 .9 2 2 ± 0 .0 0 2

10^dm oleA

lO^D 10^ far]mole A

10^1 mole A

10l:LKamole A

797 1 0 .9 8 28.75 5.0530.3563 770 8 .3 2 8 28.44 5*1401 .1 1 3 0 738 6 .6 3 9 2 8 .0 8 5.1901.6693 704 3 .2 1 2 2 7 .6 8 5.2781.9478 686 4.637 27.46 * 5.3142.4089 648 3.847 27.09 5.1552.8779 613 3 .2 0 1 2 6 .6 9 5.1903 .5 3 9 0 384 2 .6 8 7 2 6 .2 9 5.2723 .8 1 6 0 551 2 .2 5 1 2 5 .8 6 5.3344 .2 6 6 3 312 1.911 25*45 5 .1 8 6

4.7303 472 1.614 25.03 5.0375*1940 438 1.361 24.60 5.0345.6378 410 1.142 24.16 5.1876 .1213 370 0.9538 23.72 4.9976 .6780 330 0.7571 2 3 .2 0 4 .9 7 1

7.2343 293 O.587I 22.67 5 .0 2 2

7.7910 234 0.4391 2 2 .1 3 4.9838.3475 221 O .3086 2 1 .6 0 5.219

(Ka ± ^Ka ) = (5.142 ± 0.118) x 10“^ mole/l

TABLE 3.31 IONISATION.'CONSTANT OF o-HYDROXYPROPIOPHENONE?\ = 333 » c = 1 x 10 2 mole/1. ; a — 2.160 x 10” mole/1;1 = 1 cm. Dq = 0.148 1 0.001 D = 0.964 ± 0.002

10 103D 10^ [oh"] 103I 10l;LKam o le /l mole/L m oleA m o le /l

808 10.87 28.74 3.9230.3816. 787 9.149 28.33 3.9770.7632 764 7.700 2 8 .3 0 4.0321.1607 735 6.434 28.04 4.0041.3382 711 5.430 27.75 4.1311.9337 678 4.399 27.44 4.0622.3332 648 3 .9 1 5 2 7 .1 2 4.0742.7307 623 3.348 26.79 4.1943*1482 590 2 .8 7 8 26.45 4.1393 .3 6 1 6 557 2.468 2 6 .0 8 4.1053-9432 328 2.143 25.74 4.0954.3407 503 1 .8 3 6 25.38 4.1824.7382 472 I .606 2 5 .0 2 4.1323.1337 441 1.389 24 • 65 4.0663.3332 412 1.197 24.28 4.0265 .9 3 0 7 384 1 .0 2 8 23.90 3.9906 .3282 355 0.8771 23.53 3.9066.7257 331 0.7413 23.15 3.930

(Ka * ^Ka) = (4.034 * 0 .0 8 7) x 10"11 m o le /l

TABLH 3*32 IONISATION CONSTANT' OF o-HYDROXY-n-BUTYROPHENONE.—2 —4£ =. 357 mp., ; c — 1 x 10 mole/l. ; a - 2*210 x 10 mole/l.

1 = 1 cm. ; Dq = 0.157 I 0 .0 0 1 ; D± = 1.004 ± 0 .0 0 2

105dmole/l

lO^D lO^ [oH~]mole/l

lG^Imole/l

lO11^mole/

850 10.77 28.74 4.2110 .3 8 1 6 818 9 .0 6 9 28.54 3 .9 5 0

0.7791 798 7.568 28.30 4.1451.1766 762 6.345 28.03 3.9721*574-1 737 5.338 27.74 4.1021*9716 707 4.518 27.43 4.1322.3532 674- 3.872 2 7 .1 2 4.0782.7348 646 3.333 26.80 4.1313*1164 619 2*880 26.47 4.2003*4-980 590 2.498 26.14 4.2213.8796 557 2 .1 7 2 2 5 .8 0 4.1534-.2612 521 1 .8 9 2 25.45 4.0154-. 64-28 500 1.646 2 5 .IO 4.1685*0403 470 1.424 24.74 4 .1 5 0

5.4-871 440 1 .2 0 6 24.32 4.1955.8353 411 1.056 23.99 4.0886 .2328 382 0.9029 23.62 4.0396 .6 3 0 3 356 O .7653 23.24 4.045

* C7Ka^ = (4.111 *■ 0.08l) x lO**11 mole/l

measured: Mangusson, i-’ostmus and Craig [1153 reported a value ofn5.4-9 x *10 mole/litre for o-Hydroxyacetophenone at 25 C - this

is some 6.8% larger than the value found in the present v/ork. A possible reason for this moderate discrepancy may well be the instability of the phenol solutions, of which these authors were, apparently, unaware.

CHAPTER IV

SPECTROPHOTOMETRIC DETERMINATION OF THE STABILITY CONSTANTS OF SOME IRON(III) COMPLEXES

SECTION *f.l DETERMINATION OF THE STABILITY CONSTANTS OF THE COMPLEXES FORMED 3Y IRON(ill) WITH o-HYDROXY-ACETOPHENONS,-PROPIOPHENONE AND -n-BUTYRQPHENONE

INTRODUCTION

Complexes of iron(111) with phenols and related ligands (e.g. salicylic acids) have been extensively studied in aqueous solution. £6,' 7, 8, 13 to ^7] • They are invariably coloured [8] and their spectra usually show an absorption band in the visible region where iron (111) ion absorbs weakly [8, 13, 3 2 , 37, 116] and the ligands do not absorb at al3. [57, ll6j. In fact the colouration of the iron(lll)-phenol complexes is so characteristic that this reaction i^4c£ed in organic chemistry as one of the diagnostic tests for the phenolic hydroxyl group. Almost all studies of the composition and stability of the iron(lll)-phenol conplexes were carr.ied out using either potentiometry or spectrophotometry. Although the former is undoubtedly a more general method for the study of complexes in solution, the latter method has been used much more frequently for the study of these complexes because their optical properties are particularly favourable for its application. The stability constants of the complexes selected for study in the present work were all determined spectrophotometrically.

In all equilibrium studies- the presence of side reactions must be considered and, if possible, allowed for. This is particularly important in the case of reactions involving the ferric ion, which undergoes extensive hydrolysis in aqueous solution [117 to 12l] .At low pH values and not too high stoichiometric concentrations

2 rof iron(lll), the main hydrolytic species are Fe(OE) [ll7, 118 119] , Fe(OH)*' J~120, 121] , and the dimer Fe2 (0E)2 + [117, 118,

120, 12l] ; as the pH is increased, further hydrolysis and polymerisation take place, the attainment of equilibrium becomes sluggish and finally colloidal and solid phases are formed. Under the experimental conditions ( pH and the stoichiometric concentration of iron (111) ) used for the determination of the stability constants of the complexes formed by iron(lll) v/ith o-hydroxy-acetophenone, f-propiophenone and -n-butyrophenone, the concentration of the species

2 “f?-Fe(0H)2 was negligible, that of Fe(OH) quite appreciable (10% to 40£> of total iron (111 ) ), and that of the dimer Fe^OH)^* although small, could not be neglected.

The extent to which the ferric ion complexes v/ith the perchlorate ion must also be considered, since the experimental solutions contained a relatively large, essentially constant, concentration of this ion. Sutton [122] , has measured the absorption spectra of ferricperchlorate in 1-7M perchloric acid and interpreted his results in

24-terms of the ion-pair FeClO^ , v/ith an association constant of0.475 - 0.072 l./mole. Sykes [l23] and Richards and Sykes [l24], alsoon the basis of spectrophotometric data, provided further evidence infavour of this complex; they found the association constant to bebetween 7 and 14*9 l./mole. However, other workers £125 to 1283 havefailed to find supporting experimental evidence for the existence ofthis species. In view of the uncertainties associated with this equi-

2*librium constant, and considering that even if the species FeClO^ was allowed for the results would not be significantly affected, this side reaction was disregarded in the present work.

Previous studies [l3, 14, 40 to 44[J of the complexes formed between phenols and iron(lll) have shown them to be 1:1 at high acidities (pH C3)* Since in this work the acidities of the solutions used for the determination of the stability constants did not exceed a pH

of 3» the complexes studied were assumed to be 1:1. This is corroborated by :(a) the fact that the experimental data conformed to a linear relationship, predicted on the basis of this assumption, and(b) that the spectra of solutions which contained different concentrations of perchloric acid but a fixed concentration of both the ligand and iron(lll) had identical shapes in the wavelength rangein which the absorption of the latter is negligible.

The theoretical treatment which is given below is more generalthan that used by previous workers: Milburn O i l and Ernst andHerring 0 2 ], since allowance is made not only for Fe(OH) c~+ but

4+also for the dimer Fe2(0H)2 • Also an equation is derived whichis useful when, due to the low stability of the complex or/and due to the low solubility of the phenol, an excess of ferric ion has to be used.

Naturally, when the assumptions made by previous workers are operative, the equations derived here reduce to the. simpler forms used by them.

THEORETICALThe equilibrium in which a monobasic phenol HL forms a 1:1

2+complex FeL with the ferric ion, may be expressed either as3+ 2+ +HL +- Fe = FeL + H

with a formation constantKf =hfFeL2+] ^ ^ / [ hl] [Fe5+] £, (4.1)

or asL ~ +- Fe^+ ==* FeL24"

with a stability constantKs = [FeL2+] f?/[L‘][Fe3+j£1f_ (4.2)

where h is the hydrogen ion concentration.In addition to the formation of the complex, the following side

reactions must be considered:a) ionisation of the phenol

EL = H* + if*Ka = h [L'Jfi /[HL] (4.3)

b) hydrolysis of the ferric ionFe3* +■ H O — Fe(OH)2+ + H+KR = [Fe(OH)2^] h f p 2/[Fe3 *]f- (4.4)

2+c) the dimerisation of Fe(OH) :

2Fe(OH)2+ Fe2(OH)2Kp = [Fe2(0H)24+J fif/[Fe(OH)2+'] 2f| (4.5)

where f^, fp, etc. are the activity coefficients of the singly,doubly, etc. charged species, respectively.

The stability constant K is related to the formation constant KfsKf = KsKa (4.6)

If the stoichiometric concentration of the phenol is denoted by a, and that of iron(lll) by m# then we have

m = [fV*] [Fe(0H)2+] + 2 [TepCCE)^* ] + c (^.7)and

a =■ [l ~] + [HL] +•- c • .(^.8)2 +v/here c is the concentration of the complex FeL

Elimination of [Fe(OH)2+J and [Fep (CEQp^*] from (k,1/) by meansof (k.k) and and rearrangement, gives the quadratic equation

2 Kj Kjj2 f2f32 [Fe3+] + hf1fif(hf1f2 + Kfif )[Fe3+J- h2f2£2f^(m-c) = 0

(6.9)r* "3Solution of this equation for [Fe. J (only one root is physically

meaningful), followed by several transpositions, leads to equation(4.10) :

[Fe^+] = Zhf- - c)/z (4.10)in which, for convenience, z is defined by

r ■ ■ yz = f^hf-jfp-Ht^)* [f^h^fp +' Kjjf^)2 + 8KDKH2 (m-c)fp2f^^j 2 (4.11)

Substituting in (4.2) for [Fe"'+J and jjL ] from (4.10) and (4.3),(4.8), v/e obtain

Ks =• o(Ka + ■ hf?) a/2Kahf2f,£. (m-c)(a-c) (4.12)-L J. z> ■+The optical density D^ of a solution containing the complex FeL2+ and other species in a cell of path length 1, may be expressed as the sum

D1 ~ D * D2 (4.13)D being the absorbance of the complex, while Dp is the absorbance due to the remaining constituents of the solution. If the complex obeys the Beer-Lambert law, then

D = D- - = Elc (4.14)1 c. -

andc = D/El (4.13)

where E is the molar extinction coefficient of the complex. Clearly, when a wavelength is selected at which Dp is negligible compared to

Dl ’ D1 ~ D 'In view of equation (4.13),

z =- f^hf-^p +Kh f^) +• [f^h^fp+K^f^)2 +8KDK}3:m-D/Sl)fpf2f J * (4.16) and equation (4.12) which becomes

K = D(E + hf2) z/2ElKahf2f-.f, (m-D/El) (a-D/El) (4.1?)S Q. _L X >may be cast into either of the two forms:

m = 1 1— - + —

D El E1K2(Ka + hf-) ) z

■jp |_2hf£f f^a-D/El^(4.18)

a5

JLEl E1K(Ka + hff) z (4.19)

If D is regarded as the dependent variable, then each of these equations contains four independent experimental varia.bles: a, m, h and 1, and in planning an experiment these should be selected as far as possible in the best interest of accuracy. \

Equation (4.18) should be used when the experiments.1 solutions contain an excess of phenol, while equation (4.19) is useful when an excess of iron(lll) has to be used. In either case, a plot of the left hand member (either m/D or a/D) versus the appropriate expression in the square brackets should give a straight line, the slope and intercept of which may be used to calculate E and Kp. Successive approximations are of course required since the terms in square brackets include £ which is initially unknown.

Equations (4.18) and (4.19) are general equations which may be reduced to simpler forms under certain conditions. Thus the experimental conditions used for the study of the complexes discussed

2 2 in this section were such that hf^ 'p Ka ; consequently (Ka + hf^ )2was replaced by hf^ and the calculations were carried out using the

following simplified equations:

mD

1 1El E1Kf 2f^f^(a - D/El)

or for convenience

and

or

D “ El

Y.

1 + 1E1K, 2f^f^(m - D/El)

(4.21)

(4.22)

cL + z5 X. (^.23)

m _ 1 1D " El + E1KS (4.26)

X

wheredt= 1/El (4.24) and jb = 1/ElKp (4.25)

Y^ = m/D, Y2 = a/D, and X^, denote the terms in the square brackets.

When h is so much larger than m that 8K^K^(m~D/ElH^f^f^2 2 becomes negligible compared to f^ (hf^^ + K^f^) , (i.e. when the

concentration of the dimer is negligible), equation (4,20) reducesto the equation used by Ernst and Herring [42] , viz:

hf _ f ~ +- K„.f-.X d rt ^Ka(a-D/El)f3 j

A further simplification is possible if the ecess of phenol is sufficiently large to justify the approximation (a-D/El) =£=• a, leading to

m/D — (hqf2 +1£h 1x '> / + l/El (4.27)

If the experiment is carried out at a constant ionic strength, using cells with a path length of 1 cm., and at a constant concentration of both iron (ill) and the phenol, then equation (4.27) may be expressed as

1/D = (1 + k \ / s-Kjf.) / Em + h/maSXp (4.28)

where Kg and K^, are now the classical equilibrium constants at the experimental ionic strength. This equation has been used by ItLlburn [4l] , who obtained and E from a linear plot of 1/Dversus h .

Calculation of the equilibrium hydrogen ion concentrationsLet the stoichiometric concentrations of the various constituent

?/hich the test solutions contained be denoted as follows:

sodium perchlorate - [NaClOjperchloric acid - dphenol, a

sodium hydroxide - bferric perchlorate - m

In the preparation of these test solutions, to the required amount of water a predetermined volume of a stock solution of each of the constituents was added in the order indicated above, except that (a) the standard phenol solution already contained the requisite concentration of sodium hydroxide so that both these substances were added simultaneously, and (b) part of-the perchloric acid was addedwith the ferric perchlorate, since the stock solutions of the latteralways contain some of the former (see section 2.1, p.2.3 )♦ The sole reason for the inclusion of sodium hydroxide was that it enabled the preparation of test solutions containing the phenol almost at the limit of its solubility. The addition of the required volume of the alkaline stock solution of the phenol to the test solutions was carried out quickly (within an hour of preparation) because the alkaline solutions of the phenols used are much less stable than the acid solutions (see section 3»5» p. 121). Ferric perchlorate was always the last constituent added to the test solutions and it was.ascertained by calculation that the solution to which it was added was already acidic, since otherwise ferric hydroxide would have been precipitated.Optical densities were measured after mixing as explained in section 2.3* The sodium perchlorate was added in order to maintain the ionic strength at an approximately constant value of 0.05 mole/l.

The principle of electroneutrality in this case requires that: 3lje3'i‘] + 2{Fe(0H)2'i‘] + k [Fe^OH)^*] + 2 [FeL2+]+ jNa+] + h = [ci04~] (k.29)

since the concentration of both the phenolate and the hydroxyl ions may be neglected.

