Journal of Solution Chemistry, Vol. 6, No. 3, 1977

Ionization Constants and Thermodynamic Quantities of 2-Mercaptocarboxylic Acids in Aqueous Solution K. J. Ellis, ~'= k. G. Lappin, ~'" and A. M c k u l e y ~'' Received July 19, 1976; revised September 29, 1976 The earboxylie acid ionization constants of mercaptoacetic acid (MAA), 2mercaptopropionie acid (2-MPA), 2-mereaptoisobutyrie aeid (2-MIBA) and 2-mereaptosuccinie acid (2-MSA) have been measured in perehlorate media at an ionic strength of 1.0 M and over the temperature range 273-309~ Appropriate thermodynamic quantifies have been derived. The variation in the temperature To at which the constants exhibit a maximum has been interpreted in terms of the effect of hydrophobie subst#uents on the extent of solvation of the participating species.

KEY WORDS: Ionization; 2-mercaptocarboxylic acids; thermodynamic.

1. I N T R O D U C T I O N

Recent work in these laboratories has been concerned with the oxidation of mercaptocarboxylic acid substrates by hexaaquo iron(III) in aqueous acid solutionY -3~ In these reactions there is evidence for the formation of transient intermediates which are believed to be coordination complexes of the metal ion. In order to fully characterize these complexes and identify the major pathways in their formation reactions, it is necessary to know accurately, values for the ligand ionizations under the appropriate conditions of temperature and ionic strength. Over the acidity range used, 0.3-1.0 M, the sulfhydryl ionization is negligible with pK, values of the order of 11.~4,~ 1 C h e m i s t r y D e p a r t m e n t , U n i v e r s i t y o f G l a s g o w , G l a s g o w , G 1 2 8QQ, Scotland. 2 D e p a r t m e n t o f Biochemistry, J o h n C u r t i n School o f Medical R e s e a r c h , A u s t r a l i a n N a t i o n a l University, P.O. B o x 4, C a n b e r r a , A . C . T . , A u s t r a l i a 2600. a T o w h o m c o r r e s p o n d e n c e s h o u l d be a d d r e s s e d : D e p a r t m e n t o f C h e m i s t r y , P u r d u e U n i v e r s i t y , W e s t Lafayette, I n d i a n a 47907. 4 D e p a r t m e n t o f C h e m i s t r y , U n i v e r s i t y o f Victoria, Victoria, B.C., V 8 W 2Y2, C a n a d a . 183 9 1977 Plenum Publishing Corporation, 227 West 17th Street, New York, N.Y. 10011. No part of this publication may be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, microfilming, recording, or otherwise, without written permission of the publisher.

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Accordingly, this study is concerned with the evaluation of the stoichiometric carboxylic acid ionization constants at an ionic strength of 1.0 M. 2. E X P E R I M E N T A L

Mercaptocarboxylic acids were obtained and stored as described previously. ~1'~ Stock mercaptocarboxylic acid solutions were prepared immediately before a run by dissolving accurately weighed quantities of the acid in a known volume of 1.0 M sodium perchlorate and were analyzed by titration with standard base. Sodium perchlorate solutions (Fluka, Puriss, p.a.) were analyzed gravimetricaUy by evaporating samples of known volume at a temperature sufficiently high to crack the monohydrate. Carbon-dioxide-free solutions of sodium hydroxide C~) and hydrochloric acid were analyzed by titration against potassium hydrogen phthalate and sodium tetraborate, respectively. ~6) All solutions were prepared using distilled water which had been boiled out to remove carbon dioxide and cooled under a stream of nitrogen gas. Failure to carry out this procedure resulted in nonreproducibility of experimental data. The ionization constants were determined from the results of potentiometric titrations in which known volumes of 0.1 M mercaptocarboxylic acid were titrated with 0.15 M sodium hydroxide at an ionic strength of 1.0 M using sodium perchlorate as background electrolyte. Oxygen-free nitrogen gas, presaturated with water, was bubbled continuously through the titration celt to prevent aerial oxidation of the acids and to minimize the absorption of carbon dioxide. The hydrogen ion activity of the cell was measured by a C.T.F. 28 glass electrode, and a "Wilhelm" bridge Cv)was used to make the liquid junction to a silver-silver chloride reference electrode. The emf of the cell AgAgC1

reference solution bridge solution test solution glass elec1.0MNaC10~,Ag+,C1 - 1.0MNaC10~ 1.0MNaC10~ trode

