Dissociation constants of methyl orange in aqueous alcohol solvents

Jing Fan*, Xuejing Shen, Jianji Wang

Department of Chemistry, Henan Normal University, Xinxiang, Henan 453002, China

Received 15 August 1997; received in revised form 3 December 1997; accepted 20 December 1997

Abstract

The dissociation constants of methyl orange (H�Inÿ) has been determined at 258C and an ionic strength of 0.1 mol lÿ1 in

water and in mixed aqueous solutions of methanol (10±90 wt%), ethanol (10±70 wt%), iso-propanol (10±60 wt%) and tert-

butanol (10±50 wt%) by spectrophotometric measurements. It has been shown that the solvents affect the acid±base equilibria,

visible absorption spectra and color transition range of methyl orange to different extents. The pKa values decrease with

increasing composition of the co-solvent in the order: tert-butanol>iso-propanol>ethanol>methanol>water. A linear

relationship between pKa and the mole fraction of the co-solvent was observed in a limited range of the compositions for

each of the solvent systems. The results have been discussed in terms of the standard Gibbs energies of transfer of H�, �G0t

(H�), and the relative values of �G0t (Inÿ) and �G0

t (H�Inÿ) in all solvent systems. # 1998 Elsevier Science B.V.

Keywords: Dissociation constant; Methyl orange; Water�alcohol mixed solvents; Spectrophotometry

1. Introduction

The effect of solvent composition on the dissocia-

tion equilibria of organic reagents is of great import-

ance in chemical and biomedical analysis. For

example, data of dissociation constant in mixed sol-

vents can be used to plan many analytical procedures

such as acid±base titration, extraction and complex

formation in non-aqueous solutions [1]. The poor

solubility in water of many drugs and organic reagents

has also necessitated the use of water-miscible co-

solvents to prepare solutions of these compounds [2].

Therefore, studies on dissociation constants in non-

aqueous and/or mixed solvents have attracted much

attention in recent years.

Methyl orange is one of the most used acid±base

indicators. Its dissociation constant and the color

transition range in water are well known. However,

pKa values of this indicator in solvents other than

water have been published only in aqueous solutions

of methanol (43±94 wt%) [3] and of N,N-dimethyl-

formamide (9.5±79 wt%) [4].

In this work, the dissociation constants of

methyl orange have been determined spectrophotome-

trically at 258C and an ionic strength I�0.1 mol lÿ1 in

water and in aqueous mixed solutions of methanol

(MeOH), ethanol (EtOH), iso-propanol (i-PrOH) and

tert-butanol (t-BuOH). The solvent effect on the dis-

sociation equilibria, the visible absorption spectra and

the color transition range of methyl orange are inves-

tigated. The solvents were chosen for the following

reasons:

Analytica Chimica Acta 364 (1998) 275±280

*Corresponding author.

0003-2670/98/$19.00 # 1998 Elsevier Science B.V. All rights reserved.

P I I S 0 0 0 3 - 2 6 7 0 ( 9 8 ) 0 0 0 3 9 - 7

(i) the alcohols (especially ethanol) are the most

used solubilizing agents of indicators that are

slightly soluble or insoluble in water;

(ii) they are less polar than water but fully

miscible. The polarity of the solvent can be easily

changed over a large range by changing the ratio of

alcohol/water in the mixture, and for this reason,

these mixtures are useful in analytical techniques

such as liquid chromatography; and

(iii) MeOH, EtOH, i-PrOH and t-BuOH have one ±

OH group, but the number of carbon atoms in these

molecules increases successively. This allows the

examination of the effect of alkyl chains in co-

solvent molecules on the dissociation constant of

methyl orange.