The concentrations of the sodium and the perchlorate ions are given by:

[Ka+J = [KaC10z ] +■ b ( f,;0)

[010^“ ] = [hadO^] + 3m + d (4-. 31)

By means of (4.7)i (4.30) and (4.31), equation (4.29) simplifies to

_ h =-m-+f d - b - £Fe^*J (4.32)It follows from equation (4.’2) that

[l'e3+3.= [FeIT+] f2 /[lT]Ksf1f3 (4.33)

Substituting in the above equation for [l ] from (4.3)j (4.8) and2 2remembering that the approximation hf^ + hf^ is legitimate

here, we have[>e3+] =- ohfxf2 / KFf3 (a-c) (4.34)

Finally, substitution in (4.32) for [fe ] from (4.34), replacement of c by ©/El from (4.15) and rearrangement leads to the required equation:

(m +'d - b) Kp(a - D/El)f,~ ------------------------------------ (4.35)KyCa - D/El)f^ + D/El f ^

The ionic strength I is given by1= +4[Fe(0H)2 + ] + 4[FeL2*] + 16 [Fe2 (CH)^+ ] + [CiO^”] + hj-

(4.36)In view of equations (4.4), (4*5), (4.7), (4.29), (4.30) and (4.31), it becomes:

4 +■1= 6m +.- 3<a - 2h - 2b + [WaC10^]+ 4[Ve (OHg ] (4.37)/ , 4s2 (0H)2or, after elimination of [Ve?(0H)?f+J by means of (4.4), (4.5) and

(4.32),1= 6m +.- 3d - 2h - 2b + [NaCloJ + 4 Ki>KH% (m+d-h-b)2 (4.38)

h W

RESULTS AND DISCUSSION

The optical densities, D^, of the test solutions were measured at the wavelengths of maximum absorption by the respective complexes* These measured values were identified with D, since it was shown that under the experimental conditions used, D^ was negligibly small compared to D^.

The results were obtained by an iterative treatment of data according to the scheme:

1) Putting f^ =- =- f =| and h =- d-b, the approximate ionic strength, I, was calculated for each test solution from equation (^.3S )

2) Hence, approximate activity coefficients followed from the Davies equation (3*25).

3) Still putting h = d-b and using a reasonable guessed value for E (eg* E ~ 1000) in the calculation of (or X^’s), the slope,o£ , and the intercept,yG , were obtained by applying the method of least squares (see appendix A3*2, p.22f) to either equation (4.21) or (4.23) (depending on whether the experimental solutions contained an excess of phenol or of iron(lll$. The first estimate of E and followed from

E = _l_ , K_ = d (^.39)cil y3

Then the cycle of operations given below was applied repetitively until the calculated equilibrium hydrogen ion concentrations from two consecutive cycles agreed to six significant figures. In the first cycle, the values of a.ctivity coefficients found in (2) were used in step (20, and the values of B and K , found in (3) were used in steps (t) and til) Jin subsequent cycles the values of these quantities obtained from the preceding cycle were employed.

TABLE 4.1 STABILITY CONSTANT OF THE IRON(ill)-o-HYDROXYACETOPHENONECOMPLEX. ^ = 535 niji. ; a = 1.200x10 ^ mole/l. ; £•= 6.725x10**^ mole/l1 = 1 cm. ; KH = 6.7x10"^ mole/l. ; = 30 1/mole.

MlFeh10 m mole/l 10;0» J i o r

987 . A- 4208 3856 505

1130 4629 3663 5151296 5050 3469 521

1461 5470- 3276 5251634 5891 3082 520

1799 6312 2889 527

1964 6733 2696 529

2137 7154 2502 5332302 7574 2309 5382475 7995 2115 5402641 8416 1922 5442806 8837 1730 548

2979 9258 1535 5473144 9678 1343 5503309 10099 1148 5523482 10520 956.6 5543647 10941 763.2 5563820 11362 569.7 5543986 11782 376.3 5574151 12203 1 8 2 .8 560

icy Sd 106h.mole/L 105Imole/l 10^ 107Yimole/

58 3495 5027 1229 833330 4933 5000 1495 8988

28 6590 4996 1802 9692-6 8248 4993 2108 10460

-6 6 9981 4996 2429 H 329

-39 11636 4993 2735 11977-56 13293 4990 3042 12727-37 15021 4994 3363 13421-1 8 16676 4991 3669 14079-13 18404 4995 3990 14806

1 20058 4992 4296 1547118 21711 4991 4603 16125

-3 23442 4993 4923 169246 25096 4992 5230 175977 26750 4987 5535 18296

20 28477 4994 5858 18989

24 30130 4991 6164 19678

-2 31862 4995 6485 20508

-13 33514 4992 6791 2115329 35166 4989 7097 21791

CD = 0.0032 ; (E ± = (1783 * 12) 1 .mole~1cm’ 1 ;(Kf t^Kp) = 2.441 ± 0 .0 2 0 ; (Ks ±<*k s) = (4.748 1 0 .1 1 6) x 1010 1/mole

Fig.

4-1

Stab

ility

C

onst

ant

of

the

Iron

(llO

-jo-

Hyd

roxy

acet

ophe

none

C

om

ple

x.

TABLE 4.2 STABILITY CONSTANT OF THE IRON(lll)-o-HYDROXYPROPIOPHENONECOMPLEX.7k = 540 mp.; a « 2 .800x10*" mole/l.; 3*3625xlO~^ mole/l.;

_ •Z1 = 4 cm. ; Kg = 6.7x10 mole/l. ; Kp = 30 1/mole.

105dmole/l

107mmole/L

lO^fNaClQ] K?D mole/l

ioV d 106hmole/l

105Imole/l *1

i o6y xmole/l

412.5 1633 4517 323 44 909.1 5002 3 .2 2 8 3 2 1 .8

313.9 1894 4405 514 30 1921 5004 4.029 368.56 1 5 .2 2104 4284 502 -30 2933 4998 4.828 419.17 1 6 .6 2314 4172 504 41 3944 5000 3.630 459.18 1 8 .0 2525 4060 492 -40 4959 5002 6.431 313.29 2 1 .2 2733 3948 485 001 5990 5006 7.247 363.9

1022 2946 3828 483 -6 3 7003 . 4999 8.047 609.91124 3156 3716 484 -2 8 8015 5001 8.849 6 5 2 .1

1225 3366 3603 478 -6 6 9030 5003 9.651 704.21327 3377 3491 484 11 10039 5006 10.45 739.01329 3998 3259 483 31 12064 5001 1 2.06’ 827.71732 4418 3034 484 68 14088 3006 1 3 .6 6 9 1 2 .8

1933 4839 2802 479 33 16116 5001 1 5 .2 6 1010

2137 5260 2578 476 22 18144 5005 1 6 .8 7 110 52340 5681 2345 477 46 20169 5000 18.47 11912347 6102 2121 ^73 23 22234 5008 2 0 .1 1 1290

2749 6522 1888 465 -46 24268 3001 2 1 .7 0 14032932 6943 1664 463 -36 26297 5005 23.31 1500

3153 7364 1431 467 -1 0 28319 5001 24.91 13773337 7785 1207 471 39 30339 5006 2 6 .5 2 1653

C15 se 0.0046 ; (E ± = (1805 * 30) l.mole ^cm ^ ;

(KF ± G Kf) = 2.404 ± 0.042 ; (Ks ±0"ks) - (5 .9 3 1 ± 0.164) x 1010 l/mol

Rg.

4*2

S

tabi

lity

C

onst

ant

of the

Iro

n (I

II)-

o-H

ydro

xypr

opio

phen

one

Com

plex

.

c\j

oo

in co

TABLE 4.3 STABILITY CONSTANT OF THE IR0N(lll)-o-HYDR0XY-n-BUTYR0PH£N0N3 COMPLEX.^ =t 5*fO nji ; m =-3 .1 5 6 x 10 ^mole/l. ; 1 — 4 cm. ; K^= 6.7x10 ^mole/l.;= 30 l/mole.

105d 106a l o V lO^eCOQj lO^D lO^D 105h 105I \ 1q6ymole/l mole/l mole/l mole/l mol^l mol^l mole/l

6 9 2 .2 221 914.6 2613 452 28 713.6 5016 7.691 488.9879.3 247 1022 2403 456 2 873.9 5011 8.762 541.7

1037 273 1130 2198 462 -3 1032 4999 9 .801 590.91130 286 1184 2101 462 -1 8 1116 5001 10.37 6 1 9.O1244 299 1237 2004 468 26 1197 5010 1 0 .9 2 6 3 8 .91328 312 1291 1907 472 33 1271 5004 11.42 6 6 1 .01421 323 1345 1816 470 12 1357 5008 1 2 .0 1 691.51306 338 1399 1719 464 -6 5 1438 4990 12.54 728.41399 331 1453 1627 464 -67 1323 4997 13.13 756.51683 364 1506 1536 474 6 1593 5002 13.63 767.91767 377 1560 1444 476 7 1671 4999 14.15 792.01861 390 1614 1352 474 -1 0 1738 5002 14.75 8 2 2 .8

1945 403 1668 1261 475 -1 6 1833 4997 15.28 848.42123 429 1775 1078 48o 21 1996 5002 16.39 893.72291 435 1883 899.8 479 -1 1 2152 4993 17.47 949.92469 481 1991 7 2 2 .0 482 12 2315 5001 1 8 .6 0 997.92646 507 2098 544.2 48 2 9 2480 5004 19.74 1052

2815 333 2206 366.4 483 2 2635 4998 2 0 .8 2 11042992 539 2313 1 8 8 .6 481 -19 2802 4998 21.97 1X623161 385 2421 13.50 489 45 2934 5002 23.04 1196

= 0.0029 ; (E ±crE) = (1874 * '50) l.mole^cnf1 ;(Kf ± 0 k f) - 2.862 ± 0.078 ; (Ks ± 0 ;s ) - (6 .963 * 0.234) x 1010l./mole.

Fig.

4-3

S

tabi

lity

C

onst

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of

the

Iron

(111)

-a-H

ydro

xy

buty

roph

enon

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x.

CM

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ftX 2X pci0pAQX£1o

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ftft2ouwXE-»ftOcoHX<JHCO&O

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X Q H ftS ^^ X XT Hx p=i ^ o

CO H ftft co ft

Q X ft3 wXg oft £w aw S X ft w °XX

HIDcqiCSIQX<ftXOXftxPHot-HO Pio

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4->Aa)afH<d+->ai—i

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Ci

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+i 4-i +ioo oo ooMO 4 CM r- r- r- 4 4 4

r-H CO COCM CM fM4-i 4-» 4-«

N >—i •—im 4 co 4 4 4 cm cm cm

CM (M CM+i 4-t *HvO CO «—i N 00 Or- r>

00 4 CM M3 vD vOrH *H *HO' H Nm co o o o oo vO m m

CO CM CM ^

r- 4 cm m o m 4 4 co CM CM CM

O ' O CM CM CO CO

co m ^M3 O 4 t- oo oo

00 ^ NCM CM CM

CO CM (M CO CO CO

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CDPIoPiCDftftO•1—1ft0 u ft1

00 O' vO CO CO CM CM CM4-i 4h 4h0 0 CO M 3 O nO ■—I ■—i O' •—IO'mo m

CM oo oco t'- oo4-1 4* 4-c 4h 4h 4h

4 cm co 4 mo o r- oo —<co CM CM

r-A Oco m 4o4*i 4< 4h 4h 4c 4h

cn 4 m oo t'- 4 oo 4H H CM['- r i • • •CM CM CO

rH 4-i 4-i 4h 4h •h 4h 4h 4h 4i<D vO <—4m CM CM CM

H • • • • • •0 r - vO m m o MO O M3 Ocl O ' O ' O ' r- n- r- m mo ooc CM CM CM m m m ■4 -<4 ”4CM CM CMO O ' 00 co co CO MO MO CMCO CO CM CM CM CO COi—i

CD 4-1 4-i 4h 4-i 4h 4h 4-1 41 4Hi—Io <—i r- co 4< m MO MO -4 Or< CO o 00 r-H 00 m 00 CO “1s vO MD m -4 CO co M0 CO om m m <—I H <—c r —4 r H *H

H O ' CO CO CM CO

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CDPIOPI<Dft0 Pi>>4JrO1PII

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coHaDtoftcAft$t—Ift

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X<D'ft 'a xo oO PC _ 'di—} ^3 X

PC ' t j hh O

O'CM 00 — c •—l i— I CM4h 4-i 4h m co vOr- O' O'm 'O

cm m oO'

4-i 4h 4i4 O vO 4 4 WCM CM CM

CM "4 O 'O4c 4c 4coo o r-n- oo oo

CDPIoPICD43ftO+->CD0 ccJ1

CDPIOPJCD43ftOft PcO >N•rC 4-»ft SJ0 43 Pc l ft Pi1 l

(i) For every test solution, the calculation of the hydrogen ion concentration from equation (4.35) was followed by a recalculation of the ionic strength and the activity coefficients by means of equations (4.38) and (3 *2 5) respectively*(ii) The method of least squares was applied to either equation (4.21) or (4-.23) (whichever was appropriate), yielding CC and j3 •(iii) Using the values of 06 and obtained in (ii), new values of E and were calculated; Ks was found from equation (4.6), and finally all the required standard deviations were computed (see appendices A3*2 and A4, p . 22. and p. 2. -6 ) •

These calculations were performed using the ionisation constants from section 3*3 and the hydrolysis consts.nts = 0.0067 mole/l*Kp ~ 30 l/mole from Milburn and Vosburgh1 s paper [117] . The results are shown in tables 4.1 to 4.3, and are illustrated in figures 4.1 to 4.3. Unfortunately, the experimental difficulties encountered by Milburn and Vosburgh in the determination of the dimerisation constant Kp were so great that the value found by them ds only approximate.. In order to estimate the uncertainties in the stability constants on account of the uncertainty in the value of Kp, the calculations just described were repeated first with Kp = 60 l/mole and then with Kp — 0 l/mole (i.e. with Milburn and Vosburgh’s Kp plus ICO/ and minus 100%; the latter is of course equivalent to neglecting the dimer altogether). The final results of these, end the previous, calculations are summarised in table 4.A; in the case of o-hydroxy-n-butyrophenone, for which the variation in the results brought about by the changes in the value of Kp is most pronounced, a graphical illustration is included in figure 4.3* The values quoted at the bottom of table 4.4 are taken as the final results of this work. They are in fact the values obtained with Kp = 30 l/mole

but the limits of uncertainty attached to them were arrived at by assuming that the true value of could lie anywhere within the range: 0 to 60 l/mole.

SECTION 4.2 DETERMINATION OF THE STABILITY CONSTANTS OF THE COMPLEXES FORMED BY IRON(lll) WITH o - HY Pit OX Y PKBN Y LAC 5"? IC ACID AND M5LIL0TIC ACID

INTRODUCTION

At low acidities, substituted salicylic acids form 1:1 complexes with the ferric ion [lA- - 39] * These complexes are violet in aqueous solutions, and. are assumed to have the chelate structure shown below. The reaction which takes place may be represented by the equation:

O_3+ f E ? V ,C''P +*<Aoh + Fe “ + 2H" <0)

where X is a substituent in the benzene ring; the release of twohydrogen ions per molecule of the ligand (and per ferric ion) reactingis consistent with experimental observations. In the case cf the twohomologues of salicylic acid studied in this work, it could not beassumed a priori that the reaction proceeds analogously, viz:

+# = e C ' ° • -

or H^L + Fe^ ‘ — FeL+ + 2E+ where n = 1 or 2 (k,k2

though this is one possibility; another possibility is that only one hydrogen ion is liberated, according to the equation:

(ch2) c o 2 h 3+ *+ Fe = j T +H (h,k3)

OH ^ 0 % * +

or H L + Fe*+ = = FeHL2 + + H+ C>.W)

Clearly, FeHL2h is a complex monoprotic acid which may ionise in itsown right:

(CH^COJH >^=Y(CH2)u Cof

ore \ ^ - o r e+■ H+ (4.45)

or FeHL2+ = FeL+ + H+ (4. 46)

The structure of the species denoted by FeL in the above equationis different from the structure of the species given the same label in equation (4.42). The reason for this is that in equilibrium studiessuch as the present one, no direct "proof” of the structure of a. complex can be obtained - only "circumstantial11 evidence can be giveni.e. it can be shown that the mathematical formulation based on an assumed reaction scheme is consistent with the experimental data. For the present purposes, therefore, the species labelled FeL' will be regarded as identical in both equations (i.e. (4.42) and (4.4-6)), and the speculation as to whether its actual structure is that shown in equation (4.4l) or that in equation (4.45) will be left for the discussion.