(1) was measured using an E.I.L. 46A pH meter. Calibration of the apparatus, before and after each titration, with solutions of known hydrogen ion concentration at an ionic strength of 1.0 M allowed direct evaluation of the hydrogen ion concentration of the test solution from the emf. Although from day to day there were slight differences in the absolute value of the slope of a plot of emf against hydrogen ion concentration at a given temperature, successive calibrations were normally in agreement to within + 2~o. The titration cell, bridge, reference electrode, and gas-saturation towers were immersed in a large water bath of 45 liters capacity fitted with a refrigeration unit and heater in conjunction with a Shandon Circotherm Mark II

Constants and Quantities of 2-Mercaptocarboxylic Acids

185

thermoregulator. The temperature of the bath was maintained constant to within + O.I~ 3. R E S U L T S

AND

DISCUSSION

The carboxylic acid and sulfhydryl ionizations of the mercaptocarboxylic acids are widely separated and thus, provided measurements are restricted to the appropriate pH range ( < 7), the dibasic acids MAA, 2-MPA, and 2-MIBA may be treated as monobasic and the tribasic 2-MSA as dibasic. Furthermore, by working in a medium of virtually constant ionic composition, activity coefficients may be incorporated into the thermodynamic ionization constants, and stoichiometric constants, appropriate to the experimental conditions, can be obtained. The first ionization constants of the acids MAA, 2-MPA, and 2-MIBA were evaluated directly from the expression Ka-

h(h + b) a- h- b

(2)

where h, b, and a represent the concentration of hydrogen ion, added base, and mercaptocarboxylic acid, respectively. Due account of the change in volume due to addition of base was taken in each case. For 2-MSA, the Speakman solution for dibasic acids (8~was employed. A least-squares analysis of the expression h~(h+b) = v h(a-h-b) 2a - h - b -~t (2a h b) + KalK~2

(3)

which is of the form X = K~I Y + KalKa2

(4)

enabled the calculation of K ~ from the slope of plots of X against Y, and K~2 from each experimental point which corresponded to a negative value of Y. Calculated values for the ionization constants together with their rootmean-square errors, shown in Table I, were determined at each temperature from at least 16 data points. The constants exhibit complex dependences on temperature, each showing a maximum in the range examined. This behavior has been noted with many weak electrolytes and there is much discussion in the literature as to the exact nature of the expression required to describe the variationD '1~ In accord with Harned and co-workers, (9~ an equation of the form - l n K~ = A[T + B + CT

(5)

was chosen and a least-squares analysis of the data in Table I yielded the best fit parameters shown in Table II. Comparison of the observed and calculated

186

Ellis, Lappin. and McAuley

Table I. Values for the C o n c e n t r a t i o n Acidity Constants for M A A , 2 - M P A , 2-MIBA, a n d 2 - M S A in A q u e o u s Solution at 1 M Ionic Strength

10*K. (M) T (~ 273 278 283 288 293 298 303 308

MAA

1.61 4- 0.02 1.86 4- 0.05 1.98 4- 0.05 2.09 ___0.04

2-MPA

2.35 4- 0.04 2.87 + 0.10 2.68 + 0.06

2-MIBA

1.32 1.23 1.24 1.28

___0.06 4- 0.04 4- 0.04 + 0.03

2-MSA (1)

2-MSA (2)

7.35 4- 0 . 4 8 8.46 ___0 . 2 1 9.42 4- 0.44

0.3034- 0.018 0.3734- 0.018 0.429 4- 0.008

9.27 4- 0.29 9.13 4- 0.27 7.58 4- 0.22

0.475+_ 0.008 0.433_ 0.024 0.327 4- 0.014

2.10 + 0.03

values is shown in Fig. 1, a n d the t h e r m o d y n a m i c quantities presented in Table I I I were calculated using values ~n~ for the density of 1.0 M NaCIO4 a n d its temperature dependence. I n t e r p r e t a t i o n of the effect of structure o n the t h e r m o d y n a m i c parameters is complicated by the variation in To, the temperature at which the i o n i z a t i o n c o n s t a n t exhibits a m a x i m u m , as shown in Table III. A l t h o u g h it is n o t yet possible to provide a detailed quantitative a c c o u n t of this effect, some qualitative i n f o r m a t i o n o n its origins m a y be deduced. I n discussing the effect of temperature on the p r o t o n transfer reaction H A + H 2 0 ,~ H ~ O + A -