2. Experimental

2.1. Reagents and solutions

MeOH, EtOH, i-PrOH, t-BuOH, methyl orange and

potassium chloride (KCl) were obtained from Beijing

Chemical Factory, China. Sodium hydroxide (NaOH),

hydrochloric acid (HCl) and potassium acid phthalate

were purchased from Tianjin Chemical Reagent Fac-

tory, China. All chemicals were of analytical reagent

grade except potassium acid phthalate which was of

guaranteed grade. The organic solvents were used

after drying over 4A type molecular sieves. Methyl

orange was dried under vacuum before use. Other

chemicals were used as received. Stock solutions of

methyl orange (7.504�10ÿ3 mol lÿ1), of NaOH

(0.1091 mol lÿ1) and of HCl (0.1193 mol lÿ1) were

made in water. The stock solution of NaOH was

standardized by potassium acid phthalate. Then, this

standard solution was used to standardize the stock

solution of HCl. The ionic strength in all solutions was

maintained at 0.1 mol lÿ1 by using KCl as background

electrolyte. Deionized and redistilled water with a

conductivity of 1.2 mÿ1 cmÿ1 was used throughout.

2.2. Apparatus

Absorbance measurements were made on a Shang-

hai spectrophotometer (type 721) equipped with cells

of 1.0 cm path length. The temperature around the

cells was controlled at 25�0.058C by circulating

water from a modi®ed Shanghai thermostat (model

501). The measurement of H� concentrations was

conducted in cell (A) as described previously [5].

Glass electrodej0:1 mol lÿ1�KCl� HCl�;SH;H�InÿjAgClÿAg (A)

where SH denotes the solvent. A Shanghai pH glass

electrode (model 231) was used together with an

AgCl±Ag reference electrode without liquid junction

[6]. The cell potentials were recorded by means of a

Shanghai ion-analyzer (model PXSJ-216).

2.3. Procedure

Solutions containing 0.01091 mol lÿ1 NaOH and

0.01193 mol lÿ1 HCl in the required mixed solvent

were prepared from the respective stock solutions, the

stock solution of methyl orange, the necessary amount

of solid KCl, pure alcohol and water. Here, solutions

of NaOH and HCl should both have the same propor-

tion of alcohol and the same ionic strength. A 25.00 ml

aliquot of this HCl solution was titrated with NaOH

solution in cell (A). During titrations, the volume of

the titrant and the corresponding potential of the cell

were recorded. The potential of the cell (A) is given

[7] by

E � E00a ÿ klog �SH�2 � (1)

where [SH�2 ] is the concentration of the solvated

proton, k the experimental slope, and E00a the speci®c

constant of the cell. Based on the titration data, E00a and

k for each of the mixed solvents can be obtained [5] by

means of the linear relationship between E and

log �SH�2 � shown in Eq. (1).

A series of solutions of methyl orange at different

pH were prepared in the same way as the titrant and

titrand, using small volumes of nitric acid to adjust pH

of the solutions. Each of these solutions was added to

the cell (A) and the potential determined. Then, the

same solution was used for the absorbance measure-

ments against a solvent blank. Absorbance data and

cell potentials were obtained for �max in the 508±

520 nm range in all the solvents investigated. Using

the cell potentials obtained here, as well as E00a and k

values obtained above, [SH�2 ] in each mixed solvent

can be easily calculated by Eq. (1).

276 J. Fan et al. / Analytica Chimica Acta 364 (1998) 275±280

3. Results and discussion

3.1. Effect of solvent on the visible absorption

spectra of methyl orange

It is noted that addition of the alcohols in water

results in a red shift of �max for the acid form of methyl

orange (H�Inÿ), and that the shift increases by 2±3 nm

when 10 wt% more co-solvent was added to the mixed

solvents. For example, �max for the acid form of

methyl orange in water is 508 nm, whereas in a

50 wt% ethanol±water solvent, it is 518 nm. This

may be due to the indicator±solvent interaction which

changes the energy difference between the excited and

ground states of indicator molecules [8].

