SELF-ASSOCIATION AND HYDRATION OF BENZOIC ACIDIN BENZENE
3427
Self-Association and Hydration of Benzoic Acid in Benzene
by Roger Van Duyne, S. A. Taylor, S. D. Christian, and H. E. Affsprung Department of Chemistry, The University of Oklahoma, Arorman, Oklahoma
73069
(Received February 27, 1.967)
Measurements at 25" are reported of the partition of benzoic acid between water and benzene and the solubility of water in solutions of benzoic acid in benzene at various water activities. The data indicate that the benzoic acid is highly self-associated and hydrated in the organic solvent. It is proposed that the important associated species are the acid dimer, the monomer monohydrate, the monomer dihydrate, and the dimer monohydrate. The distribution constant of the acid monomer and the formation constants for the associated species were evaluated together with their standard errors by a weighted nonlinear least-squares analysis of the data.
Introduction Previous reports from this laboratory have described methods for determining self-association and hydration constants of polar solutes in organic solvents from parIt has been demontition and water solubility strated that partition data alone, in the absence of water solubility measurements, cannot be used to calculate self-association constants of polar solutes in organic solvents. A recent article appearing in this journal presented partition data Eo? the system benzoic acid-benzenemater, from which dimerization constants of the acid were calculated assuming that water does not interact with the acid in the organic phase.6 The calculated dimerization constants are very much smaller than those obtained by Allen, Watkinson, and Webb' from a careful study of the infrared spectra of anhydrous solutions of benzoic acid in benzene. We report here a study of the hydration of benzoic acid in benzene a t 25", from which we have inferred equilibrium constants for formation of 1:1, 1 : 2 , and 2:l complexes between the acid and water. The results clearly indicate the important role played by small concentrations of water in the partition equilibria of carboxylic acids.
Experimental Section Reagent grade benzoic acid (Baker and Adamson) was used without further purification. Benzene was purified by distillation through a 30-plate Oldershaw column. The temperature for all measurements was controlled at 25.0 0.1".
*
The benzoic acid was partitioned between water and benzene by techniques similar to those previously reported.* The equilibration of water with benzoic acid-benzene solutions at reduced water activities was achieved as described earlier.3 All benzoic acid concentrations were determined by titration with standard base. End points were detected with the aid of a Beckman Zeromatic pH meter. Measurements of water solubilities were made using a Beckman KF-3 Aquameter. The Karl Fischer reagent used in the titrations for n-ater n-as standardized with solutions of pure benzene saturated with water. The solubility of water in benzene at 25" n-as taken to be 0.0349 A1.j
Results and Discussion Partition data for the system benzoic acid-benzenewater at 25" are presented in Figure 1, in which the distribution ratio, f A o / C ~ " , is plotted against CAW. Table I contains a compilation of the symbols used. (1) S. D. Christian, H. E. Affsprung, and J. R. Johnson, J . Chem. Soc., 1896 (1963). (2) S. D. Christian, H. E. Affsprung, and S. A. Taylor, J . P h y s . Chem., 67, 187 (1963).
(3) S. D. Christian, H. E. Affsprung, J. R. Johnson, and J. D. Worley, J . Chem. Educ., 40, 419 (1963). (4) T. F. Lin, S. D. Christian, and H. E. Affsprung, J . Phys. Chem., 69,2980 (1965). (5) J. R. Johnson, S. D. Christian, and H. E. Affsprung, J. Chem. Soc., 77 (1966). (6) A. K. M. S. Huq and S. A. K. Lodhi, J . Phys. Chem., 70, 1354 (1966). (7) G. Allen, J. G. Watkinson, and K. H. Webb, Spectrochim. Acta, 22, 807 (1966).
Volume 71, Number 11
October 1967
R. VAN DUYNE, S. A. TAYLOR, S. D. CHRISTIAN, AND H. E. AFFSPRUNG
3428
represents the formal concentration of the acid in benzene and CA" is the acid monomer concentration in the aqueous phase, calculated from the formal concentration of the acid and the acid ionization constant, assuming the ionic activities conform to the extended Debye-Huckel equation.* Water solubility data are given in Figure 2, presented as the formal concentrations of water and acid in benzene, fwo vs. fAo, corresponding to several fixed values of the water activity, aw. Several choices of plausible hydrate species were proposed including monomer monohydrate, monomer dihydrate, and dimer monohydrate, singly and in combination in attempting to fit the partition and water solubility data by weighted, nonlinear least-squares analysis. A preliminary analysis of data following the method which has been previously described in detail2 showed that hydrates of both dimer and monomer must
fAo
I
4
8
12
16
~z"x~~~(mo~e/t)
0.051
Figure 1. Partition data: 0,results of this study; A, taken from ref 8.
