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Simplified Spectrophotometric Determinationof Acid Dissociation ConstantsJohn 0 FrohligerlDepartment of Occupational Health, Graduate School of Public Health, University of Pittsburgh, Pittsburgh, Pa. 15213Joseph E. Dziedzicz and Omar W . StewardDepartment of Chem istry, Duquesne Unive rsity, Pittsburgh, P a. 15219A s imp l i f ied m ethod fo r the spect ropho tometric de -te r m in a t i o n of acid d issociat ion constants has beendeveloped. Equat ions for ca lcu lat ing the acid d is-soc ia t ion constan ts a re p resen ted . The measure -me n ts a r e ma d e o n a sys tem a t e q u i l i b r i u m co n tain in ga weak acid and t he sodiu m s al t o f a second weak acid.For each system, th e to ta l concen t r a t ion of the twoac ids and th e d issoc iat ion constan t o f on e of t h e a c id smust be known, and the concen t ra t ion o f one o f thean ion ic spec ies must be de te rmined spect ropho to -metr ica l l y . Ac id d issoc iat ion constan ts o f the typeRRR MCOOH wh e r e R, R, R ma y b e H, CH,, or C6Hand M may be C, S i, o r Ge were de te rmin ed in 5 weigh tper cen t e thano l , 76 weight per cen t e thanol , and d i-methyl su l foxide.ACID DISSOCIATION CONSTANTS in nonaqueous systems havebeen determined using po tentiometric 1-9, onductimetric 8)and spectrophotometric methods (9 , lO ) . Although the poten-tiometric method usually suffers from the lack of standardbuffer solutions, an d unknown liquid junction potentials I I ) ,i t has been preferred over the more tedious spectrophoto-metric procedure (12) . The spectrophotometric procedurerequires that at least one species, either the anion or the un-dissociated acid, have an absorption band region which ad-heres to Beers law. After the spectra are obtained, the ab-sorbances of several solutions buffered at different pH aredeterm ined. Wh en the activity of the anio n equals the activityof the undissociated acid, the pH equals pK,. Usually theactivity coefficients are taken to be u nity, an d concentrationsar e used instead of activities.In order to measure the pK, of a substance that does nothave a pure absorption spectrum, indicators have been used.A small know n amoun t of an indicator with a known pK, is

To whom correspo ndenc e should be addressed.Present address, FM C C orp., Princeton, N. J.1 ) C. D. Ritchie and P. D. Heffley, J . Amer. Chem. SOC., 7,5402

(2) E. Grunwald, ibid. 73 4934 (1951).3) E. Grunwald and B. J. Berkowitz, ibid. p 4939.

(4) J. 0. Frohliger, R. A . Gartska, H. W. Irwin, and 0. W. Steward,

(1965).

ANAL.CHEM.0 1408 (1968).(5) C. D. Ritchie and R . E. Uschold, J . Amer. Chem. Soc., 89,1721 (1967).(6) C. D. Ritchie and G. H. Megerle, ibid. p 1447.(7) Ibid. p 1452.(8) H. 0. Spivey and T. Shedlovsky, J Phys . Chem., 71, 21719) I. M. Kolthoff and T. B. Reddy, Inorg. Chem., 1 189 (1962).(10) B. W . Clare, D. Cook, E. C. F. KO, Y. C. Mac, and A. J.Parker, J . Amer. Chem. SOC. 8 1911 (1966).(11) L. Meites and H. C. Thomas, Advanced Analytical Chem-istry, McGraw-H ill Book C o., Inc., New York, N . Y . 1958,p 22.(12) C. E. Meloan and R. W . Kiser, Problems a n d Experimentsin Instrumental Analysis, Charles E. Merrill Books, Inc.,Columbus, Ohio, 1966, p 9.

(1967).

added to a solution containing known quantities of a weakacid and its salt . Th e absorbance of the indicator at a knownwavelength is measured. The acid dissociation constant isthen calculated from th e equation,PKHA = p K m n + log [HA] - og [A-] og 01

where ~ K H I ,s the dissociation constant of the indicator a nda is the ratio of the absorbance of H In to In-.In this investigation a simplified approac h t o the indicatormethod is presented that permits the determination of dis-sociation constants of compounds which have either an un-stable acid form or an unstable base form. The procedureused in this method does not require that both the acid formand the base form of the com poun d be available, that a buffersolution be prepared, or that the pH of the solution be d eter-mined by an independent method . This metho d has theadded advantage that a spectrophotometric measurement ismade at on e wavelength on o ne species an d thus does not re-quire an elaborate experimental procedure. A s many as 12separate measurements can be made in 1 hour.The simplified spectrophotometric method utilizes theequilibrium con ditions of weak acids and bases.