The scheme represented by equations (4.4j>) and (4.45), snd adopted in this work, is attractive because of its generality : the

•f*release of any number of gram-ions.of H between 1 and 2 per gram-ion of Fe can be explained on it, and it includes equations (4.41) and (4.45) as the two extremities.

Before proceeding with the derivation of equations, it is expedient to consider the basis for the other assumptions.which will be

made. Figure shows the spectra of solutions containing- fixedconcentrations of both melilotic acid and ferric perchlorate, but varying concentrations of perchloric acid. These spectra were recorded immediately after the preparation of solutions, and in the wavelength range used the absorption of both melilotic acid and the ferric ion was negligible. All the absorption curves shown in figure A.A have the same shape; similar results were obtained in experiments inwhich o-hydroxyphenylacetic acid was used in place of melilotic acid.Results such as these indicate one of three possibilities;

a) only one complex which absorbs in this region is formedb) two (or more) complexes are formed with identical spectrac) two (or more) complexes with different absorption spectra are

present but the concentration of one of these is so much larger than the coneentrations of the remaining ones that the contribution of the latter to the total absorption of the mixture is negligible.

Examination of these possibilities in the light of the proposedreaction scheme leads to the rejection of the first one, since both

4* 2 "t"FeL and FeHL are iron(lll)-phenol complexes, end as such would be expected to absorb in the visible region. The second possibility -normally very unusual - is likely in this case on the grounds ofanalogy v/ith and HL which, it will be recalled (sectionp.|05), were found to have identical spectra for both o-hydrcxyphenyl- acetic acidWmelilotic acid. Thus, it will be assumed that it is legitimate to express the measured optical density, D, at a wavelength at which neither iron(lll) nor the ligand absorb, as

D — El{[FeL+ ] + [FeHL2+] J ( ^ 7 )

where, in an obvious notation E_, T + - S„ ,TT2+ = E5 FeL FeHLPossibility c), though trivial, will in any case be covered by the

LEGEND TO FIGURE 4.4

The scan of the spectrum was started about one minute after the preparation of each solution, at the scanning rate of 200 my. /minute.Each solution contained a fixed concentration of ferric perchlorate

-3 —2(1.8 x 10 mole/1.) and of melilotic acid (?.5 x 10 mole/1), butthe concentration of perchloric acid was varied as follows:

(1) 1.8 x 10 ^ mole/l. (*§■) 3*2 x 10 ^ mole/L.(2) 2.2 x 10~2 mole/l. (3) ^.0 x 10~2 mole/L.(3) 2.6 x 10 2 mole/l.

LEGEND TO FIGURE 4.5

The spectrum of a solution with the following composition:—3ferric perchlorate 1.8 x 10 mole/l.-2melilotic acid 7*3 x 10 mole/l.-2perchloric acid 1.2 x 10 mole/l.

was recorded at the scanning rate of 200 mji /minute at the following approximate times after its preparation:

(1) 1 minute (7) 13 minutes(2) 3 tt (8) 13 tt

(3) 3 it (9) 17 it

(4) 7 tt (10) 19 tt

(3) 9 tt (11) 21 tt

(6) 11 tt

Fig.

4-4

Sp

ectr

a of

Ir

on-(

lli)

Mel

iloti

c Ac

id

Com

plex

in

Aqu

eous

S

olu

tio

ns.

\0

in

m

CMcn

E

XHOZin

LU><

A 1 I S N 3 Q 1 V O U d O

Fig.

4*5

Effe

ct

of Ag

ing

on th

e Sp

ectr

um

of

Iron

(ill)

-Mel

iloti

c Ac

id

Com

plex

in A

queo

us

So

luti

on

.

yQj

m

co

LO

VOCO

A 1 I SN 30 IVOIldO

WA

VE

LE

NG

TH

.

IT yu

above assumption, since if one of the complexes is present at a negligible concentration, then it is immaterial what its extinction coefficient is assumed to be, provided that the value assigned to itlies within reasonable bounds, and the choice E_ _+ — £„ TTT+ is asFeL FeHLgood as any.

Under the experimental conditions used in this study, it was possible to neglect not only the concentration of FeCGH)* [l20j 121}

Zj.4.but also the coneentration of the dimer Fe^COH^ - it was estimated by calculation (with Kq = 30 l/mole [ll?3 ) that the least acid solution used contained no more than 0*1% of the total iron(ill) in this form; the amount present in the more acid solutions was even less.

The last point to be made is that the optical densities used in the calculations were obtained by extrapolating the measured optical densities to zero time, as described in the experimental section*The data obtained in this way are valid only if it- is assumed that all the equilibria considered are established within the time of mixing, and that the fading of the colour is due to subsequent oxidation-reduction reactions. This assumption was taken to hold throughout the present work, but it is mentioned here because it is particularly crucial in the case of the complexes studied in this section. Figure -*3i showing the changes with time in the spectrum of a solution containing melilotic acid and iron(lll), illustrates this well.

t h e o r e t i c a l

In accordance v;ith the proposed reaction scheme, the following equilibria are considered:

the formation of the complexH2L -k Fe3* FeHL2* + H* (4.48)

ionisation of the complex2+ Ka 4- 4- (4.49)FeHL FeL 4- H yj

3+hydrolysis of Fe

Fe3+ 4- H20 JSL FeOH2+ 4- H+ (4.50)

ionisation of the ligand

H2L Kal HL" . +. H* (4.51)

andHL“ — iL IT 4- H* (A.32)

The respective thermodynamic equilibrium constants are defined by the expressions:

1^ = [FeKL2+J h f ^ / Ch2LJ p e 3"'] *3 (4.53)

Ka = [FeL+] hf 2 / [FeHL2+] f_, (4.54)

Kh = [FeOH2+] hl1t2 / [Fe3'1'] (4.55)

K.al = [HL-] hf2 /[H2L] (4.56)

ICa2 = [L=] kf2 / [ < ] (4.5?)

The stoichiometric concentrations of iron(111) and the ligand are given by :

m - [Fe-5*] +• [FeOH2*] 4- [FeHL2*] +- [FeL+] (4.58)a = [H?L] + [HL“] 4- [l“] 4- [FeL+] 4- [FeHL2*] (4.59)

In view of the assumption implied by equation (4.47), the above two equations transform to:

Dm - gj- [Fe"5*] + [FeOH2*] (4.bO)

anda - D

El = [HpLJ + [HL"] + [L=] (4.61)

It follows from equations (4.55)j (4.56) and (4.57) that:

[j-eOH2*] == ICHf3 [Fe3q / h f ^

[HL-] = Kal[H2L]Afx2

[l==] = KalKa2[H2L]

(4.62)

(4.63)

(4.64)

Using these and the preceding two equations5 we obtain:

|>e3+] ■« (m - D/B1) hflf2

and

[ hpl ] = (a - D/El) h2f2f2

^ ^1^2 + ^s.1^^2 * ^3-l^a2

(4.65)

(4.66)

Elimination of [FeL*] from equation (4.47) by means of (4*54) gives

D =- El^jFeHL2*] + KAf2[FeHL2*] /hf^ J (4.67)and

[FeHL2*] '= Dhf2 /El(hff +:-K,f^)JL J. ii (4.68)

Substitution for [FeHL2*], [Fe^*] and [h ~l] from (4.68), (4.65) and(4.66) respectively into equation (4.53) leads to :

2.2K1 ~

D(hf, f 0 + K.Tf7)(h ftTf- + K nhf0 +■• K -K 0)1 2 n 3_____1 2____al 2____al a2El(hff + KAf2)(m - D/El)hf.,f,(a - D/El)

(4.69)2^3

This expression may be readily rearranged to the required form, viz:(hfjf2 + KHf^)(h fxf2 -t- Kalhf2 4- K&1Ka2) (4.70)m _ __1_

D El ElKi, hf2f3(hf1£d + f2)(a - D/El)

which reduces to:

m (hfnf0 +: Kaf7)(hf 2+ K .. )1 d xi 1 a I (4.71)I) 321 E1K-. f,(hf.2 +- K,. f 0)(a - D/El)i L ; JL A d

0r, for convenience

Y =• oi + j?> X (4.72)

since the pH range employed in this work was such that

h2f2q » KalKa2 ' and hf2 > Kk2

Equation (4.71) predicts that a plot of m/D ( = Y) versus the term in the square brackets ( — X) should give a straight line, the

independently, it was estimated by trial and error on the assumption that its correct value is the one which leads to the best linear plot of Y versus X.

The two independent equilibrium constants and K^, oncedetermined, may be used in conjunction with the ionisation constants of the phenols to calculate a number of equilibrium constants dependent on them. Thus the equilibrium constants for the reactions represented by the equations :

slbpe ( ) and the intercept (oC) of which may be used to calculate E and . As the value of K ,. though required, cannot be determined

K- (4.73)

(4.7*0

(4.75)are given by:

K2 = D?eL+]hZi ^ / [H2L] [?e3+J

Kgl = QfeHL2+] f2/[HL_]§-e3+]f:Lf, =

KS2 = [FeL+]f1/ [L=][Fe3+] f ^ = (4.78)

(4.76)

(4.7?)

Calculation of the equilibrium hydrogen ion concentrations

The test solutions were prepared by adding predetermined amounts

of standard solutions of sodium perchlorate, perchloric acid and

ferric perchlorate to a mixture containing a fixed volume of the

phenol solution and the reqxiisite amount of water. Ferric perchlorat

was added just before measurements of optical density were made at

the wavelength of maximum absorption by the complex. Sodium per

chlorate was added in order to maintain the ionic strength constant.

If the concentrations of both OH and L~ are neglected, then

the condition of electroneutrality may be expressed as :

3[Fe3+] + 2 [Ire OH2+] + 2 [FeHL2*'] + [peL+] + [h^J + [Na+]= [ c l o g ] + [h iT ]

(4-.79)The total concentrations of the sodium and the perchlorate ions

are given by :

[Na+] = [NaClO^"] (4.80)

[CIO^” ] = [HaClO^] +- d + J>m (4.8l)

where d is the stoichiometric concentration of perchloric acid.

By means of (4.5&)i (4.80) and (4.8l), equation (4.79) simplifies to:

h = m + d + [Hlf] + [FeL+3 - [Fe^+] (4.82)

Remembering that is negligible, and using equations (4.47),(4.^6) and (4.^9)» we have:

[HL~J = (a - D/El)Kal / (Kal + hf£) (^.83)

vdiilst elimination of JjFeHL +] from equation (4.47) by means of(4.^4) gives:

[FeL+'l = DK. f _/El (hf + K.f«) (4.84)J A c. X A c.Substitution in equation (4.82) for [HL~], [VeL+’]and [Fe^+J

from (4-.8 3), (A.8A) and (A.6 5) respectively, yields the cuartic equation in h;

(a-B/Sl )K - DK.f0 (m-D/El)hf-, f0 th Q(rvh = m +r d +■ al + a 2 - ' 1 2 (A c 85 )K - -4- hf.,2 El(hf2 + IC.f„) hfn f0 +■ K„f_al l 1 A 2 1 2 H 3

which may be solved by Newton-R&phson method (see appendix A2, p. ). The ionic strength, given by:

1= % <j~9 [Fe^+] +, A [PeOH2"] + A £FeHL2+] -f- [FeL*5*] + [h+] + [cio£“ ] + [Na+] + [HL“] (A.86)

may be readily simplified toI = 3m ■+ 2d - h + [KaClO^] +-[Fe5 + ] + 2 [HL-] ( -•8 7 )

or, on substitution fo'rfire^J and £hl J,

1= 3m + 2d - h + [NaClO^] + + 2 a“D/51 Kal (A.88)hfif2 + KHf3 Kal + hV

CALCULATIONS AND RESULTS

For each selected value of K^, the following iterative calculations were carried out:

(i) Putting f^ = = f^ = 1 and h = d, and using an assumed value of E (eg. 1000), the ionic strength was calculated for each test solution from equation (A.88).

(ii) Activity coefficients were calculated by means of the Davies equation (3.25)

(iii) Still putting h = d, the intercept oL and the slope y3 in equation (A.7 2 ) were estimated by the method of least squares (see appendix A3«2, p.2-2.1). Then E, K^, K^, ^32 arlc* standarddeviations associated with these quantities and with D were found (see appendices A3«2 and AA, p . a n d p.£2.6).

(iv) Equation (A.6 5) was solved-for h using the Newton-Kaphson procedure (see appendix A2, p.22/).

TABLE 4.5 STABILITY CONSTANT OF THE IRON(ill) - MELILOTIC ACID COMPLEX. RESULTS OBTAINED WITH DIFFERENT VALUES OF K^.

% K l K2 • * S 1 K S 2 E 105 c

m o l e / l m o l e / l 1 / m o l e l / m o l e 1 / m o l e cm

10 ^ 4 . 4 6 x l O ~ 6 4 * 4 6 x l 0 ~ 2 2 . 3 7 X 1 0 * 1 1 . 66x 10^ 9 6 8 9 5

I O 3 4 . 4 6 x l 0 ~ 3 4 . 4 6 x l 0 ~ 2 2 . 3 7 1 • 66x l 0 1 f 9 6 8 9 5

i o 2 4 . 4 6 x l 0 ~ * f 4 . 4 6 x l 0 ~ 2 2 . 3 7 x 1 0 1 . 66x l 0 l i f 9 6 8 9 4

10 4 . 4 2 x 1 0 ~ 3 4 . A2x l 0~2 2 . 3 5 x l 0 2 1 . 6 4 x l O l i f 9 6 890

8 5 . 52x l 0 “ 3 4 . 4 l x l 0 ~2 • 2 . 93x l 02 1 . 6 4 x l 0 l i f 9 6 888

5 8 . 77x l 0 “ 3 4.38x 10~2 4 . 66x l 02 1 . 63x l O l 2 f 9 6 885

4 1 . 09x 10 *"2 4.37x 10"2 5 . 8 l x l 0 214

1 . 62x 10 9 6 882

2 2 • l 4 x l O ~2 4.27x 10“2 I . l 4 x l 0 3 1 41 . 59x 10 9 7 8 7 0

1 4 . 1 0 x l 0 ~2 4 . 1 0 x l 0 ~2 2 . l 8x l 03 1 41 . 52x 10 9 8 8 4 6

9 X 1 0 "1 4 . 5 2 x l O ~2 4 . 0 6 x l 0 ~2 2 . 4 0 x l 0 31 41 . 51x 10 9 8 8 4 1

8 X 1 0 * 1 5 . 02x l 0 ” 2 4 . 02x 10 "*2 2 . 67x l 03 1 . 4 9 x l O l2 f 9 8 8 3 5

7x l O ~1 5 . 66x 10 2 3*96x 10~2 3 . O I X I O 3V 4

1 . 4 7 x 1 0 9 8 827

6x l O ~1 6 . 4 8 x l 0 ~ 2 3.89x10“2 3.45x 103 1 . 4 4 x l O lZ f 9 9 8 1 7

5x 10 “ 1 7 . 5 7 x l 0 " 2 3 . 7 9 x l O * 2 4 . 03x 1O314

1 . 4 1 x 1 0 9 9 803

^ x i o ” 1 9 . 11x l 0 ” 2 3.64x 10'2 4 . 85x l O 3 1 41 . 3 5 x 1 0 100 7 8 3

5X 10” 1 l.itoo”1 3.43x 10"2 6.07x103 1 41 . 27x 10 101 7 5 2

2 . 5X 1 0 "1 1 . 3 1 X 1 0 " 1 3 . 2 7 x l O “ 2 6.95x 103 1 41 . 21x 10 102 7 2 9

2x 10-1 1 . 52X 1 0 "1 3 . 05x l 0 “ 2 S . l l x l O 31 4

1 . 13x 10 1 0 4 696

1 . 8 X 1 0 * 1 1 . 6 3 X 1 0 ” 1 2.94x 10‘2 8.69x103 1 41 . 09x 10 1 0 5 680

1 . 6 X 1 0 "1 1 . 7 6 X 1 0 * 1 2 . 8 l x l 0~2 9.34x 103 , ■; 41 . 0 4 x 1 0 106 660