Table I : Definitions of Symbols A W
A2 AW AWz A2W KD Kii Kiz Kzo KZ1
fA' fwO CAW CA
CN C w' aw Afwo
S WA
ww SA
sw
Acid monomer Water monomer Acid dimer Monomer monohydrate Monomer dihydrate Dimer monohydrate Distribution constant for the acid monomer Formation constant for monomer monohydrate Formation constant for monomer dihydrate Acid dimerization constant Formation constant for dimer monohydrate Formal concentration of the acid in benzene Formal concentration of water in benzene Concentration of the acid monomer in the aqueous phase Concentration of the acid monomer in the benzene phase Concentration of the water monomer in the benzene phase Value of C v at unit water activity Water activity Increase in fwo due to hydrated acid species Error function defined by eq 5 Factor weighting uncertainty in partition ratio Factor weighting uncertainty in water solubilities Root-mean-square deviation in partition ratio Root-mean-square deviation in water solubility values
The Journal of Physical Chemistry
0,03
1
0.01
0.20
0.x)
:f
0.30
(rnole/l.)
Figure 2. Water solubility data: 0, a, = 1.0; A, a, = 0.658; 0, a, = 0.400. Dashed a, = 0.790; 0, lines were calculated from met'hod A; solid lines from method B.
(8) S. A. Taylor, Ph.D. Dissertation, The University of Oklahoma, 1965.
SELF-ASSOCIATION AND HYDRATION OF BENZOIC ACIDACIDIN BENZENE
be assarned in order to obtain a satisfactory correlation of the results. When a smaller set of hydrates was assumed, the calculated ciirves deviated significantly from the experimental points. For these reasons the species AW, -4W2, and A2W were selected as being a minimum set of chemically reasonable hydrates, consistent with all of the solubility and partition results. Here, unlike the case where diphenylmethane was the s o l ~ e n t ,the ~ addition of a monomer monohydrate was required before the minimum uncertainties in the parameters were reached. Assuming the presence of these three hydrates, the acid dimer (Az), and the acid and water monomers (A and W), each of which obeys Henry's law, the data should be related by jAo/cA"
=
KD(I
+~
+
+
fAo
CA
=
culated values of CA and CWand the set of equilibrium constants into eq 2. The weight factors in eq 5, WA and WW, are estimated from observed uncertainties in partition ratio and water solubility measurements. The set of values of KD,Kl1, K12,and Kzl leading to an absolute minimum in Sz is the least-squares set of parameters for method A. Errors in the four parameters are calculated by the method of Sill&." Method B differs from method A only in that Kzo is treated as an additional parameter to be obtained from the present data, rather than assumed to be known from the literature.
Table I1 : Least-Squares Parameters for Partition and Water Solubility Data
i i ~ ~w1 2 ~ w 2 )
+ K21CW)CAW KllCACW + 2K12CACWz + KZlCA2CW 2KD2(K20
AfW0
3429
(1)
(2)
+ KllCACW f K12CACWz f 2K20C~~ + ~ K Z ~ C A ~(3)C W CW
=
aWCw0
(4)
where CA and CWare monomer concentrations of A and W in benzene, respectively, KD is the distribution constant for the acid monomer; &o, K11, K I Z ,and Kzl are equilibrium constants for formation of the complexes A2, AW, AW2, and A2W from the monomers. Afw is the increase in the formal concentration of water at a given aw owing to the presence of the acid, and CWO = 0.0349 ill is the concentration of the water monomer in benzene at unit water activity at 25.0°e5 Two methods have been utilized in analyzing the data. I n method A, it is assumed that Kzo = 589 l./ mole (obtained by extrapolating results of Allen, Watkinson, and Webb' to 25') is accurately known. Then, values of KD, Kl1, K21, and K12 are determined by nonlinear least-squares analysis in the following way. The expression
W W[AfWOexptI ~ -
A f ~ ~ c a l c d ] (5) ~
is minimized with respect to all four parameters by means of a numerical optimum seeking method.1° The calculated ~A"/CA"values are obtained from eq 1 by substituting K2,, trial values of K21, K12, K11, and KD, known values of CWcalculated from eq 4, and measured values of C A ~ .Calculated values of A~wOare obtained by first solving eq 3 for CA, using K2o and the trial values of the constants, and then substituting the cal-
Kzo,l./mole Kll, l./mole K I Z 1.2/mole2 , KZ1,1.2/mole2 KD SW,mole/l. SA a
Method X
Method B
589" 12.4 f 1 . 5 248 f 30 582 f 81 0.950 =k 0.002 0.00071 0 0357
298 =k 25 0 . 7 i2 . 0 222 =k 18 602 32 1.31 f 0.05 0.00043 0.0298
I
Taken from ref 7.