We have observed that when the alcohol content of

the mixed solvents is high, the basic form of methyl

orange (Inÿ), when exposed to light, shows a decrease

in the absorbance at a particular �max. This phenom-

enon has been found by Thiel [9] long ago. De Ligny

et al. [3] attributed this effect to cis±trans isomeriza-

tion of Inÿ caused by light. In order to avoid the

possible experimental error resulting from this phe-

nomenon, all test solutions used in this work were kept

in the dark for 24 h before measurements.

The colour transition range of methyl orange also

changes because of a shift of the dissociation equili-

brium in the presence of alcohol in water. For exam-

ple, the transition range in water [10] is 3.1(red)±

4.4(orange), whereas it is 2.3(red)±3.8(orange) in

50 wt% MeOH±H2O and 1.5(red)±2.6(orange) in

50 wt% EtOH±H2O mixed solvents. Obviously, the

same indicator can be used to indicate the titration

end-points of different systems by choosing the appro-

priate co-solvent and changing the co-solvent content

of the mixed solvents. This is interesting from a

practical point of view.

3.2. Determination of the dissociation constants in

aqueous alcohol solvents

The acid form of methyl orange is a zwitterion [3].

Its dissociation equilibrium can be described in terms

of a single process as follows

SH� H�lnÿ � SH�2 � lnÿ (2)

where SH�2 denotes a solvated proton, H�Inÿ and Inÿ

refer to the acid and base forms of methyl orange,

respectively. According to Bjerrum's theory, ion-pair

formation may be disregarded in media with permit-

tivities >35±40 [11]. Only under this assumption, the

key process in solution for methyl orange may be

written in the form of Eq. (2). Based on the data of

Akerlof [12], the limiting percentage of alcohol in

aqueous±alcohol mixed solvents which prevent ion-

pair formation are as follows: 0±90 wt% for MeOH,

0±70 wt% for EtOH, 0±60 wt% for i-PrOH and 0±

50 wt% for t-BuOH. Therefore, these limiting percen-

tages were chosen in the present work.

The concentration dissociation constant (in pKa

form) for methyl orange is given by

pKa � p�SH�2 � � log f�H�lnÿ�=�lnÿ�g (3)

If A1 and A2 are the absorbance of the acid and base

forms of methyl orange, respectively, and A is the

absorbance of equilibrium mixtures of acid and base

forms at a particular pH, it follows that [13]

pKa � p�SH�2 � � log f�Aÿ A2�=�A1 ÿ A�g (4)

Since A, A1 and A2 can be determined spectro-

photometrically, and [SH�2 ] can be known potentio-

metrically, pKa in a particular solvent can be obtained

immediately.

As an example, Table 1 lists the observed absor-

bances of methyl orange, potentials of cell (A) at

different pH, and the calculated values of p�SH�2 �and pKa in 30 wt% t-BuOH±H2O mixed solvent.

Table 1

The observed absorbances of methyl orange, potentials of the cell

at different pH's, the calculated values of p[SH�2 ] and pKa in

30 wt% t-BuOH±H2O mixture (258C, I�0.1) a

No. Ab E (MV) p[SH�2 ] log[(AÿA2/(A1ÿA)] pKa

1 0.268 218.5 2.690 ÿ0.685 2.01

2 0.299 223.5 2.607 ÿ0.587 2.02

3 0.339 231.2 2.480 ÿ0.476 2.00

4 0.372 236.8 2.387 ÿ0.395 1.99

5 0.390 239.3 2.346 ÿ0.354 1.99

6 0.447 246.8 2.222 ÿ0.230 1.99

7 0.514 254.0 2.102 ÿ0.096 2.01

8 0.553 258.8 2.023 ÿ0.020 2.00

9 0.602 264.6 1.927 0.075 2.00

10 0.664 272.1 1.803 0.198 2.00

Mean 2.00�0.01

a A1�1.013, A2�0.114, E00a �381.0�0.3, K�ÿ60.4�0.1.

b �max�514 nm.

J. Fan et al. / Analytica Chimica Acta 364 (1998) 275±280 277

pKa values of methyl orange in water and in the mixed

solvents are given in Table 2.