1 . 3x 1 O ’ 1 1 . 9 3 X 1 0 ” 1 2.57x 10“2 1 . 05x 10 ^ 9 . 5 5 x l 0 13 108 623

l.lxio”1 2 . 1 5 X 1 0 -1 2 . 37x l O ~24

1 . 15x 10 8 . 80x l 0 13 110 5 9 0

io"1 2 . 2 5 X 1 0 ” 1 2 . 25x 10~2 1 . 20x 10 ^ 8.37x 1013 111 5 7 2

9. io"2 2 . 36 X 1 0 *1 2 . 1 2 x l C f 2 1 . 25x 10^ 7.88x 1013 113 5 5 0

KAm o l e / l

K1 K2/m o l e / l

K S 11 / m o l e

K S 21 / m o l e

E1 / m o l e cm "

I O 5 C

8x l 0 ‘ 2 2 . 4 7 X 1 0 " 1 1 * 9 7 x 1 0 " 24,1 . 31x 10 7 •33x l 0 1 ^ 1 1 4 526

7xio”2 2 . 5 8 X 1 0 ” 1 1 . 8l x l O " 2 1 . 3 7 x 1 0 ^ 6 . 71x l 013 1 1 7 4 9 9

6x 1 0~2 2 . 7 0 X 1 0 " 1 1.62x 10"24

1 . 4 3 x 1 0 6 . 0 2 X 1 0 1-5 120 4 6 8

3 x l 0~2 2 . 8 1 X 1 0 **1 1 . 4 0 x l 0 “ 2 1 . 4 9 x 1 0 ^ 5 • 22x 1O 1 ^ 1 2 4 4 3 2

4xio“2 2 . 9 0 X 1 0 " 1 l . l 6x l o “ 24

1 . 5 4 x 1 0 4 . 3 1 x l 0 15 1 3 0 - 3 9 3

3 . 3 x l 0~2 2 . 9 3 x 1 0 ~1 1 . 02x l 0 “ 24

1 . 56x 10 3 * 8l x l O 13 1 3 4 3 7 2

. .3 x l 0~2 2 . 9 4 X 1 0 " 1 8 . 8 1 X 1 0 ” -5 1 . 56x 10^ 3 . 2 7 x l 0 13 1 3 9 3 3 2

2 . 5 x l 0 " 2 2 . 91x l O -1 7 . 29X 10"*5 1 . 53x 10^ 2 . 7 1 X 1 0 1*5 1 4 6 3 3 2

2x l 0~2 2 . 85X 10 -1 5-69x10“3 1 . 51x 10^ 2 . 12x l 015 156 3 1 4

1 . 5x l 0 " 2 2 . 7 0 X 1 0 ” 1 4 . 0 6 x 1 0 ” ^ 1 . 4 4 x 1 0 ^ 1 . 51x l 013 1 7 1 302

10~2 2 . 4 4 X 1 0 * 1 2 . 4 4 x 1 0 " ^ 1 . 30x 10^ 9 • 07x l 0 12 196 2 9 3

5x l O ~3 1 . 9 7 X 1 0 ' 1 9 * 86x 10 ^ 1 . 05x 10^ 3*66x1012 250 296

10 1 . 3 4 x 1 0 * " ^ 1 . 3 4 x 1 0 " ^ 7 . 1 1 X 1 0 3 4 . 9 7 X 1 0 11 3 7 1 296—4

5x 10 1 . 2 3 X 1 0 * 1 6.17x10~5 6 . 5 7 x 1 0 ^ 2 . 2 9 X 1 0 11 4 0 2 296

io~k 1 . 15X 1 0 ” 1 1 . 15x l o " 5 6 . 10x 10 ^ 4 . 2 6 x l 0 10 4 3 3 2 9 5

1 0 - 5 1 . 1 3 X 1 0 " 1 1 . 13x l O ~6 5 * 9 9 x l 0 3 4.19x 109 4 4 0 2 9 3

io~6 1 . 1 2 X 1 0 ” 1 1 . 12x l O ~7 5 - 9 8 x 1 0 ^ 4 . l 8 x l 0 8 4 4 1 2 9 3

10~7 1 . 1 2 X 1 0 ” 1 1 . 12x l O " 8 5 . 98x 10 ^ 4 . l 8 x l 0 7 4 4 1 2 9 3

Fig. 4 - 6 Iron ( lIU -M elilo tic A c id Com plex. Dependance

of C d on the Choice of

' O 3 ^

■8

O 2 43 5

TABLE >.6' STABILITY CONSTANT OF THE IRON(111)-o-HYDROXYPHENYLACETICACID COMPLEX. RUN 1. RESULTS OBTAINED WITH DIFFERENT VALUES OF K A.A

KAm o l e / l

K i k2m o l e / l

% 11 / m o l e

* S 21/ m o l e

E 1 3 / i o l e cm 1 £ ? C

1012 - 1 41 . 20x 10 1 . 20x l 0 “ 2 3 . 3 4 x l 0 " 10 4 . 3 ' 2 x l 0 13 8 6 4 2 6 7

IO7 1 . 20x l 0 " 9 1 . 20x l 0 “ 2 3 . 34 x 1 0 ~3 4.32x 1013 8 6 4 2 6 7

io 2 - 41 . 20x 10 1 . 20x 10” 2 3 . 3 4 4.32x 1013 8 6 4 2 6 7

10 1 . 20x l 0~3 1 . 20x l 0 “ 2 3 * 3 4 x 1 0 4.32x 1013 8 6 4 2 6 7

1 1 . 19x l O " 2 1 . 19x l 0~2 3 - 3 2 x l 0 2 4.29x 1013 865 2 6 3

1 . 6x l O ” ^ 7 . 22x l 0 " 2 I . l 6x l 0 " 2 2 . 00x 1 O3 4.15x 1013 869 2 4 6

io ” 1 1 . 1 3 X 1 0 ” 1 1 . 13x l 0 " 2 3 . 12x l 03 4.04x 1013 8 7 3 236

7 x l O ~2 1 . 3 7 X 1 0 " 1 1 . 09x l 0 “ 2 4.34x 103 3 . 9 3 x l 0 13 8 7 7 228

4 x l O ~2 2 . 56x 1 0 ^ 1 . 02x 10” 2 7 . 10x l 03 3 . 68x l 0 13 886 218

2 . 5 x l 0~2 3 . 7 5 X 1 0 " 1 9 . 36x l O ~3 1 . 0 4 x 1 0 * * 3.36x 1013 8 9 9 2 3 0

1 . 6x l O ~2 5 . 15X 1 0 -1 8.25x 10~3 1 . 4 3 x 1 0 * * 2 • 96x 1013 9 1 9 280

io " 2 6 . 8 2 X 1 0 **1 6 . 82x l O ~3 1 . 8 9 x 1 0 * * 2 . 4 5 x l 0 13 9 3 2 3 8 5

8x l O * 3 7 . 56X 1 0 "1 6 . o 6xlO”3 42 . 10x 10 2 • l S x l O 13 9 7 4 4 5 4

6x l 0 ” 3 8 . 4 5 X 1 0 ” 1 5 . 07x l 0~3 2 . 3 4 x 1 0 * * 1 . 82x l 0 13 1 0 0 9 5 5 5

5x l O ” 3 8 . 8 8 X 1 0 ' 1 4 . 4 4 x l O ” 3 2 . 4 6 x 1 0 * * 1 . 5 9 x l 0 13 1038 6 2 4

4 x lo “3 9 . 2 4 x 1 0 ” ^ 3 . 69x l O “ 3 2 . 56 x 10 ** 1 . 33x l 0 13 1082 7 1 2

3 x lo “3 9 . 3 7 X 1 0 " 1 2 . S l x l O ” 34

2 . 60x 10 1 . 01x 1013 1156 826

2 . 5x 10 ” 3 9 * 2 4 x l 0 - 1 2 . 31x l O ” 3 2 . 56x 10 ** 8.29x 1012 1218 8 9 4

2x 1O”3 8 . 8 4 x 1 0 - 1 1 . 77x l O * 3 2 . 4 5 x 1 0 * * 6.35x I O 12 1 3 1 4 9 6 9

1 . 6x l O * 3 8 . 1 9 X 1 0 ’ 1 1 . 31x l 0 “ 3 2 . 27x 10 ** 4.70x 1012 1 4 4 2 1 0 3 3

1 . 3 x l 0 “ 3 7 . 3 9 X 1 0 ” 1-4

9 * 61x 10 2 . 05x 10 ** 3.45x 1012 1 6 0 4 1078

1x 1 0 ” 3 6 . 1 8 X 1 0 ’ 1 6 . 18x 10 " * * 1 . 71x 10 **122 . 22x 10 1 9 0 3 1 1 1 3

- 49x 10 5 . 6 4 X 1 0 ” 1

_ 45 - 08x 10 1 . 56x 10 ** 1 . 82x l 012 2068 1120

8x 10 ” ** 5 - 0 2 X 1 0 " 1 4 . 0 2 x 1 0 “ ** 1 . 3 9 x 1 0 * * 1 . 4 4 x l 0 12 2 2 9 9 1 1 2 3

-47x 10 4 . 3 0 X 1 0 ’ 1 3 . 01x 10 ” ** 1 . 1 9 x 1 0 * * 1 . 08x l 012 2 6 4 6 1 1 1 9

TABLE 4.6 (concluded)

k am o l e / l

K i K pm o l e /1

K S 11 / m o l e

k S 21 / m o l e 3 /m o le Xcm 1 105 C D

- 45x 10 2 . 4 9 X 1 0 *"1 1 . 2 5 x 1 0 ” ^ 6 . 91x 10^ 4 . 4 7 x 1 c ?1 4 3 7 6 1 0 8 3

- 44 x 1 0 1 . 3 4 X 1 0 ” 1 3 . 36X 1 0 "5 3 . 72x 10^ 1 . 92x 1c?1 7 8 5 5 1 0 4 0

—43x 10 - 1 . 1 4 x 1 0 “ ^ - 3 . 4 1 x 1 0 ~ 7 - 3 * 16x 10 - 1 . 22x l 09 - 8 8 6 4 8 7 9 7 0

- 42x 10 - 1 . 6 1 X 1 0 ’ 1 - 3 . 2 3 x l 0 " 5 - 4 . 4 8 x 1 0 ^ - l . l S x l O 11 -58 9 8 8 5 7

- 41x 10 - 3 . 52x l 0~1 - 3 • 52x l 0~5 - 9 • 7 5 x 1 0 ^ - 1 . 26x 1 c?-1 - 2 5 0 3 676

4 x l 0 ” 5 - 4 . 82x l 0 " X - 1 . 92x l 0~5 - 1 . 3 4 x l 0 2f - 6 . 92x l 010 -1 7 1 8 518

2x 10 “ ^ - 5 . 29x 10*’ 1 - 1 . 06x l 0“ 5 - 1 . 4 7 x 1 0 ^ - 3 • 7 9 x l 0 10 - 1 5 3 1 4 5 5

H O1 VJ1 - 3 . 5 3 X 1 0 " 1 - 5 . 5 3 x 1 0 ” 6 - 1 . 3 3 x 1 0 ^ - 1 . 98x 1010 -1 7 2 6 4 2 1

3 x l O " 6 - 5 . 69x 1 0 “ 1 - 1 . 71x l 0 " 6 - 1 . 38x 10^ - 6 . 13x l 0 9 - 1 3 9 3 3 9 7

10~ 6 - 5 . 7 4 x l 0 ‘ 1 - 3 . 7 4 x 1 0 “ 7 - 1 . 3 9 x 1 0 ^ - 2 . 06x l 0 9 - 1 3 7 7 3 9 0

3x l O ~7 - 3 . 7 6 X 1 0 " 1 - 1 . 7 3 x l O * 7 - 1 . 3 9 x 1 0 ^ 'Q

- 6 . 20x 10 - 1 3 7 2 3 88

io “ 7 - 3 • 76x 10 - 3 . 7 6 x 1 0 “ - 1 . 3 9 x 1 0 ^0

- 2 . 07x 10 - 1 3 7 1 3 8 700IoH

- 5 .76X 1 0 *1 - 5 . 76x 10 ’ 9L

- 1 . 56x 10 - 2 . 07x 107 - 1 3 7 0 3 8 7

io ~ 9 - 3 . 76X 10*"1 - 5 * 7 6x 10 "1 0 - 1 . 56x 10^ - 2 . 07x l 06 - 1 3 7 0 3 8 7

Fig.

4-7

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TABLE 4.7 STABILITY CONSTANT OF TEE IRON(lll)-o-HYDROXYPHENYLACETICACID COMPLEX HUN 2. RESULTS OBTAINED WITH DIFFERENT VALUES OF KA .

K am o l e / l

*1 k 2 / m o l e / l

K S11 / m o l e

k S 2 B - ] l _ x 1 / m o l e 1 / m o l e cm

A

i o 3 c l

i o 12- 1 4

1 . 22x 10 1 . 22x l 0 “ 2 3 . 3 9 x l O ”10 4 . 3 9 x 1 c 13 832 362

I O 7 1 . 22x 10“ 9 1 . 22x l 0 " 2 3 . 3 9 x l O “ 5 4 . 3 9 x 1 c ?3 832 ; 362

OJOH

1 . 22x 10 “ ^ 1 . 22x l 0~2 3 - 3 9 4 . 3 9 x 1 c ?3 832 362

10 1 . 22x l O ~3 1 . 22x l 0” 2 3 . 3 9 x 1 0 4 . 3 8 x 1 c ?-3 8 3 3 363

1 1 . 20x l 0 ” 2 1 • 20x l 0~2 3 . 3 3 x 1 0 ^ 4 . 3 1 x 1 c ?3 838 368

H1OH

1 . 02x l 0 “ 1 1 . 02x l 0“ 2 2 . 83x l 03 3 . 66x 1c?3 9 1 3 ^ 4 7

7x l 0 -2 1 . 3 5 X 1 0 " 1 9 . 4 3 x l O *"3 3 * 7 4 x l 0 3 3 . 3 9 x l 0 13 9 4 0 491

6 x l 0~2 l . S l x H f 1 9 . 07x l 0~3 4 . 1 9 x 1 0 ^ 3 . 26x l 013 9 5 6 316

3x l 0~2 1 . 7 1 X 1 0 -1 8 . 37x l 0~3 4 . 7 3 x l 0 3 3 . 08x 1 c?3 9 7 8 3 3 1

4 x l 0 ~2 1 . 9 7 X 1 0 " 1 7 . 88x l O ~3 3.47x 103 2 . 83x l 013 1 0 1 3 603

3 x l 0~2 2 . 2 9 X 1 0 * 1 6 . 88x 10 3 6 . 36x 103 2 . 4 7 x l C ?3 1 0 7 3 683

2 . 5 x l 0~2 2 . 4 8 x 1 0 6 . 19x l 0~3 6 . 87x l 03 2 . 2 2 x l C ?3 1125 7 4 7

2x l 0~2 2 . 6 3 X 1 0 ' 1 5 . 30x l O ~3 7*36x 103 1 . 90x l 013 1 2 0 9 833

1 . 5x l O " 2 2 . 73X 1 0 *1 4 . 1 3 x l 0 “ 3 7 . 63x 1 c 3 1 . 4 8x 101-3 1 3 6 9 9 3 9

i o ’ 2 2 . 52x 10 “ 1 2.32x 10"3 6.99x 103 9 • 05x 1012 1 7 9 3 1 1 5 3

8x l 0~3 2 . 1 6 X 1 0 ” 1 1 . 73x 10" 3 5 * 9 9 x l 0 3 6 . 21x l 012 2268 1266

6x l O ~3 1 . 4 2 x 1 O " 1 8 . 3 4 x 1 0 * ^ 3 * 9 3 x 1 0 3 3 »06x l 012 3 7 3 4 1 4 0 4

5x l O ~3 7 . 9 3 x l 0 “ 2 - 43 * 9 9 x 1 0 2 . 21x 1c 3 1 . 4 3 x l 0 12 6 9 1 7 1 4 8 4

4 x l 0 ~3 - 1 . 1 4 x 1 0 ~ 2 - 4 . 3 8 x l 0 “ 3 - 3 . 17 x l 02 - 1 . 6 4 X 1 0 1 1 - 4 9 8 2 7 1 5 7 2

3x l O ~3 - 1 . 4 8 X 1 0 " 1. I t

- 4 . 4 3 x 1 0 - 4 . 09x 1 O3 12- 1 . 3 9 x 1 0 - 3 9 6 1 1661

2x l 0"*3 - 3 . 38X 1 0 -1 - 7 . 16x 10 *“^ -9«94x 103 12- 2 . 37x 10 - 1 6 4 4 1 7 3 6

l x l O ~3 - 7 . 0 0 X 1 0 " 1 - 4- 7 . 00x 10 - 1 . 9 4 x 1 0 ^

12- 2 . 31x 10 -8 1 2 1 7 4 0

-.if.1x 10 - 1 .2 2 - 1 . 22x 10 “ ^ - 3 • 38 x 10^ - 4 . 3 7 X 1 0 11 - 4 1 2 1 4 9 4

l x l 0~3 - 1 .2 8 - 1 . 28x l O ~3 - 3 * 5 7 x 1 0 ^ - 4 . 6 l x l 0 10 -3 8 1 1 4 3 7

l x l O “ 6 - 1 . 2 9 - 1 . 29x l O ” 6 - 3 . 3 9 x 1 0 ^ - 4 . 6 4 x l 0 9 - 3 7 8 1 4 3 1

l x l O “ 7 - 1 . 2 9 - 1 . 29x l O “ 7 - 3 . 3 9 x 1 0 ^ - 4 . 6 4 x l 0 8 - 3 7 8 1 4 3 1

Fig.