Table I1 summarizes results obtained by the two methods for analyzing the data. Values of the equilibrium constants, standard errors in the constants, and the individual root-mean-square deviations in the distribution ratio (SA)and in the water solubility values (Sw) are included in the table. It is apparent that method B, in which Kzo is treated as an adjustable parameter, gives a statistically superior fit of the results. However, it should be observed that method B involves the determination of five adjustable parameters and that only slight systematic errors in the water solubility or partition ratio values would be required t o increase the values SAand SW from their minima to the values obtained by method A. To illustrate, we have included calculated curves in Figure 2 corresponding to the parameters obtained using both method A and method B. I n Figure 1 the line is calculated from the results of method B and is practically the same as the line calculated from method A (method A: slope = 1100, intercept = 1.65; method B: slope = 1095, (9) G. 0. Wood, D. D. Mueller, S. D. Christian, and H. E. Affsprung, J. Phys. Chem., 70, 2691 (1966). (10) D. J. Wilde, "Optimum Seeking Methods," Prentice-Hall, I ~ ~Enalewood . -, Cliffs, N. J., 1964. (11) L. G. SillBn, ~ c t a Chem. Scand., is, 1085 (1964).
Volume 71, Number 11 October 1967
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R. VANDUYNE,S. A. TAYLOR, S. D. CHRISTIAN, AND H. E. AFFSPRUNG
intercept = 1.70). It is apparent that both methods are capable of fitting all of the data to within expected analytical uncertainties. We incline toward the belief that method A is the better fitting method, since it appears unlikely to us that the spectral results given by Allen, Watkinson, and Webb conceal systematic errors large enough to account for a 50% error in K20. It is interesting to compare the magnitudes of the hydration constants obtained using methods A and B. The largest variation occurs in KI1, which contributes significantly t o the fit of data in method A but is not an important parameter in method B. Calculated values of the other two hydration constants, K12and Kzl, are approximately the same in both methods. It is reasonable that the 1:1 hydrate formation constant should fall in the range 2-15 l./mole, considering known values of hydration constants of other polar solutes in nonpolar solvents.12-13 The equilibrium constant for the reaction Az W = A2W can be shown to be equivalent to K21/K20, which equals 1.0 by method A and 2.0 by method B. Either of these values is smaller than might be predicted for the hydration constant of the cyclic acid dimer, A2. However, the hydroxyl hydrogen of the acid monomer is expected to be capable of forming a strong hydrogen bond and this could explain the relatively large value of K1l calculated by method A. I n the dimer, the hydroxyl hydrogen is presumably not available for hydration. We believe that the large values obtained for K12 lend further support to our previous assumption that the 1:2 complex is a cyclic species (see the structure above). We proposed this species to explain vapor pressure data for the system water-benzoic acid-diphenylmethane a t 25" and obtained the value Klz = 483 f 21 L2/ m ~ l e ~A. similar ~ stoichiometry has been found and
+
The Journal of Physical Chemistry
H
0-- -H-0
CsH5-C
//
\
0-H---0
/ '\\
H
/ \
H
proposed for a trifluoroacetic acid hydrate in the vapor phase.14 This value for K12 is somewhat greater than the values obtained using either of methods A or B, which might be expected, since benzene is a more reactive solvent than diphenylmethane. The results presented here indicate that hydrated acid species are present in relatively large concentrations in solutions of benzoic acid in benzene a t various water activities. By considering the present results along with the spectral data of Allen, Watkinson, and Webb,? it is possible to infer both the stoichiometries and reasonable values of equilibrium constants for the hydration reactions which occur in benzene. However, it is not possible to infer association constants from partition data alone. Dilute solut,ions of carboxylic acids in moist organic solvents are far more complicated than has been realized by most previous users of the partition method.
Acknowledgment. This research was supported by the National Institutes of Health. (12) D. D. Mueller, Ph.D. Dissertation, The University of Oklahoma, 1966. (13) M. D. Gregory, S. D. Christian, and H. E. Affsprung, J . Phys. Chem., 71, 2283 (1967). (14) S. D. Christian, H. E. Affsprung, and C . Ling, J. Chem. SOC., 2378 (1965).