The value of pKa in water obtained in this work was

3.39�0.03, which is in excellent agreement with the

values of 3.39, 3.37 and 3.46 reported in literature

[3,4,10]. In addition, our pKa values in aqueous solu-

tions of 50, 60, 80 and 90 wt% methanol also agree

well with those interpolated from the results reported

by De Ligny et al. [3]. To the best of our knowledge,

no pKa data in other alcohol±water mixed solvents

have been reported before.

3.3. Effect of solvent on the dissociation equilibrium

It is evident from Table 2 that Ka values increase in

the following order: t-BuOH>i-PrOH>EtOH>-

MeOH>H2O. This is similar to that observed in case

of thymolsulfonephthalein in aqueous binary solutions

of urea and dimethyl sulfoxide [14], and of methyl

orange and methyl yellow in aqueous N,N-dimethyl-

formamide solutions [4]. The variation of pKa as a

function of mole fraction (X2) of the co-solvent in the

mixed solvents is shown in Fig. 1. As can be seen,

there is a linear relation between pKa and X2 in a

limited range of co-solvent compositions for each of

the solvent systems. The slope may be considered as a

measure of co-solvent effect on pKa in the water-rich

media.

The effect of solvent on the dissociation equilibrium

is determined by the interactions of H�, Inÿ and

H�Inÿwith the solvent molecules, and is better under-

Table 2

pKa values of methyl orange in aqueous solutions of alcohols

(258C, I�0.1)

Alcohol pKa

(wt%) MeOH±H2O EtOH±H2O i-PrOH±H2O t-BuOH±H2O

0 3.39�0.03 3.39�0.03 3.39�0.03 3.39�0.03

10 3.28�0.02 3.19�0.02 3.13�0.01 3.02�0.01

20 3.13�0.01 2.91�0.02 2.67�0.02 2.45�0.02

30 2.95�0.03 2.49�0.02 2.17�0.01 2.00�0.01

40 2.77�0.02 2.14�0.02 1.87�0.02 1.75�0.01

50 2.58�0.01 1.85�0.01 1.54�0.03 1.51�0.02

60 2.28�0.02 1.71�0.02 1.44�0.02

70 2.06�0.01 1.50�0.03

80 2.00�0.01

90 a 2.11�0.01

a The solubility of potassium chloride is so poor in this mixture that

it precipitates in solutions. So, the pKa value obtained here is for

reference only.

Fig. 1. Variation of the dissociation constants (pKa) as a function of mole fraction (x2) of alcohol in the mixed solvents: (*), MeOH; (~),

EtOH; (~), i-PrOH; and (*), t-BuOH.

278 J. Fan et al. / Analytica Chimica Acta 364 (1998) 275±280

stood in terms of the standard Gibbs energies of

transfer for the three species from water to mixed

solvents. If we disregard all participation of the sol-

vent, the standard Gibbs energies of transfer for the

dissociation reaction, �G0t , can be represented by

�G0t � �G0

t �H�� ��G0t �lnÿ� ÿ�G0

t �H�lnÿ� (5)

where

�G0t � 2:303 RT �pKT�s� ÿ pKT�w�� (6)

In this equation, pKT(s) and pKT(w) are the thermo-

dynamic dissociation constants in mixed solvent and

in water, respectively. According to Meretoja [15], De

Ligny et al. [3], pKa(s) and pKa(w) determined in this

work can be used to calculate �G0t without serious

error. Values of �G0t thus obtained are given in

Table 3. Lahiri et al. [16±18] determined �G0t (H�)

values from water to various aqueous solutions of

alcohol (MeOH, EtOH, i-PrOH and t-BuOH). The

interpolated values in the appropriate solvents are

included in Table 3. Values of �G0t �lnÿ�ÿ

�G0t �H�lnÿ� calculated from �G0

t and �G0t (H�) at

particular proportions of the co-solvents are also

included in this table.