4-8

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TABLE 4 . 8 STABILITY CONSTANT OF THE IRON( i l l )-o-HYDROXYPHENYLACETIC ACID COMPLEX. RUN 3. RESULTS OBTAINED WITH DIFFERENT VALUES OF K^.

m o l e / h . 1 2m o l e /1 1 / m o i e

a S 21 / m o l e

-1 -1 1-m dLe cm 1C? 6 1

C\JHoH —1 41 . 2 4 x 1 0 1 . 2 4 x l 0 - 2 3 . 4 3 x 1 0 ” 10 4 . 4 4 x l 0 13 8 5 7 1 9 9

107 1 . 2 4 x l O ~ 9 1 . 2 4 x l 0 * * 2 3 . 4 3 x l O -5 4 . 4 4 x 1 0 13 8 5 7 1 9 9

io 2 1 . 2 4 x 1 0 1 . 2 4 x l 0 - 2 3 . 4 3 4 . 4 4 x 1 O 13 8 5 7 1 9 9

io 1 1 . 2 4 x l 0 ~ 3 1 . 2 4 x l 0 - 2 3 . 4 3 x 1 0 4 . 4 4 x l 0 13 8 5 7 1 9 9

1 1 . 22x 1 0 " 2 1 . 22x 10-2 3 . 3 7 x l 0 2 4 . 3 7 x 1 O 13 862 200

io -1 1 . 0 4 x l 0 - 1 I . p 4 x l 0 r2 2 . 90x 1 0 3 3 . 7 3 x l 0 13 9 0 7 3 2 3

io -2 3 . l 6x l O -1 3 . l 6x l O ~3 8.76x 103 1 . 13x 1 0 13 1 4 8 4 1526

8x l O -3 2 . 9 7 X 1 0 ” 1 2.38x 10~3 8 . 2 4 x 1 O 3 8 . 5 3 x l 0 12 1 7 1 5 1706

6x 10” 3 2 . 4 9 x 1 c -1 1 . 4 9 x l O ~3 6 • 89x l 03 5 . 3 3 x 1 0 12 2 2 3 4 1 9 3 0

5x l O ~3 2 . 03x 1 0 _1 1 . 02x l 0 “ 3 5 • 6 4 x l 0 3 3 . 65x l 0 12 2 8 4 7 2062

4 x l O ~3 1 . 3 4 x l 0 -1- 4

5 * 36x 10 3 . 71x l 03 121 . 92x 10 4 5 0 1 2 2 0 5

3x l O -3 2 . 4 4 x 1 O -2 7 . 3 2 x l 0 -5 6.77x 102 2 . 6 3 X 1 0 11 2 5 5 2 1 2 3 3 4

2x 10 “ 3 - 1 . 33x l 0 -1 - 3 . 09x l 0 -Z f -4.29x 103 12- 1 . 11x 10 - 4 0 9 6 2 4 8 2

l x l O -3 - 4 . 6 6 x 1 0 1—4

- 4 . 66x 104

- 1 . 29x 10 - 1 . 67x l 0 12 - 1 3 3 0 2 4 9 3

- 43x 10 - 7 . 12x l O -1 - 3 . 56x 10 " ^ -1.98x 10^ - 1 . 28x l 012 -8 3 0 2 3 3 1-d*ioH -9.82x 10-1 - 9 . 82x l 0 -54

- 2 . 72x 10 - 3 . 5 2 X 1 0 11 -5 6 0 2 0 4 7

10 “ 3 - 1 . 0 5 - 1 . 05x l 0 -3 - 2 . 92x 10^ - 3 . 7 8 x l 0 10 -5 1 0 1 9 3 7

io " 6 - 1 .0 6 - 1 . 06x l 0 -6 4- 2 . 9 4 x 1 0 - 3 . 8l x l 0 9 - 5 0 5 1 9 2 5

H O 1

- 1 .0 6 - 1 . 06x l 0 -7 4- 2 . 95x 10 - 3 . 8 l x l 0 8 - 3 0 5 1 9 2 4

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TABLE 4.9 STABILITY CONSTANT OF THE IRON(lll)-o-HYDROXYPHENYLACETIC ACID COMPLEX HUN 4. RESULTS OBTAINED WITH DIFFERENT VALUES OF K •

kamole/lK, K2mole/l l/mo£< K2S £■, c1/mole l.mrile cm IC^^D

io 12_ l A

1 . 23x 10 1 . 23x l 0~2 3 • ^ O x l O -1 0 4 . 4 0 x l 0 1 3 863 121

I O 7 1 .23xlo"9 1 . 23 x l 0~2 3 . 4 0 x l 0 “ 3 4 . 4 0 x l 0 1 3 863 121

io 2 1 . 23x 10 “ ^ 1 . 23x l 0 “ 2 3 . 4 0 4 . 4 0 x l 0 ^ 3 863 121

I O 1 1 . 23x l 0~3 1 . 23x l 0 " 2 3 . 4 0 x 1 0 4 . 4 0 x l 0 1 3 863 121

1 1 . 21x l 0~2 1 . 21x l 0~2 3.36x 102 4 . 3 5 x l 0 13 866 123

H1oH

l . O S x l O " 1 1 . 08x l 0 ‘ 2 2 . 99x l 03 3 . 8 7 x l 0 13 896 2 3 1

egioH

4 . 2 8 X 1 0 " 1 28x 10“ 3i f

1 . 19x 10 1 • 5 i » -x l013 1225 1147- 310 p - 2 . 3 1 X 1 0 " 1 - 2 . 31x 10 - 6 . 97x l 03 - 9 . 0 2 X 1 0 11 - 2 9 9 6 2068

-4*1orH -8 .76X10”1 - 8 . 76x l O ~3 - 2 . 4 3 x 1 0 ^ - 3 . 1 5 X 1 0 11 - 7 4 7 1628

lA1OH

- 9 - 7 1 X 1 0 ” 1 - 9 - 71x l 0 “ 6 - 2 . 69x 10 ^ -3 . 4 8 x l 0 1 0 -654 1300

k T 6 -9 .81X10"1 - 9 . 8 l x l O " 7 - 2 . 72x 10^ -3*5 2 x 1 0 9 - 6 4 5 1 4 8 5

10~7 - 9 . 8 2 X 1 0 " 1 -9.82x 10"8 i f- 2 . 72x 10 -3.5 2 x 1 0 8 - 6 4 4 1 4 8 4

H O1 00

- 9 . 82x 10 ’ -1 -9.82x 10“9 - 2 . 72x 10^ - 3 * 5 2 x l 0 7 - 6 4 4 1 4 8 3

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The only difference'between this cycle and subsequent cycles was

that in the latter h, f^, f^ and E found in the preceding cycle

were employed in steps (i) and (iii). The continuous approximations

were stopped when the hydrogen ion concentrations calculated in two

successive cycles agreed to six significant figures.

The results of these calculations, with various values of

for all five runs, are summarised in tables to (There were

four runs with o-hydroxyphenylacetic acid at the ionic strengths: 0.005,

0.01, 0.02, 0.0k mole/l; and one run with melilotic acid at an ionic

strength of 0.005 mole/l). The standard deviation in D, <7^, was

used as a criterion of fit of the experimental data to equation (^f.71)

and for the selection of the correct value of The xalots of

versus pK. for these runs are shown in figures to 4.10.The results obtained for the melilotic acid-iron(111) complex

will be discussed first. The - pK^ plot is S-shaped, has neither

a maximum nor a minimum and for pK^ values larger than about 2 or

smaller than about -1, (T is practically independent of the choice

of K^, while in the intermediate pK^ range it decreases with increasing

pK^. This behaviour is partly explicable in terms of equation (^.71)1 if it is remembered that the choice of can only affect the values

of X - the values of Y being determined by the experimental conditions1alone. Since the pH s of the test solutions were in the range to

1.9 (see table ^f.lO), for small values of K* (p K a 3)« hf?+K. f~ ~ hf?’ ■ ■ A ‘ A ' * 1 a 2 1and the choice of does not affect the results; for large values of

pK. "l)i hf^ +. ~ K^f^ and the choice of different

values of is merely equivalent to the multiplication of all values

of X by a constant factor - consequently the "goodness of fit” measured

remains unaltered. In the intermediate range of values,

(-1 < pKA <3), when an( are comparable magnitude, it

is clear that changes in will bring about changes .in , although the actual shape of the ■ (TJ «-’pK^ plot is not predictable.

The conclusion drawn from figure 4.6 (and table 4.5) is that although the ionisation constant, K,, of the complex formed betweenA x

melilotic acid and iron(111) cannot be determined unequivocally from the present data, it is smaller than about 0.1 mole/l (the actual figure selected for this limit will depend to some extent on what is regarded as an acceptable upper limit of C~ ). The present data allows an unambiguous calculation of the extinction coefficient E and of the two equilibrium constants K. and Kcn . The constants K0 and areJL d bd

not determinable since a knowledge of is required for their cal-—2 13culation; however an upper limit of 10 mole/l and 10 l/mole respec

tively may be placed on them. Detailed results obtained with K, =10 ^mole/l are shown in table 4.10 and illustrated graphically in figure 4.11 ; a curvature which develops in a plot of Y versus X (according to equation (4.71) ), when progressively increasing values are assigned to K^, is illustrated in the same diagram.

In attempting to understand the shape of the (7 - pK^ plots obtained in the case of the complex formed by o-hydroxyphenylacetic acid v/ith iron (111), it has to be borne in mind that a change in thevalue of K. brings about a change in the values of X (equation (4.71) iias a result of the values of h being altered, 1/EL being altered (and

2-hence (a-D/Bl) ), and the term (hf^ -f- K^f^) being altered. The reason for the levelling off in these <T - plots at very high andat very low values of K. is precisely the same as that given above for

ii

melilotic acid. The maxima in the curves (figures 4.7 to 4.10) are obtained because, as progressively decreasing values are assigned to K^, the decrease of the term (hf^ + K^f^) in equation (4.71) results in

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TABLE if.15 STABILITY CONSTANTS OF THE COMPLEXES FORMED BY IRON(ill)WITH o-HYDROXYPHENYLACETIC ACID AND MELILOTIC ACID. SUMMARY OF RESULTS.

In dec id ing the range o f values of the constants which could not be determined un eq u ivocally , i t was assumed th a t fo r an acceptable f i t o f the data the standard d e v ia tio n in o p tic a l d e n s itie s must l i e w ith in the range (Td < 0 . 0 0 5 -

m in imum

va lu e

Ligand kamoled

*L k 2• mole/l

KS13/mLe

KS21/mole

El.mde 'em ^

of 10? CT

o-hydroxyphenylacetic acid

Run 1 > 0.01 < 0.1 1.20X10"2 < 10^ if.32xl013 86if 26?Run 2 > 0.1 < 0.1 1.22xl0"2 <1(P if.39xl013 852 362Run 3 > 0.1 < 0.1 1. 2ifxl0~2 HV

if.ififxlO1-5 85? 199Run if > 0.1 < 0.1 1.23xl0“2 HV if.ifOxlO1^ 863 121

Overall results > 0 .1 < 0 .1 1.22XKT2

"bHV

if .39x10^ 859 ^ ■

m e lilo t ic ac id < 0 .1 0 . 112 < 0 .0 1 5 .98x10^ <1013v!'r

k k l 2 9 5

a shift of X ’s to larger values, and consequently a lower intercept (oC = 1/El); however, a lower intercept leads to higher values of(a - D/El) which partly counteracts the increase in X fs due to the decrease in K. (the small and uniform decrease of the h fs withii.decreasing values of does not affect this argument). Eventually the values of X are shifted so much that a negative intercept (and hence negative E) is obtained - then the results are completely meaningless physically. Unfortunately in this case an unequivocal assignment of a correct value of is also not possible (the slight dip in figure 4.7 at a pK^ of about 1.5 is not pronounced enough to be regarded as significant).. It is concluded that whatever the ionisation constant of the o-hydroxyphenylacetic acid-iron(lll) complex may be, it is not less than about 0.1 mole/1. The three quantities E., K^ and are determinable from the present data,and also an upper limit of about 0.1 and 10^1/mole may be placed on

and respectively.2Detailed results obtained with = 10 mole/1 are shown in

tables 4.11 to 4.14 and are illustrated graphically in figures 4.12 to 4.15; these diagrams also illustrate the curvature which develops in the plots as progressively decreasing values are assigned to K^#

The final results of this section are collated in table 4.15.

SECTION 4.3 DETERMINATION OF THE FORMATION CONSTANT OF THE COMPLEX FORMED BY IRON (ill) ,7ITH 3-HYDNOXY CO UHAN IN

It is assumed that in the pH range (pH <^2.3) used in this work, iron(lll) forms a 1:1 complex with 3-hydroxycoumarin according to the equation:

Since 3-hydroxycoumarin is a monobasic acid, all equations derivedin section 4.1 are applicable here, provided that the ionisation

- 6constant of this ligand is smaller than about 10 , which was assumedto be the case.

The experimental solutions were prepared exactly as described in section 4.1', except that .sodium hydroxide was not added to the . stock solution of 3“hydroxycoumarin. The green complex which is formed has an absorption maximum at 600 mp. - optical density measurements made at this wavelength were used in the calculations. Since the colour of the solutions containing the complex faded, the measured optical densities had to be extrapolated to zero time (see section 2.3 p.2.6) The values obtained in this way.were identified with D in equation (4.13) because under the experimental conditions employed, the absorption of all species but the complex was negligible.

Due to the low solubility of 3-hydroxycoumarin, an excess of iron(lll) had to be used in all runs and consequently the calculations were performed using equations (4.22), (4.35) and (4.38). Detailed results of the calculations, in which Milburn and Vosburgh’s values [117] for Kg and v/ere used (6.7 x 10 ^mole/l and 30 l/mole respectively), are shown in tables 4.16 to 4.20 and illustrated in figures 4.16 to 4.20.

In view of the uncertainty in the value of (see section 4.1) the calculation was repeated for each run v/ith = 60 1/mole and Kq =- 0 1/mole; the results obtained with all three values of are summarised in table 4.21. In two cases a negative intercept ot v/as obtained (runs 1 and 2 with Kp = 60 1/mole; these results are meaningless physically.

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TABLE

4.21

FORM

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N CO

NSTA

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IRON

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HYDR

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The fit of the experimental data to equation (4.22) is equally good with all three values of IC (the variation in is insignificant). As a result of the long extrapolation required to obtain the intercept, the spread in the values of E obtained from different runs (column 7j table 4-.21), and their very pronounced dependence on the choice of K^, is not surprising. In contrast, the values of /3 (slope) obtained from different runs are in fairly good agreement (column 6^table 4.21) and only marginally affected by the choice of the value of K^. Hence although a reasonably accurate value of the product K^E may be determined, neither of the two factors in this product is obtainable with comparable reliability. The final values of E and quoted at the bottom of table 4.21 were calculated from the results obtained with = 30 1/mole as follows: average

were f i r s t found, and then E and Kj, c a lc u la te d from the r e la t io n

ships E = 1/cC l and Kp =

CHAPTER V

COLLATION OF RESULTS AND DISCUSSION

The equilibrium constants determined in this work are summarised in tables 5*1 and 5*2. The indicator constant of bromocresol green and the ionisation constants of acetic acid and propionic acid are not included, since these have been discussed fully in Chapter III.

SECTION 5*1 IONISATION CONSTANTSBefore proceeding to a detailed discussion of the ionisation

constants in table 5»1» a few comments of a general nature will be made about the. relationship between acid strength and molecular structure.