(6)

(where H A is a weak acid a n d A - its conjugate base) it is c o n v e n i e n t ~12~to divide the free-energy change into two parts A G ~ = ~XG~xT + AG~'r~T

(7)

Table II. Parameters for the E q u a t i o n - l n K . = A[T + B + CT for 2-Mercaptocarboxylic Acids Acid MAA 2-MPA 2-MIBA 2-MSA(1) 2-MSA(2)

A 2.1913 • 3.4576 • 6.5020 • 2.7393 • 4.3711 •

B 104 104 103 104 10~

-1.3488 -2.2774 -3.6742 -1.8301 -2.9262

C x • • • x

102 102 10 102 102

2.3442 • 4.0244 • 8.0298 • 3.2928 • 5.2357 •

10 -1 10 -1 10 -2 10 -1 10 -1

Constants and Quantities of 2-Mercaptocarboxylic Acids

187

4-5 2

~

4'1-

4-0-

4-4

MAA

-4"3

3.9~J 2~

3"83.7-

-3"3 3-8-

[] ~

~

Ii3"1 2 A1 '0

I

280

1

I

290 TCK) 300

I

310

Fig. 1. Variation of the apparent pKa for carboxylic acid dissociation of 2-mercaptocarboxylic acids with temperature at I = 1.0 M. Right ordinate: (1t, 2-MSA. Left ordinate: O, MAA; D, 2-MPA; A, 2-MIBA.

where AG~xT, dependent on the environment, may be equated with the electrostatic work required to form two charges of opposite sign, while AGenT, independent of the environment, is concerned mainly with the chemical effects of bond making and bond breaking. By assuming that AH~Nr is independent of temperature, Gurney (12,13)

Table III. Thermodynamic Quantities and Values of To for Carboxylic Acid

Dissociation of 2-Mercaptocarboxylic Acids (I = 1.0 M, T = 298~ Quantity

MAA

2-MPA

AG~(kcal-mole- 1) AH ~(kcal-mole-1) AS ~(cal-~ -1) ACp~ (kcal-mole-l-~ -1) To(~

5.1 2.2 -9.7 -0.27 306

4.9 -2.2 -23.8 -0.47 293

2 - M I B A 2-MSA(I) 2-MSA(2) 5.4 -1.2 -22.1 -0.09 285

4.4 -3.6 -26.8 -0.39 289

6.0 -5.5 -38.6 -0.62 289

188

Ellis, Lappin, and McAuley

derived an expression for the temperature To which is dependent only on the ratio AG2NT/AG~.x~and independent of the overall free energy of ionization To~ = 02 1 + AG~xT]

(8)

where 0 is a constant for a particular medium. From the observed order in the values of To, the trend in AGenT should thus be M A A > 2-MPA ~ 2-MSA > 2-M!BA

(9)

~ and/or that for AG~xT 2-MIBA > 2-MPA ~ 2-MSA > M A A

(10)

Gurney used a hypothetical ionic model for comparative purposes while most other workers have preferred to use real systems as standards. In order to decide which, if any, of the trends (9) and (10) dominates in these systems, it is necessary to use this latter approach. The use of the proton transfer reaction HA1 + A f ~ - H A 2 + Ai-

(11)

where HAa is a reference acid and HA2 is closely related and of similar structure, is preferable to the proton transfer (6) because of the possibility of isolating specific effects by matching one acid carefully against another. I f the idea of internal and external effects is applied to equilibrium (11) 3AG ~

o o o o --= AGINT1 -t- A GEXTz -- AGINT2 -- AGExr2 = 3AG~% +

~AG~x~

(12) (13)

the change in acidity due to the intrinsic structural features of the acid and its conjugate base will comprise the internal part, and the external effects may then be identified with the effect of structure on solvation. Hepler and others (14'15~ have shown that, for similar acids, 3AS~z ~ 0 so that the observed thermodynamic properties are largely determined by 3AH[NT and changes in solvation. Evidence (14) that solution processes afford a partial compensation of 3AH ~ by 8AS ~ leads to an expression

~AH~xT =/3 ~AS~xT

(14)

giving ~6G o = ~AH?~

+ (~ -

r) ~As ~

(15)