�G0t (H�) may be regarded as a measure of the

basicity of the solvents relative to water [19]. This

increasingly negative �G0t (H�) values in Table 3

suggest increasing relative basicities of the mixed

solvents. It is obvious that the basicity of the mixed

solvent increases in water-rich regions with increasing

composition of the co-solvent in the following order:

t-BuOH>i-PrOH>EtOH>MeOH. It is well known that

the nature of the dissociation is the abstraction of a H�

from H�Inÿ by an acceptor solvent molecule. Thus,

the more basic characteristic of the mixed solvents

compared to water is one of the important factors for

the observed increase of the Ka in the alcohol±water

mixtures.

It is interesting to note that values of

�G0t �lnÿ� ÿ�G0

t �H�lnÿ� are increasingly negative

with addition of the co-solvent for a given alcohol±

water solvent system. They are also increasingly

negative in the following order: t-BuOH>i-PrOH>

EtOH>MeOH at a particular composition for different

solvent systems. This is related to the hydrophobic

interaction between the indicator and the alkyl group

of alcohols. According to Brandts et al. [20], hydro-

phobic interaction is only possible with the uncharged

part of the indicator molecules. It presents the inter-

action of the alkyl group of alcohols with the dimethyl-

aniline moiety in Inÿ in the present case. Therefore,

�G0t �lnÿ� should be more negative compared to

�G0t �H�lnÿ�. Considering the fact that hydrophobic

interaction is affected greatly by the size of the alkyl

groups, the above order is understandable.

Acknowledgements

The authors are grateful to the Natural Science

Foundation of Henan Province for ®nancial support,

and to the reviewers for their suggestions.

Table 3

Values of �G0t , �G0

t �H�� a, and �G0t �lnÿ� ÿ�G0

t �H�lnÿ� from water to aqueous alcohol mixed solvents at 258C (in KJ molÿ1)

Alcohol MeOH�H2O EtOH�H2O i-PrOH�H2O t-BuOH�H2O

(wt%) �G0t �G0

t (H�) � b �G0t �G0

t (H�)� b �G0t �G0

t (H�) � b �G0t �G0

t (H�) � b

10 ÿ0.6 ÿ0.9 0.3 ÿ1.1 ÿ1.2 0.1 ÿ1.5 ÿ1.2 ÿ0.3 ÿ2.1 ÿ1.7 ÿ0.4

20 ÿ1.5 ÿ1.5 0 ÿ2.7 ÿ2.2 ÿ0.5 ÿ4.1 ÿ2.8 ÿ1.3 ÿ5.3 ÿ3.2 ÿ2.1

30 ÿ2.5 ÿ2.0 ÿ0.5 ÿ5.1 ÿ3.1 ÿ2.0 ÿ7.0 ÿ4.0 ÿ3.0 ÿ7.9 ÿ4.0 ÿ3.9

40 ÿ3.6 ÿ2.8 ÿ0.8 ÿ7.1 ÿ4.1 ÿ3.0 ÿ8.7 ÿ4.9 ÿ3.8 ÿ9.4 ÿ3.7 ÿ5.6

50 ÿ4.6 ÿ3.6 ÿ1.0 ÿ8.8 ÿ5.1 ÿ3.7 ÿ10.5 ÿ5.4 ÿ5.1 ÿ10.7 ÿ2.8 ÿ7.9

60 ÿ6.3 ÿ4.6 ÿ1.7 ÿ9.6 ÿ5.6 ÿ4.0 ÿ11.2 ÿ5.6 ÿ5.6

70 ÿ7.6 ÿ5.4 ÿ2.2 ÿ10.8 ÿ5.6 ÿ5.2

80 ÿ8.0 ÿ5.5 ÿ2.5

90 ÿ7.3 ÿ5.0 ÿ2.3

a �G0t (H�) values have been obtained from Refs. [16±18] by interpolation.

b � � �G0t �lnÿ� ÿ�G0

t (H�lnÿ).

J. Fan et al. / Analytica Chimica Acta 364 (1998) 275±280 279

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