The strength of an acid HL at a given temperature and pressure in a given solvent is measured by its thermodynamic ionisation constant, Ka, which is related to the standard free energy change of ionisation by

AG° = -RT In Ka = RT(ln 10) pKa (5*1)Measurement of Ka in dilute solutions ensures that the activity of water remains constant,, and then AG° is given by

AG° = ^°(H+) +./i°(L-) - / ’(HL) (5.2)if we represent the ionisation by the reaction

HL(aq) = H+(aq) + L"(aq) (5*3)or by

AG° =J1°(H30+) +- yU°(L"”) - a°(HL) - (H20) (5*^)if.we represent the ionisation by

HL(aq) +-H^OCl) =* H30+(aq) + L “(aq) (5*5)where j x a (H^O) is the molar* free energy of water at the temperature and pressure in question, andji°'s are the standard chemical potentials of the species indicated in the hypothetical state of unit molarity and unit activity coefficient (mean activity coefficient in the case of ions). The use of thermodynamic ionisation constants ensures that solute-solute interactions are eliminated although

TABL

E 5.1

IONISATION CO

NSTA

NTS

AT 25, C

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NSTA

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OF IRON (111)

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CO

V'

o I S+i

CAW

co

03 00 ONiH rH• • •o o 03

+ 1 +i +1m co sON. / v v -• • •

in NO

cooW S

co

co X00ON•m

03I

fa

+i

«

W oa03 m O mrHO o ON rH• • •o o o o4-i -H +1 +«ON

o vO mnp 00 in• • • •03 03 03 o

W

xro03 O\/

03

O O

o/N

o\/

noprtoo

<D nOP •rHO oo p rto p <0p o rP oo p ft ’•£»p <D O <D<u rP S4 •rH O

.p f t >N u nJAQ O•rH dP r—I4-> f t rQ P nO P<D 0 1 P a <DV P O d ,PnJ ft 1 o 00 ft>N >N >S >N •H >>X X X X Xo o o o 0u u Un3 no no ■P nO>N >N >>A1 rP| ,P| A1 rP11o o 0 CO o

n3•rloPo«rl4-»O

solute-solvent interactions still remain and have a profound effect on pKa values.

In attempting to relate the strength of acids to molecular structure, it is easier to discuss relative rather than absolute values of Ka , because then the properties of the bulk solvent do not have to be considered' [129] * The relative strength of two monoprotic acids HL^, HL2 is determined by the difference

/ ( L “) - °(HL2 ) -[ju°(L") - ji°(HL^)J

= + ju°(HL^)-- [u°(L") +yi°( HL2 )] (5.6)

which represents the standard free energy change for the reaction:

hl2 + Lx ,=r. HLX + L2 (5 .7 )and is given by-

A G 0 = -RTln[Ka(HL2) / Ka(HIp] = RT (lnlO ) A pKa (5-8)where

A p K a = pKa(HL2) - pKa(HX,1) (5.9)

Some insight into the value of AG° for reaction (5*7) roay be gained by considering the following scheme:

AG °(g)HL2 +, Lx

step 1 vAG°T (g)

HL2 + Lstep 2

HL^ .+ L2 ideal gases at 0 K

heating

HL^ + L2 ideal gases at T°Ksolvation

(5-10)

(5-11)

AG^(aq)HL2 (aq) + (aq) = HL^(aq) + L2(aq) solutes in their standard (5.12) states in water at T°K.(Changes in other thermodynamic functions referring to this scheme will be labelled analogously to the notation used forAG° values).

At a given temperature (T) and pressure (P), the standard free energy change of a chemical reaction is related to the standard internal energy change (AU°) and standard enthalpy change (AH°) by

A G ° = A H 0 - TAS° (5 .1 3)and

AH° =: AU° +, P AV° (5.1^)

In the standard states, the difference in the partial molar volumes (AV°) is zero for reactions (5 .10) and (5«ll)i and virtually zero for reaction (5*12). Thus in the first two cases AU° — A H 0 and the third case AU° ~ AH°. At the absolute zero,A S ° = 0 and therefore o

A g° = A h° = A U ° (5 .1 5 )

The internal energy change, AU° , represents the differenceAU° = TJ°(HL, ) + U ° (L p - U° (H L ,) - U °(l 7 ) (5 .1 6 )

O . O l O d O d O 1

where U° ‘ s represent the molar internal energies of the species indicated, when each of these species is in its lowest energy state; AU° may also be expressed as the difference in the proton affinities at the absolute zero ( ”|j ) of the two acids

A u° = T „ ( h l .,) -T T ( hlp ) (5 *1 7 )O O 1 O d

where the proton affinity represents the enthalpy change for thereaction

H+(g ) + L " (g ) =, HL(g) (5 .1 8 )

These quantities ( T o and AU° ) are the ones which the theories about the energies of molecules (e.g. resonance and inductive effects) attempt to predict. Arguments of this nature will be used to discuss the pKa values obtained in this work, and for this reason it is important to consider how far may AG^(aa) values be expected to r e f le c t AU° values fo r a series of closely related acids.

Bell [129] has argued that of the two quantities: AG° and A H ^ t the former may be more commonly expected to be a closer approximation to AU° than the latter. In the language of statistical thermodynamics, since

A G ° = AU° - RT In [QCHLpQap/QCHLpiULp] (5-19)and

AH° = Au° + KT2(dln/dT)[i(HL1)q(L")/Q(HL2)Q(Lp] (5-20)

where Q*s represent the molecular partition functions, this statement may be paraphrased: at a given temperature the inequality

lnfe(HL;L)Q(L")/5(HL2 )Q(L‘)] < T(dln/dT) [Q(HL1 )Q(L“)/Q(HL2)Q(L“)] may be expected to hold more frequently than not.

When both acids participating in reaction (5«11) are organic, it may be expected that these acids will most commonly be sufficiently complex to ensure that the number of degrees of freedom of each type is conserved. In.such a case, both translation and rotation will contribute to AG° (these contributions may be expected to be very small) but neither will contribute to AH° ; both functions will, however, contain a vibrational contribution. Therefore, in order to assess the validity of Bell's generalisation on the basis of the statistical formulation, it v/ould be necessary to analyse the difference between the two acids in the three vibrational frequencies which each acid loses on ionisation and to compare the remaining frequencies'with those of the conjugate base for both acid base pairs. Be that as it may, it is quite safe to say that neither AG° nor AH° will in general be very different from AU° , because - putting it in the crudest terms - the number of degrees of freedom of each type is conserved.

Next the effect of solvation on AG°(aq) is considered. If the free energy of transfer of one mole of a -compound from the standard state in the gas phase to the standard state in solution (i.e. standard free energy of solvation) is denoted by

G?(S) = GT " GT(a<l) (5.21)

and if is defined by

AG?(S) = GT(S)(HV " GT(S)(HL2) + G°'(S)(L2) - GT(S)(Li} (5-22)theuAG° and AG°(aq) are related by

A G °(aq ) = AG ° - AG° (s ) • . (5 -2 3 )

There is some evidence £l30 to 133j that for a series of closely related compounds in a given solvent, the entropies ) andenthalpies ) of solvation are related by

TS°(S) =-OCH°(s) + j3 (5-24)

where oC and p are constants characteristic of the solvent and OC is positive and usually lies between 0.*f and 1 £l2SQ • For ions,such a correlation is predicted on the basis of the simple electrostatic theory. The electrostatic molar free energy of solvation of an ion of charge z and radius r is given by [13*0

GT(S) = Nz2e2(l/£> -l)/2r (5.25)

where N is Avogadro's number, e the electrostatic charge and & the dielectric constant of the solvent. The entropy of solvation is obtained from

s°T ( S ) ^ ( S )“c)-T J

= ( 0lnE/0T)p Nz2e2/2r£ (5*26)P

and the enthalpy of solvation from

^(s) ~ gt (s ) + t s t (s )

= (Nz2e2/2r) [l/S -1+ Oln&/3T) ?/&] (5-27)

From the last two equations it follows that

ST(S) = H?(S) [ T * (5-28)

For a given solvent at a given temperature and pressure, the term in the square brackets is constant and therefore a proportionality between the enthalpy and entropy of solvation is predicted.

Assuming that equation (5*24) applies to the unionised acids(with constants CC- » ^ ) and to the acid anions (with constants cC^ *j3^ ), then for reaction (5 *1 2 )

rn A — m f~o° ( tjt \ _ c® ( u t j . cf* f t “ \ _ c ° f t “ ,\”1*“ WT(S) ~ * L~T(S)V“*1' - ~T(S)V"2/- (S) v "“1y J

= CC1 [n£(s)(HV-H£(s)(HL2y] +0C2 K ( s)(L-)-h5(s)(L )] , (5.

and therefor

. A g t (s j = A H t (s ) “ T A S T(S)

~ [Ha}(s)^HLi^“Ha?(s)^HL2 ^ 1"<xi^+ [?T(s)(L2 ''Ha?(s)^Li^J(5-30)

In the special case of cC- =oC2 = ^ GT(S) = 0 then

A G °(a q ) = A G ° =Ar A U ° (5 -3 1 )

In general, since 06 usually lies between [129] 0.4 and 1, it may be expected that AG°^g^ < AH°^g^, and consequently that AG°(aq) will be a closer approximation to AH° than will AH^(aq). This is the justification for discussion of pKa values in terms of molecular structure.

Ionisation Constants of o-Hydroxy-acetophenone, -prooiophenone and -n-butyrophenone

It is interesting to compare the ionisation constant of o-hydroxyacetophenone and its meta and para isomers with those of the corresponding hydroxybenzaldehydes (table 5*3)* Both CHO and CH., CO are electron withdrawing groups [135] and therefore should increase the acidity of phenol (pKa = 9*99 D-33] )• There are two reasons for this:

firstly, because the withdrawal of electrons from the ring leads to a shift of electron density from the OH group to the ring, and therefore results in the weakening of the OH bond, and secondly because of the stabilisation of the anion by resonance. The second of these factors is thought to be the more important. The decrease in acid strength on replacement of CHO by CH^CO may be interpreted as being due to the inductive effect of the methyl group which partially mitigates the electron withdrawing pov/er of the CH_CO group. The meta substituted phenols are weaker than the para substituted phenols because the groups in the meta position cannot conjugate directly with the phenolic OH.

TABLE 5.3pKa at.23°C

' ACID ortho meta parahydroxybenzaldehydes 8.37a 9.02a 7. 6lahydroxyacetophenones 10.289° 9 .25k 8.05bhydroxypropiophenones 10.392° - -hydroxy-n-butyrophenones 10.397° - -

a= ref. fl36 c, b= ref [86] , c= present work

In the ortho substituted phenols, specific effects come into play. Thus in both o-hydroxybenzaldehyde and o-hydroxyacetophenone, hydrogen bonding between the hydroxyl group and the oxygen atom of the carbonyl group (see I below) would be expected to stabilise the unionised acids and therefore have an acid weakening effect. On this basis alone, however, it is difficult to understand the large difference (ApKa = 1 *9 2) between the ionisation constants of these phenols. Of the two possible configurations (II) and III) which the anions may take,

c Oo"

it is plausible to assume that the second (III) is adopted in order

to minimise the repulsive interaction between the negative oxygen

atom and the dipole of the carbonyl group. If this is the case,

then the solvation of the negative oxygen would be expected to be

more seriously impeded in o-hydroxyacetophenone than in o-hydroxy

benzaldehyde. The difference between the ionisation constants of

these phenols is attributed to the difference in the strength of

the hydrogen bonding in the unionised acids and to the steric imped-

ence to solvation in the anions.

The ionisation constant of o-hydroxypropiophenone is slightly

smaller than that of o-hydroxyacetophenone, and within the experi

mental error of the ionisation constant of o-hydroxy-n-butyrophenone.

These differences are in line with the strength of the inductive

effect of the alkyl groups [135] which is M e < E t ~ P r n . It is reasonable to assume that in this series the replacement of the

methyl group by either an ethyl or an n-propyl group does not alter

the steric situation and therefore that the decreasing acid strength

of these phenols merely reflects the increasing strength of the

hydrogen bonding in the unionised acids.

Ionisation Constants of o-Hydroxyphenylacetic Acid and Melilotic

Acid.The pKa values of o-hydroxvphenylacetic .acid and melilotic

acid will be discussed with reference to the pKa values of a number

of other acids listed in table

o-Hydroxyphenylacetic acid (pKai) a stronger acid than acetic acid, but weaker than phenylacetic acid. A similar trend

is observed with the corresponding three propionic acids, although in this case the differences are less pronounced. The introduction of the phenyl group into acetic acid or propionic acid enhances the strength of these acids because of the electron withdrawing inductive effect of the phenyl group. This inductive effect may be expected to be considerably reduced in the o-hydroxyphenyl group, because of the electron releasing properties of the hydroxyl group; (the electron releasing properties of the OH group are evident in p-hydroxybenzoic acid which is weaker than benzoic acid). The inductive effect quickly dies away in a saturated chain; for this reason the ionisation constants of the three .propionic acids lie closer together than the ionisation constants of the three acetic acids.

pICa2 reference[99][137]

11.112 present work[110]D-38]

10.844 present work

[139]. [1^0]

[136]

The trend in the second ionisation constants of the two acids under discussion may be explained on the basis of the inductive

TABLE 5.4

ACID pKai

acetic 4.757phenylacetic 4.31o-hydroxyphenylacetic 4.443propionic 4.873-phenylpropionic 4.66

o-hydroxyphenylpropionic 4.726benzoic 4.20p-hydroxybenzoic 4.382o-cresol 10.287

effect of the already ionised carbo&yl group, since this group would

be expected to inhibit the stabilisation by resonance of the doubly

charged anion to a larger extent in o-hydroxyphenylacetic acid than

in melilotic acid. Another factor of some importance in the destabi

lisation of these anions may be the electrostatic repulsion between

the negatively charged oxygen atom and the carboxylate group.

It is nor surprising, therefore, that both these acids are

weaker than phenol (pKa = 9 * 9 9 ) • Further, it would be expected that

as the chain length (n) is increased in the series o-OH-CgH^-CCH^^CO^H

the second ionisation constants should decrease and approach the

ionisation constants of the acids in the series o-OH-C^H,-(CH~) CH2 •6 4 d. n $

The pKa value of only o-cresol, the first member of the latter series,

could be found in the literature, and it is in accord with this

prediction (the pKa values of its higher homologues would be expected

to be slightly larger).

An attempt will now be made to obtain an estimate of the ioni

sation constant, k ^ i » for the reaction

(cH2.)aC02 H / v ( CH^ c o i “

O'+ H

or h 2l h'l” + H+

(5.32)

( 3 . 3 3 )

which is required later on in the discussion of the stability constant

of the melilotic acid - iron(lll) complex. The ionisation of melilotic

acid may be represented by the scheme:

OH a z

OH

H

U - c r + H

(V)

in which the fpur microscopic ionisation constants are related by

kai ka2 -- kai ka2

and the two measured ionisation constants Kai» Ka2, are identified-

with kajL and ka2 respectively. Since the carboxyl group in melilotic

acid is separated by two carbon atoms from the benzene ring, and in/view of the comments made above, pkap would be expected to lie between

P^a2 of melilotic acid (10.844) and the pKa of o-cresol (10.287), say

pka^ -- 10.5* (The best estimate for pka^ would probably have been

obtained by identifying it with the pKa value of the ester o-OE-C^H^^CfLp^O^Me, but unfortunately this compound has not been

studied yet).

SECTION 5.2 STABILITY CONSTANTS

The stability constant of a complex, ML, formed by a metal ion M

and a ligand L, is the thermodynamic equilibrium constant for the

re ci ction

M + L = ML (5.34)

(for simplicity, charges are omitted)

The relative strengths of two ligands L^, L^ with respect to a

particular metal ion in water at a given temperature and pressure is measured by the standard free energy change, AG°(aa), of the

reaction

Lx(aq) + L2M(aq) = L^'Kaq) + L2(aq) (5.35)By definition,

AG°(aq) = p°(L1M) + p°(L2 ) - p?(I^M) - p° =

= RT(lnlO)loS (K1/K2 ) (50'6)

where .0|s are the standard chemical potentials and K^, K2 are the

stability constants of the complexes ML^ and ML2 respectively. On

the basis of an argument analogous to the one used in the case of

ionisation constants, it may be expected thatAG°(aq) for reaction

(5*35) will be a closer approximation to AU° (internal energy

change in the gas phase at the absolute zero) than AH°(aq).

Therefore, for a series of -closely related ligands, a trend in the

stability constants may be interpreted in terms of a trend in the

molecular energies of the species participating in the complexing

reaction.