The fact that the constant fl ~_ T f o r aqueous solutions near room temperature

Constants and Quantities of 2-Mercaptocarboxylic Acids

189

leads to the suggestion that 3AH~T, and hence 3AG2Nvmay be identified more closely with gAG~ than 3AH~ (14~ Observed trends in SAH~~ with the structure of aliphatic carboxylic acids may be explained by inductive and resonance effects.(16) Electronwithdrawing and positively charged substituents stabilize the conjugate base relative to the acid, whereas electron-donating and negatively charged substituents have the opposite effect. Internal hydrogen bonding can also play a significant role in determining the relative stabilities. Using mercaptoacetic acid as a reference, the thermodynamic parameters for reaction (11) may be evaluated and the following conclusions drawn. Relative to MAA, the first ionization of 2-MSA is enhanced while the second is retarded. Both of these observations may be attributed to internal hydrogen bonding in the species. CH2-CO2H

t

(16)

HS-CH~-COs which stabilizes the ionized form of the first dissociation and the unionized form of the second. The effects of charge are also significant in the latter. While these effects are important, the similarity of the 3A H~x~ values of the first ionization of 2-MSA with those of 2-MPA is, however, particularly noteworthy. For the acids 2-MPA and 2-MIBA, gAG~ _~ ~AG~NT-~ 0, implying that the explanation for the variation in To is contained largely in trend (10) and that reactions are best discussed in terms of changes in solvation. Besides providing a volume of low dielectric constant in the proximity of the carboxyl group, the effect of hydrophobic methyl groups also reduces the number of solvating water molecules. King ~1~ has suggested that the effect on an anion might be greater than on neutral molecules, the resulting solvent exclusion giving rise to positive enthalpy and entropy changes. Both these properties vary markedly with temperature. It may be of significance, however, that the change in heat capacity ~A C~ for 2-MIBA is in the opposite sense to those for the other acids. Possibly in this case, solvation of the neutral acid is dominant. The present data are also in accord with previous observations (2~ in which variations in the formation constants of iron(III) complexes with the mercaptocarboxylic acids are ascribed to changes in solvation. Although the exact nature of the interaction is obscure, the results are in agreement with a study (~v~ of aqueous solutions of substituted carboxylic acids in which conductivity anomalies are ascribed to the replacement of water by un-ionized fatty acid in the solvent medium. These acids also show a trend in the values of To, becoming more positive with increasing hydrophobicity.

190

Ellis, Lappin, and McAuley

ACKNOWLEDGMENTS The technical assistance o f Mr. A. Sharp is gratefully acknowledged, as are the receipt o f an I.C.I. R e s e a r c h F e l l o w s h i p (K.J.E.) a n d financial s u p p o r t f r o m the Carnegie T r u s t to the Universities o f S c o t l a n d (A.G.L.).

REFERENCES 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17.

K. J. Ellis and A. McAuley, J. Chem. Soc. Dalton Trans., 1533 (1973). A. G. Lappin and A. McAuley, J. Chem. Soc. Dalton Trans., 1560 (1975). K. J. Ellis, A. G. Lappin, and A. McAuley, J. Chem. Soc. Dalton Trans., 1930 (1975). D. D. Perrin and I. G. Sayce, J. Chem. Soc. (A), 82 (1967). G. R. Lenz and A. E. Martell, Inorg. Chem. 3, 378 (1965). A. I. Vogel, A Textbook for Quantitative Inorganic Analysis, 3rd ed. (Longmans, London, 1961). W. Forsling, S. Hietanen, and L. G. Sill6n, Acta Chem. Scand. 6, 901 (1952). J. C. Speakman, J. Chem. Soc., 855 (1940). H. S. Harned and B. B. Owen, The Physical Chemistry of Electrolytic Solutions (Reinhold, New York, 1964), Chap. 15. E. J. King, Acid-Base Equilibria (Pergamon, London, 1965), Chaps. 7 and 8. International Critical Tables, E. W. Washburn et aL, eds. (McGraw-Hill, New York, 1933). R. W. Gurney, lonic Processes in Solution (McGraw-Hill, New York, 1953). R. W. Gurney, J. Chem. Phys. 6, 499 (1938). P. D. Bolton and L. G. Hepler, Quart. Rev. 25, 525 (1971). L. G. Hepler, Can. J. Chem. 49, 2803 (1971). L. P. Hammett, Physical Organic Chemistry, 2nd ed. (McGraw-Hill, New York, 1970). R. B. Simpson, J. Phys. Chem. 79, 1450 (1975).