H A + N a + Z - H Z + Na+A- 1)Th e concentration relationships involved in an ionic equilib-rium of a w eak acid with the base form of a second weak acidare,

(3)

[H+l + [Na+l = [A-I + [Z-I (6)when [A]T an d [ZIT are th e analytical con centration s of t hespecies present in the system. These equations hold as longas the autodissociation of the solvent is negligible. In theequilibrium system described by Equations 2 through 6, [A]Tand [ZIT can be obtained by dissolving a weighed amount ofeither the acid or base form into a known volume of solvent.The n, if [Z-] can be measured spectrophotometrically and oneof the ionization constants is known, the equations can besolved and the other dissociation constant calculated. Sinceone of the two acids is in the base form and one of the twoionization constants is known, there are four possible combi-nations of the variables which can be used to solve Equations2 through 6. The four combinations or cases are given inTable I . In all cases [Z-] is determined spectrophotomet-rically.

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Table I. Cases for the Determinationof Acid Dissociation ConstantsKnowndissociationCase No. constant Acid form Base form

I KHZ HA Z-I1 KEA HA Z -

I11 KHZ HZ A-IV KEA HZ A-Table 11. Dissociation ConstantsDetermined by Direct Spectrophotometry

2,6-Dinitrop henol 45 wt Ethanol-water 3.97 0.042,4-Dinitrophenol 76 wt Ethanol-wate r 4.7 6 i 0.022,4-Dinitrophenol Dimethyl sulfoxide 5.05 i 0.02

Compound Solvent PK=

Case I. Th e acid dissociation constant of the ba se form isknown and the anion of the base form is measured spectro-photometrically.[H+] = K H Z 2 1) (7)

[HA] = [A], A-I (9)Case 11. Th e acid dissociation constant of th e acid form isknown and the anion concentration of the base form ismeasured spectrophotometrically. The expression for the[H+] is a quadratic.

[H+12+ ( K H A+ [HZI) [H+lK H A [A], 1 = 0 10)

[HZI = [ZIT z-1 (11)Case 111. The acid dissociation constant of the acid formis known and the anion concentration of the acid form ismeasured spectrophotometrically.

[HA] = [Z-] KHZ (Q 1)[Z-ICase IV. The acid dissociation constant of the base formis known and the anion concentration of the acid form ismeasured spectrophotometrically. The expression for the

[H+] is again a qu adratic equation.[H+I2+ (KEA+ [A]T- [Z-I)[H+l KHA[Z-]= 0 (15)[HA] = [ZIT - z-] (1 6)

EXPERIMENTALApparatus. All spectrophotometric measurements weremade on a Cary Model 14 Spectrophotometer using 10-cmcells at 25.0 i 0.1 C. Calculation s were carried out on aControl Data G-20 Computer.Reagents. The acids and salts, obtained from commercialsources, were purified as indicated below: benzoic acid,salicylic acid, 4-nitrophenol, 2,4-dinitrophenol (Fisher Certi-

fied Reagent Grade), 2,6-dinitrophenol (Eastman Grade)dimethylphenylacetic acid (City Chemical Co.), diphenyl-methylacetic acid, and triphenylacetic acid (Aldrich ChemicalCo.) were crystallized several times from ethanol-water;bromcresol purple (Fisher Scientific Co.) from acetic acid;sodium benzoate (Allied Chemical Corp.) from acetone-water; sodium salicylate (Allied Chem ical Corp .) fromethanol. Dimethylphenylsilane-, diphenylmethylsilane-, tri-phenylsilane-, and triphenylgermanecarboxylic acid wereprepared and described previously 13) by a modification ofthe method of Gilman and coworkers 14,15) an d were crystal-lized several times from benzene-petroleum ether or petro-leum ether. Sodium 4-nitrophenoxide, sodium 2,4-diNtro-phenoxide, and sodium 2,6-dinitrophenoxide were preparedfrom the corresponding acid forms and were crystallizedseveral times fr om distilled w ater.Solvents. Dimethyl sulfoxide (Fisher Certified ReagentGrad e) was distilled un der reduced pressure from calciumhydride, bp C (4.1 mm). The solvents, dimethyl sulf-oxide, 95% ethanol (USP Reagent), and distilled water,employed in the determination of the pK, values of the acids,were distilled prior to use. Purified dimethyl sulfoxide wasstored in the dark un der a nitrogen atmosphere. Th e 45 wtz thanol-water solvent was prepared by addin g 495 mof water at 25 C to a 1-liter volumetric flask. This was thendiluted to the m ark with 95 ethanol at 25 C . In a similarmanner, the 76 wt ethanol-water solvent was prepared.In this case, 150 ml of water was used.Spectrophotometric Procedures. A known volume of sol-vent containing a k nown concen tration of th e species whichshows no absorbance at the wavelength employed was placedin a 10-cm cuvette. The cell was allowed to equilibrate inthe temperature controlled cell compartment of the spectro-photom eter. An aliquot of the indicator solution was addedfrom a microburet 0.001-ml subdivision), the cell was shak ento mix the solution, and the absorbance was recorded. Ad-ditional aliquots were added, and the absorbance wasrecorded after each addition. In this manner, as many aseight measurements could be obtained. A second analysiswas made in every case using different concentrations of thesolutions.