Iron(ill) Complexes of o-Kydroxy-acetophenone, -propiophenone and

-n-butyroph enone

Table 5*5 summarises the logarithms of the various equilibrium

constants of the title compounds and also includes the corresponding

data for met^a and para hydroxyacetophenones.

TABLE 3.3 •

LIGAND pKa - ^pKa logKs i < logKs logKy ±- logl

o-hvdroxy-acetophenone 10.289 ± 0.010 10.677 t 0.011 O .387 * 0.004

o-hydroxy- 10.392 ± 0.009 10.773 ± 0.013 O.38O i 0.009propiophenone

o-hydroxy- 10.386 0.009 10.843 ± O .138 0.436 ± 0.137n~butyrophenone

p-hydroxy- 8.03 7.20 -O.85acetophenone [ll6j

The stability constants of the complexes of iron(lll) with hyotroxy

o- , in** , and placetophenones follow the same trend as do the proton

complexes of these ligands, but whereas in the case of the ortho isomer the pKa value is less than log Kgi the reverse is true for

the other two isomers. Furthermore, the stability constant of the

ortho isomer is over 100 times larger than the stability constant of

the meta isomer, and over 1000 times larger than the stability constant

of the para isomer. A simple explanation of the enhanced stability of

the ortho isomer may be offered on the basis of the assumption that

only in the case of the ortho isomer is a chelate complex formed.

On chelation, the iron(lll) ion will be more strongly bound to be

ligand and the process will be accompanied by the release of two

water molecules (in the case of the meta and para isomers only one

water molecule will be released) from the first coordination sphere

of the metal, thus making both the enthalpy and the entropy changes

favourable to a strong ortho complex. The difference in the stability

constants of the complexes formed by the meta and para isomers is very

close to the difference between the pKa values of these ligands; the

comments made-about the pKa values also apply here.The stability constants of the complexes formed by iron(111)

with the three ligands under discussion follow the order o-hydroxy

acetophenone < o-hydroxypropiophenone — o-hydroxy-n-butyrophenone,

which reflects the order of the electron donating inductive effect of

the alkyl groups [l35] which they contain (i.e. Me<Et — Pr11). This is presumably so because an increase in electron density on the

carbonyl oxygen increases the strength of the carbonyl oxygen-iron(lll)

bond.

Finally, it is noted that within the accuracy of the present work,

the three complexes studied have the same value of logK^.

It follows from the identity

log Kf = log Ks - pKa (3.37)that for these complexes a graph of log ‘Kg against pKa should be linear with a slope of unity. This signifies that the stability of the

iron(111) complexes is affected to the same extent by substitution

as the stability of the corresponding proton complexes £39 > 37 3 •

A number of workers C39» ^2, *f9? 1 -lJ have drawn conclusions about the nature of the metal-ligand bond on the basis of such plots.

However, in view of the small number of complexes studied, the small

spread in their log Kg values and the comparatively large standard

deviations in log K^ values, it appears unwise to attempt a similar

speculation in this case.

Iron(lll) Complexes of o-Hydroxyphenylacetic Acid and Melilotic Acid

Table 3*6 shows a summary of the equilibrium constants deter

mined in section

pK^ log log K2 log Kgl log Kg2

< 1 < - 1 -1 .9 1 < 3 13«64-

> 1 -0 .9 3 < - 2 3 .7 8 < 1 3

It is clear from table *f.3 and figure *f.6 that a satisfactory

fit ( GjJ 0 .003) of the data for the melilotic acid-iron(lll) com

plex may be obtained with pK^ values larger than 1.0, but that the

best fit is obtained with pK . values larger than 2. The present data

are thus consistent with the formation of a complex acid

o-FeO-CgH^ -(0^ ) 2* CO2H which is only slightly ionised withinthe pH range used. Since this complex acid would be expected to be

stronger than melilotic acid itself (pKal = .73) it is concluded that

its pK^ value lies within the range 1 < pK^ <C A oomplex with

the structure o - OH * C^H^- ^^2^2 1 a-*-though also consistent with the quantitative data, may be rejected outright, because it

TABLE 3.6

LIGAND

o-hydroxyphenylacetic acid

melilotic acid

could not account for the visible charge transfer absorption band

attributed to the phenolic oxygen-iron(111) bond.

In order to ascertain whether the melilotic acid-iron(111) com

plex fits the linear relationship of Ernst and Herring [42, 116]

l o g L = - 0.8 pK +0.3 (3*38). a

approximately obeyed by a large number of monosubstituted phenols,

it is necessary to estimate the value of the equilibrium constant,

Kg , for the reaction

(cHj^COiH x r w ( cfo>.C0iHp 3* =^= I (5*39)

+ Fe = f I (3 ^ 1 )Fe* +

or h 'iT + Fe3+ = FeHL"T (5*40)

This equilibrium constant cannot be measured directly and should be

clearly distinguished from the constant Kg^ which refers to the

reaction:

or HL~ + Fe3+ = FeHL2+ (3.42)

Using the value of log K^ ="0.93 from table 3*8 and a previous esti

mate of = 10*3 (p«2.11 )j an estimate of log Kg= 9«33 is obtainedfrom the identity Kg = » with the same value of pk^, equation

(3*38) yields log Kg = 8.90. The satisfactory agreement between these

two values may be regarded either as corroborative evidence for the

proposed structure of the complex or as support for the correctness

of the estimate p k ^ = 10.3 «

In the case of the o-hydroxyphenylacetic acid-iron(111) complex,

an acceptable fit( 0 .003) of the data for all four runs may be

obtained with pK^ ^ 1, but the best fit is obtained with pK^ 0

(see figures -.7 to ^f.10 and tables f.6 to *f.9)« The present data

(pH range 2 to 3 ) are thus consistent-with the formation of the

complex FeL , only a small fraction of which, if any, exists in2+the protonated form FeHL , where

FeHL = 1+O F t

and FeL^+ may exist in either the open form I or the' chelate form II.

a cnzco£

o r f

Structures I and II are meant to represent two extremities: structure I

implies that there is no interaction whatsoever between the iron atom

and the carboxyl oxygen (CO^ -Fe interaction for brevity), whereas

structure II indicates that a fully fledged ’’chemical11 bond exists

between those two atoms.

If the complex exists in form I, then the equilibrium constant,

Kg2 » refers to the reaction:

CIUCO* CHjCOi+ Fe3+ = II J ' (5-^3)

and therefore should conform to the free energy relationship obeyed

by simple monosubstituted phenols in which it may be safely assumed

that there is no direct interaction betv/een the substituent and the

reaction centre i.e. equation (5*38). With pK = pK ? = 11.11,a a<—equation (3*38) predicts a value of log Kg = log = 9*^* Since

this predicted value is far below the experimental value of 13*6*f

not only is structure I eliminated, but it follows further that whether

electrostatic or ’’chemical” in nature, the interaction CO^ -Fe is quite strong.

Ernst and Menashi [39 J found that the stability constants (Kg)

of 1:1 chelate complexes of iron (111) with substituted salicylic acids

fit the equation

log Ks = 0.73(pKal + pKa2) + 5.0W ( 3 - W

with high accuracy. The o-hydroxyphenylacetic acid-iron(111) complex

does not conform to this equation: insertion of the values pK&^ = k*kk

and P K ^ = 11.11 into equation gives a result log Kg — log Kg2

= l6#7i considerably higher than the experimental value of 13«6*f.

Obviously, an iron(lll) complex of a substituted salicylic acid with

the same pKa values as o-hydroxyphenylacetic acid would be much

stronger than is the complex of o-hydroxyphenylacetic acid. This

could be due to a difference in the nature of the metal-ligand bond

in the two cases and/or due to the inherent difference in strength

between a six and a seven membered chelate ring (steric strain).

It is v/orthwhile to note that the difference (equal to *f.2*t)

between the experimental value (13*6*0 of log Kg2 and the value (9»*0

predicted on the basis of equation (3*38) is not vastly different

from the equilibrium constant (log K = 3*7) for the reaction

CELCOJ" +: Fe2* = CELCO-Fe + (3*^3)3 ^ 3 ^(the value of log K = 3«7 is obtained by converting by means of the

Davies equation the stoichiometric value of log K = 3*2 [l**2] at an

ionic strength of 0.1 mole/1 into a thermodynamic value). This is

taken to imply that the C02 -Fe interaction in the iron(111)-o-

h^droxypheiiylacetic acid complex is similar in nature to the corres

ponding interaction in the ferrous acetate.ion pair (the ferrous phenylacetate ion pair would be more apt for the above comparison,

but the value of its stability constant could not be traced).

The final conclusion of the arguments presented above is that

the iron(lll)-o-hydroxyphenylacetic acid complex has a chelate structure

in which the C02 -Fe interaction is as strong, if not stronger,

than in ferrous acetate.

APPENDICES

APPENDIX A 1

It was thought instructive to compute the pH values of three

sodium acetate / acetic acid buffers by a procedure similar to the

one described in section 3»1» and compare these with the pH values

reported in the literature [l*f3l for the same buffers. The latter

values were obtained from the measurements of the emffs of the cell

without liquid junction

Pt, H2/H0Ac(m^), NaOAcCm^), KCl(m^) / AgCl, Ag

as follows.

The pwH values were determined for three or more portions of

the buffer solution with different small concentrations of added

soluble chloride (KCl) by measuring the emf, E, of the above cell.(E-E° ) FpwH = -log m f„f = — + log mRT In 10

where E° is the known [l*f*fj standard electrode potential, m's are

the molalities and f ’s are the activity coefficients on the molal

scale of the species indicated by postscripts. The limit, pwH°,

approached by pwH as the concentration of the added chloride in the

buffer approaches zero was evaluated for each buffer solution by a

linear extrapolation [l**-3j« Finally, pH values were computed from

pwH° values, by introducing the conventional individual ionic activity coefficient

pH = -log mHfH = pwH0 + log f ^ and using the Debye-Huckel equation (3*29)With a = 5 S to

evaluate f^. The pH values obtained in this way are shown in

column three of Table A 1 .

The pH values shown in the last column of this table ?/ere

calculated from the equations

h + m2 = KwAf-j2 + Ka ^mi + ^ Ka + hfl2

I = m + h

pH = -log hfH = -log h + 0.5 [i^ /(l + 1^) - O v3l]

by a series of successive approximations similar to those described

in section 3»1* The values, adopted for the ionisation constants K

and were 1.734 x 10 ^mole/1 £78] 1*008 x 10*"^mole^/l^ [80]respectively.

TABLE A1 pH values at 25°C

mlmoles/l moles/l

fromref. [l 43]

presentcalculation

0.1 0.1 4.656 4.651

0.05 0.03 4.679 4.6730.01 0.01 4.718 4.714

The agreement between the two sets of values is 0.006 pH units 1

better, corresponding to a maximum difference in hf- of 1.4%.H

APPENDIX- A2 NUMERICAL SOLUTION OF ALGEBRAIC EQUATIONS BY THE

NEWTON-RAPHSON METHOD.

A real root of an algebraic equation f(h) = 0 may be approximated

as closely as desired [145] hy a repetitive application of the formula

n+1 n n n

v;here h^ and hQ+^ are the n'th and (n+l)’th approximations to the root

and f(h ) k f^(h ) are the values of the function f(h) and its first n J nderivative for h = h .n

For each equation in the text solved by this method, the values

of f(h), f^(h) and the first approximation to the root, hoi a**© given below.

Equation (3.18)

f (h) ~ h + b - Kw/hf2 - (D.,-D)Ct /(D, -D*.) - K c/(K +hf 2 ) = 0 • x x xn x cl a a x

f1(h) =- 1 + K w A 2f,2 + K cf 2/(K + hf 2 )2x a 1 a x

2ho was obtained by neglecting the term Kw/hf^ in equation (3*18)

and solving for h the resulting quadratic equation, i.e.

hr> — 2f. CInfl ‘ bfl - Ka +Dl-D2

EllE CT f 2In 1L' V D 2■bf 2 - K )2 + 4K f 2 (c - b +, C D1"D1 a/ a 1 In V D2 -

Yt

Equation 4.85

f(h)=. m+d-h+ * — DKAf2.Kal + hfp El.Chf p +KAf2 )

(m-D/El)hf f2

hflf2 + KH f3

fr(h) = -1 - (a-D/EPKaifi (Kal + h f * ) 2

( m - D / E D K ^ ^ f ,1 > ElChf^t KAf2 ) (hf1f2 + KHf,)'

APPENDIX A 3 THE .METHOD-OF'LEAST SQUARES

A3.1 The “unweighted1* method of least squares.

In section 3«1 it was required to evaluate the parameters^

(sbpe) and 06 (intercept) in. a linear relationship of the type:

y =: oC + fh xwhere Xjy are the experimental variables. This was done by means of

the method of least squares [l46] which in its simple form relies on

the following assumptions:(i) the values of x are known precisely and hence are error-free.

(ii) the errors to which the values of y are subject are: random,

independent of the value of y and normally distributed.

The best estimate of the parameters cC ,y3 Ts such that the sum,

S, of the squares of the residuals is a minimum,'YL 'fl,

i.e. S =: [^(observed) ^(calculated)] ~ ^ [^(observed) (o(x+A )J 1 / '

is a minimum.D S O SThe normal eauations are obtained by putting — and ---- equal toooC D/3

zero. In this case they are:

[y] - n <L - y3 [x] 0

and [xy] - 06 [x] - ft) [x ] = 0

or, solving for oC and ^ , we have:i v

06 ~=. [y] Cx2] -_[xy]...Cx] (A3.1)n[x2] - [x]2

and

(h =: til-xy] - [xl [ y 3 . (A .3-2)‘ n[x2] - [x]2

where n is the number of observations and square brackets denote theTV

sum from 1 to n, i.e. ^ ,1

The standard deviation in y, C"y, was obtained by first obtain

ing the residual for each point Sy

<$y = y(obs.) - y(calc. ) y(ob£f. ) - ( ot +y3 x) and then using &A.6]

l i i x ) 2 ' *n-1

This in turn allowed the standard deviations in the slope and the intercept to be calculated from:

Cf » [x2]_(n-l) (n [x ] - [x] )

_C3r _______n(n-1 ) (n £x2] - £xj2 )

These last two quantities were used to calculate the standard deviations in the quantities derived from the slope and the intercept

(see appendix A ^)*

A.3«2 The "weighted" method of least squares

Equations (A-.20), (A.22) and (4-.71) all have the same algebraic form, namely

y = A/d = oi + /3 x (A3 .3 )where oL and are constants, and A equals either m (in equations

(A.20) and (4-.71) ) or a (in equation (A*22) ).

Equation (3«3^) say be included in this generic form by writing

it asy = A/D1 = o6 + ^5 x

where A = 1, D1 ~ D-D^, oC =: l/CDg-Di^* = 1/ a2^D2“Dl^ and

x = Kwf2/[0ir]f12 .

Evaluation of 06 and by the "unweighted*1 method of least

squares would give an equal weight to values of y and hence a weight Aof 1/D to readings of D which should have an equal weight (see p.

ATherefore, by giving the equations in y a weight of D , equal weight

was restored to all readings of D [ i w ] . This was done by multi-2plying each observation equation by D • Thus from equation (A3«3)

we have

AD = c6 D2 + jb xD2

).

or, dividing by A,

D =:o6D2/A +p>xD2/A

The values of cL and A which made the sumyA whi3 ^ r p 2 ^

S = 2. | D-(oC'D /A + 1$ xD /A)J*1 'SSa minimum were then obtained in the usual way by putting --— i = 0 and

o\c = 0. and solving the resulting equations. Thus

M 2-, r ^3 nrJf

06 =

f t [ f t l - f t ]

A A A

where square brackets are again used to denote the sum ^ .iBy adopting this procedure, it is assumed that the values of A

and x are free of error, and that the errors in D are random, indepen

dent of the value of D and normally distributed. In the case of

equation the same assumptions are made a.bout errors in D**’.

In equations (zt-.20), (4-.22) and ("+.71) the values of x themselves

depend on D. The procedure just described, therefore, is not strictly

applicable to these cases. This reservation is considerably mitigated

by the fact that, under the experimental conditions employed, for a given percentage error in D the percentage error in x is lower by at

least one order of magnitude.

Standard deviations in D were calculated by means of the

equation D a s ]

where

= D (obs.) " D (calc.) = D (Obs.) " (A/Cod.+/3x)

The standard deviations in the slope and the intercept were found

from the formulae:%

O r

< s - < 7

/ 1-3-1

' D^X2 1 .T fL A2 J L a 2 J I A2 J J

D, 2 *- A.

r d 4 i ~ d S c2 ’—1O

L,2 L A . 1- A2 -

<\]1 J

For the calculation of the standard deviations in the quantities

derived from 06 and , see appendix A A.