RESULTS AND DISCUSSIONThe determination of the acid dissociation constant by thismethod requires that one of the two compounds used have aknown acid dissociation constant. Three compounds werechosen as the standards, sodium 2,6-dinitrophenoxide for the45 wt z thanol-water solvent, sodium 2,4-dinitrophenoxidefor the 76 wt thanol-water solvent, and 2,4-dinitrophen olfor the dimethyl sulfoxide solvent. The values obtained ar eshown in Table 11.The application of the spectrophotometric method dependsupon the equilibrium conditions of the equation.H A + N a Z = N a A + H Z (19)

If the equilibrium is shifted too far to the right or left , theresults will not be valid. The equilibrium conditions arecontrolled by the acid dissociation constants and the analy ticalconcen tration of two species used in the determination . Al-though it is not possible to accurately determine the necessaryequilibrium conditions prior to the measurement, the pro-cedure of adding small increments of the absorbing speciesfrom a microburet offsets this disadvantage. This procedure(13) 0. W . Steward, H. W. Irwin, R . A. Gartska, and J. 0. Froh-(14) A . G. Brook a n d H. Gilman, J . Amer . Chem. SOC., 7, 232215) H. Gilman and W . J. Trepka, J . Org. Chem., 25, 2201 (1960).

liger, J . Chem. SOC A ) , 3119 (1968).1955).

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Table III. pK, Values for Acids in Dimethyl Sulfoxide at 25 CUsing All Four CasesaPK.Acid Base De tns Case No. Found Lit.

2,4-Dinitrophenol 9 5.05 .02bpc 5.2dSalicylic~ cid Sodium 2,4-dinitrophenoxide 8 I 6.79 . 10 6 . 9 ~Bromcresol purple Sodium salicylate 13 IV 10.08 .10Bromocresol purple 9 111 10.06 0.1 7 10.0dge 11.0,odium benzoateenzoic acidAcetic acid

Sodium 4-nitrophenoxideSodium Cnitrophenoxide

1410

I1 9.87 .01I 11.41 0.02

a Underlined compounds are compounds for which dissociation constants were determined.I, pK, value determined by direct spectrophotometry.c Standard deviation.d Ref. 10).e Ref. 9).Ref. 16).0 Ref. 5).

9.9d 10.401 1 . 4 ~1.60

Table IV. pK, Values Determined in Various Solvents at 25 C-5 Wt Ethanol-W ater0No. PKL3M.p., C detns Found Lit.d

11 5.61 .016 5.64 0 .0 634 -35 23 6.41 .0879.5-80 11 6.05 .01 6.0 0 0.03177.5-180 11 5.81 .01 5.7 7 0.0 4274 -27556.5-58 16 6.06 0.05' 5.9 6 .10139 -140 11 5 .9 7 0.030 5.66 0.05183 -185decdec

dec187 -190a Case I : base sodium 2,6-dinitrophenoxide.b Case I: base sodium 2,4-dinitrophenoxide.c Case I: base sodium 4-nitrophenoxide.d Ref. (13).* Standard deviation.Small amoun t of base-catalyzed decom position of the acid.0 Significant base-catalyzed decom position of the acid.

~ No.detns1219612101210

911

76 Wt Ethanol-Water6 Dim ethy l sulfoxidecPKG No.Foun d Lit.d detns

6.57 .0287.96 0.05 137.45 0.04 7.45 0.02 167.15 .0 9 7.20 0.0 3 246.78 0.02 6 .70 0.03 217.28 0.057.04 0.056.10 0.106.27 0.03 6 .32 0 .02 6

6.78 0.02

7.03 0.096.23 .04

P K ~12.39 .12811.10 0.0510.00 0.049.29 0.07

8.43 0.06

gives a wide concentration variation in the system and thesubsequent additions can be adjusted to give absorbancevalues that yield valid results. The concentra tion ranges usedin the method are usually dilute enough to allow activityeffects to be neglected. N o corrections for activity were mad ein these measurements.To avoid large differences in the ionization constants ofH A a n d HZ, it is sometimes necessary to utilize comp oundswith intermedia te ionization constants. Table I11 shows howthe pK, of 4-nitrophenol was obtained from the known pK,of 2,4-dinitrophenol by the use of several intermediate com-pou nds . All fou r equilibrium cases were employed sincesome of the compounds used do not have absorption spectrain the visible region.Table IV shows the results of the determinations of aciddissociation constants in 45 wt thanol-water solvent on a(16) C. D. Ritchie and R. E. Uschold, J . Amer. Chem. SOC. 0,2821 (1968).

series of carboxylic acids. The values obtaine d by thismethod agree well with the values obtained by a potentio-metric method (23). Similar results are found in 76 wtethanol-water solvent, except tha t the pK, for acetic acidappe ars to be lower than the values reported in the literature.These results are shown in Table IV.The method also was applied to the solvent dimethylsulfoxide. The se results ar e given in Tab le IV. The silicon-subst ituted carboxylic acids were very unstable in this solventand their dissociation constants could no t be determ ined.

RECEIVEDor review Feb ruary 25, 1970. Accepted June 18,1970. Presented in part at the 154th National Meeting,American Chemical Society, Chicago , Ill,, Sept. 1957. Theauthors gratefully acknowledge the financial support of theDow Corning Corporat ion, Midland, Mich., and a grantfrom the National Science Foundation for the Cary Model14 Spectrophotometer.

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