APPENDIX A. k. COMBINATION OF ERRORS •

Throughout the present work it was often necessary to estimate

the standard deviation in a quantity which was calculated from two or

more other quantities, the values of which were themselves liable to

error. This was done by means of the Law of Propagation of Errors

, which may be stated as follows.

If V is a derived quantity which depends on the variables

x, y, z etc.i.e. V = f (x, y, z ... )

then the error to be feared in V, if the errors in x, y, z etc. are

£x, Jy, $z etc. respectively, is

,v dv ( ^ x )2 + 2 L (Sy)2 + If.2 x_ 7>z_

( <£ z)^ +%

For example, in the First Method of section 3»1

therefore

and

KIn

» 2 = { ^ /o l ' - ^ y

APPENDIX A 3

In section 3«1 it has been shown that the use of the Debye-

Huckel equation in the calculation of the indicator constant of

bromocresol green by the First Method revealed a difference between

runs in which the ionic strength was varied and those in which it was

fixed. The determination of the indicator constant by this method

relies on a linear plot of =■ l/(D-D^) versus = hf^ according

to the equation (3 *7 )

1D-D.'1 D2~D1 ■"Tn'~2 ri*

For runs at constant ionic strength it was found that the intercept

06 =- l/CD^-D^) - and hence the extrapolated D^ - was independent of

the choice of the ion-size parameter a in the Debye-Huckel equation,

but the slope ^5 ~ l/K^CD^-D^) - and hence did depend on it.

Whilst, when the ionic strength was varied, both oi and jb have

shov/n a dependence on the ion-size parameter a.

This behaviour may be understood by considering the equation

based on the principle of electroneutrality (equation (3*24-)) and. used

for calculating the equilibrium hydrogen ion concentrations:

+> K t (D0-D,) hf2

b +,h = (pH-] *■ [iT] *-CIn + [in-]'

Neglecting the four terms: h, (OH J, [in-] and , which are

smaller by about two powers of ten than the remaining terms in

this equation, and substituting for [l ] from equation (3»13)i we

haveb ~ K c/(K + hf-2) a a 1

Consequentlyh = K (c-b )/bf2 3- 1

andX n = hf0 — K f~(c-b) / b f 2 1. c. a d. 1

In this equation, K (c-b)/b has a value which is fixed by thea2experimental conditions for each point in a run; the value of *

however, depends on the equation selected for the calculation of

activity coefficients. Accordingly, for a given run, the values of

in equation (3*7) depend on both the experimental conditions

and the arbitrarily assigned value of the ion-size parameter in

the Debye-Huckel equation; the values taken by Y^ are predetermined

by the experimental conditions alone.

Since the Debye-Huckel equation expresses the activity coeffi

cient as a function of the ionic strength only, for a given selected

value of the ion-size parameter a , f ^ / f 2 will have a constant

value for every point in a run, provided that the ionic strength

is not varied. A choice of a different value of the ion-size

parameter merely alters the value of this constant, and consequently

is equivalent to the multiplication of all values of X^ in equation

(3*7) by a common factor.

When a linear relationship exists between two variable, multi

plication of the independent variable by a constant factor will alter

the slope, but not the intercept (this is obvious,but may also be

inferred from equations (A3«l) and (A3«2). Hence for runs at con

stant ionic strength, the extrapolated value of should be indepen

dent of the choice of the ion-size parameter, whereas should depend

on it, which indeed was found to be the case.

In the case of runs at variable ionic strength, the values 2taken by f^/f^ , for consecutive points in a run, show a progressive

decrease with increasing ionic strength. Furthermore, a choice of a

different value for the ion-size parameter alters (and hence X^)to a different extent for each point in the run. It is to be expec

ted, therefore, that both the intercept oC and the slope 5 should

depend on the ion-size parameter. This conclusion is borne out by

the results.

On the basis of the interpretation given above, the standard

deviation in would be expected to be independent of the

ion-size parameter for runs at constant ionic strength. Examination

of table 3*10 shows that this is not so. This table (see also

table 3*12) also shows that the extrapolated value, of is not quite

constant. It changes from 0.861 to 0.839 for a change in a from 0 to o O . Both these minor discrepancies arise due to the neglect in this

discussion of the four small terms in equation (3*2*f). Nevertheless,

the above interpretation explains adequately the major features of

the difference between the runs in which the ionic strength was constant and those in which it was varied.

REFERENCES

M Lowenheim, "Modern Electroplating” (John Wiley and Sons Inc. 1963)

[2] Silman, "Chemical and Electro-plated Finishes" 2nd Ed. (London, Chapman and Hall Ltd., 1952)

ra Private communication from Wilmot Breeden Co. Ltd.

w Ashurst, Trans. Inst. Metal Finishing, 1963, 40, 74

[5] Jorgensen, "Inorganic Complexes" (London, Academic Press, 1963)

[6] Hantzsch and Desch, Ann., 1894, 28l, 340

[?] Weinland and Binder, Ber., 1912, 45, 2498.

£8] Wesp and Brode, J. Amer. Chem. Soc., 1934, ^6, 1037

[9] Bent and French, J. Amer. Chem. Soc., 1941, 63, 568

[10] Edmonds and Birnbaum, J. Amer. Chem. Soc., 1941, 63, 1471

N Vosburgh and Cooper, J. Amer. Chem. Soc., 1941, 6^, 437

d.2] Gould and Vosburgh, J. Amer. Chem. Soc., 1942, 64, I63O

'h1

1_1 Broumand and Smith, J. Amer. Chem. Soc., 1952, 74, 1013

N Babko, Zhur. Obshchei Khim., 1945, 1^, 745

[15] Babko, Zhur. Obshchei Khim., 1947, 17, 443

[16] Bertin-Batch, Ann. Chim. (France), 1952, 7, 481

[17] Argen, Acta Chem. Scand. 1954, 8, 1059

[18] Vareille, Bull. Soc. Chim (France), 1955, 1493

[19] Agren, Svensk. Kem. Tidskr, 1956, 68, 185

N Agren, Svensk. Kem. Tidskr, 1956, 68, 189

[21] Chanley and Feageson,J. Amer. Chem. Soc., 1956, 78, 2237

[22] Perrin, Nature, 1958, 182, 741

[23] Eomain and Colleter, Bull. Soc. Chim., 1958, 867[24] Colleter, Ann. Chim. (France), i960, 1£, 415

[25] Schigol, J. Inorg. Chem. Russ. 1961, 6, 664

[27] Ernst and Menashi, Trans. Faraday Soc. 1963, £9, 1794[28]- Park, Nature, 1963, 197, 283

[29] Park, J. Chem. Soc.(A), 1966, 8l6

[30] Kennard and Johnson, Proc. Trans. Texas Acad. Sci., 1944, 27, 45

[31] Foley and Anderson, J. Amer. Chem. Soc., 1948, 70, 1195

[32] Foley and Anderson, J. Amer. Chem. Soc., 1950, 72, 5609

Banks and Patterson, J. Amer. Chem. Soc., 1951, 73, 3063

Agren, Acta Chem. Scand., 195^, 8, 266

Vareille, Bull. Soc. Chim (France), 1955, 872

Nanda and Aolitya, J. Indian Chem. Soc., 1957, 34, 577Tsin-Jao, Sommer and Okac, Coll. Czech. Chem. Comm., 1962, 27,

Tsin-Jao, Sommer and Okac, Coll. Czech. Chem. Comm., 1962, 27,1161, 1171Ernst and Menashi, Trans. Faraday Soc., 1963, 59,, 2838

Babko, Zhur. Obshchei Khim., 1945, 15_, 874

Milburn, J. Amer. Chem. Soc., 1955, 77, 2064

Ernst and Herring, Trans. Faraday Soc., 1965, 61, 454Jabalpurwala and Milburn, J. Amer. Chem. Soc., 1966, 88, 3224

Agren, Acta Chem. Scand., 1955, 9, 39Agren, Svensk Kem. Tidskr, 1956, 68, l8l

Herbst, Close, Aazzacua and Dwyer, J. Amer. Chem. Soc. 1952,24, 269Jatkar and Mattoo, J. Indian Chem. Soc. 1953, 30, 592

Sarmousakis, J. Chem. Phys., 1944, 12, 277

Jones, Poole, Tomkinson and Williams, J. Chem. Soc. 1958, 2001

Milburn, J. Amer. Chem. Soc., 1967, 89, 5^*

Williams, J. Chem. Soc., 1955, 137 Williams, J. Chem. Soc., 1956, 8

Stability Constants, Chem. Soc. (London), Special Publication No. 17, 1964Orndorff and Purdy, J. Amer. Chem. Soc., 1962, 48, 2218

Thomas, J. Chem. Soc., i960, 4913

Dictionary of Organic Compounds, 4th Edition (London, Eyre and Spottiswoode Ltd.)

Menashi, Ph.D Thesis (London University, 1963)Vogel, "A Textbook of Quantitative Inorganic Analysis" (3rcl« Ed Longmans, 1961)

Schumb and Sweester, J. Amer. Chem. Soc., 1935, 57, 871

Righellato, Analyst, 1934, 59., 104Vogel, "A Textbook of Practical Organic Chemistry" (2nd Ed. ,Lon mans, 1951)•

Offe and Jatzkewitz, Chem. Ber. 1947, 80, 472

Mellon, "Analytical Absorption Spectroscopy" (London, Chapman and Hall Ltd., 1950)

Waters, "Mechanism of Oxidation of Organic Compounds". (London, Methuen, 1964)

Kortifm, Vogel and Andrussov/, "Dissociation Constants of Organic Acids in Aqueous Solution" (London, Butterworths, 196l)

King, "Acid-Base Equilibria" (Pergamon Press Inc., 1965)

v. Halban and Kortllm, z. Phyzik. Chem., 1934, A170, 351

Ernst and Menashi, Trans. Faraday Soc. 1963, £9, 1803

Hall, De Vries and Gantz, J. Amer. Chem. Soc., 1955, 77, 6507Monk, "Electrolytic Dissociation" (Academic Press, 1961)

Jones and Stock, J. Chem. Soc., i960, 102Bates, "Determination of pH; Theory and Practice" (John Wiley and Sons Inc., 1964)

Kolthoff and Guss, J. Amer. Chem. Soc., 1938, 60, 2516

Ernst and Menashi, Trans. Faraday Soc., 1963, 59, 230

Jones, Ph.D. Thesis (London University, 1957)

Indelli and Saglietto, Trans. Faraday Soc., 1962, 38, 1033

Cartwright and Monk, J. Chem. Soc., 1955, 2500

Harned and Ehlers, J. Amer. Chem. Soc., 1932, 54, 1350

Harned and Ehlers, J. Amer. Chem. Soc., 1933, 2379Harned and Robinson, Trans. Faraday Soc., 1940, 36, 973

Davies "Ion Association" (London, Buttleworths, 1962)

Sager, Maryott and Schooley, J. Amer. Chem. Soc., 1948, 70, 732Ker , ■Hochberg and Lai H e r , J. Amer. Chem. Soc., 1941, 63, 3110

Rudra and Das, J. Chem. Soc. (A), 1967, 630

Hilckel, Physik. Z. 1925, 26, 93Ernst and Herring, Trans. Faraday Soc., 1964, 60, 1053

Cohen, Public Health Reports U.S.A., 1923, 38, 199

Holmes and Synder, J. Amer. Chem. Soc., 1925, 47, 221

Hastings, Sendroy and Robson, J. Biol. Chem., 1925, is- 381

Cohen, Public Health Reports U.S.A., 1926, 4l, 3051

Sendroy and Hastings, J. Biol. Chem., 1929, 82, 197

Chase and Kilpatrick, J. Amer. Chem. Soc., 1932, 54, 2284

Guggenheim and Schindler, J. Phys. Chem., 1934, 38, 5^3

Minnick and Kilpatrick, J. Phys. Chem., 1939, 43, 259 Kilpatrick, J. Amer. Chem. Soc., 1941, 63, 2667

Karkham, Glover and Knight, J. Elisha Mitchell Sci., 1951, 67, 267

Bruckenstein and Nelson, J. Chem. Eng. Data, 1961, 6, 605

Harned and Ehlers, J. Amer. Chem. Soc., 1933, 652

Harned and Owen, J. Amer. Chem. Soc., 1930, 52, 5079

Grunwald, J. Amer. Chem. Soc., 1951, 73, 4934Bates, J. Amer. Chem. Soc., 1951, 73, 2259

Ives, J. Amer. Chem. Soc., 1933, £5, 731

Maclnnes and Shedlovsky, J. Amer. Chem. Soc., 1932, ^4, 1429

Dippy and Williams, J. Chem. Soc. 1934, 1880

Jeffery and Vogel, J. Chem. Soc., 1933, 1637

Darken, J. Amer. Chem. Soc., 1941,. 63, 1007Maclnnes, J. Amer. Chem. Soc. 1926, 48, 2068

Saxton and Danger, J. Amer. Chem. Soc., 1933, 363Kilpatrick, Chase and Riesch, J. Amer. Chem. Soc., 1934, J>6, 2051

Belcher, J. Amer. Chem. Soc., 1938, 60, 2744

Herington and &ynaston, Trans. Faraday Soc., 1957, £3, 138Harned and Davis J. Amer. Chem. Soc., 1943, 6,5, 2030

Harned and Scholes, J. Amer. Chem. Soc., 1941, 63, 1706

Albert and Serjeant, "Ionisation Constants of Acids and Bases" (London, Methuen, 1962)

Mangusson, Postmus and Craig, J. Amer. Chem. Soc., 1963, 85, 1711 Herring, Ph.D. Thesis (London University, 1964)

Milburn and Vosburgh, J. Amer. Chem. Soc., 1955, 77, 1352

[118] Milburn, J. Amer. Chem. Soc., 1957, 79, 537

[119] Siddal and Vosburgh, J. Amer. Chem. Soc. 1951, 73, 4270

[120] Mulay and Selwood, J. Amer. Chem. Soc., 1955, 77., 2693Jl2l] Hedstrom, Arkiv. Kemi., 1953, 6, 1.

[122] Sutton, Nature, 1952, 169, 71

[123] Sykes, J. Chem. Soc., 1959, 2473[124] Richards and Sykes, J. Chem. Soc. , 1960, 3626

[125] Rabinowitch and Stockmayer, J. Amer. Chem. Soc., 1942, 64, 335

[126] Coll, Nauman and West-, J. Amer. Chem. Soc., 1959, 8l, 1284

(127J Jones, Jones, Harmon and Semmes, J. Amer. Chem. Soc., 1961, 83, 2038

[1283 Klanberg, Hunt and Dodgen, Inorg. Chem. 1963, 2, 139

[129] Bell, "The Proton in Chemistry" (London, Methuen, 1959)

[130] Butler, Trans. Faraday Soc., 1937, 33, 229

[131] Bell, Trans. Faraday Soc., 1937, 33., 496[132] Barclay and Butler, Trans. Faraday Soc., 1938, 34, 1445

[133] Leffler, J. Org. Chem. 1955, 20, 1202[134] Kortum, "Treatise on Electrochemistry", (London, Elsevier, 1965)

[135] Hine, "Physical Organic Chemistry", (London, McGraw-Hill, 1956)

[136] Biggs, Trans. Faraday Soc., 1956, 52, 35

[136a] Robinson and Kiang, Trans. Faraday Soc., 1956, £2, 327

[137] Jeffery and Vogel, J. Chem. Soc., 1934, 166

[138] Dippy and Lewis, J. Chem. Soc., 1937, 1008[139] Brockman and Kilpatrick, J. Amer. Chem. Soc., 1934, J?6, 1483

[140] Briegleb and Bieber, Z. Electrochem. 1951, £5, 250[141] Sigel and Kaden, Helv. Chim. Acta, 1966, 49, 1617

[142] Sommer and Pliska, Coll. Czech Chem. Comm.

[143] Bates, Pinching and Smith, J. Res. Nat. Bur. Stand., 1950, 55, 2179

[144] Harned and Ehlers, J. Amer. Chem. Soc., 1933, £5, 2179[145] Margenau and Murphy "The Mathematics of Physics and Chemistry"

(van Wostrand, London, 1956)

[146] Paradine and Rivett, "Statistics for Technologists", (English Universities Press, London, 1953)*

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