Thermodynamics of Transfer between Soivents (18) V. F. Dorr, S . Kotschy. and H . Kausen, Ber. Bunsenges. Phys. Chem., 69, 11 (1965). (19) W . T . Simpson and D. L. Peterson,J. Chem. Phys., 26, 588 (1957).
2363 (20) P. Hemmes, J. Amer. Chem. SOC., 94, 75 (1972). ( 2 1 ) W . Cooper and N . 8.Liebert, Phofogr. Sci. Eng., 16, 25 (1972). (We thank a referee for providing us with this reference.)
Thermodynamics of Transfer of Molecules and Groups from Nonpolar to Aqueous Environments. 1. Method. n-Butyric Acid at 25' Kenneth J. Breslauer, Bruce Terrin, and Julian M. Sturtevant' Department of Chemistry, Yale University, New Haven, Connecticut 06520 (Received April 8, 1974) Pubiication costs assisted by the National lnsfitufes of Heaffh and the National Science Foundation
A method involving flow microcalorimetry is described for determination of the enthalpy of transfer of acidic or basic molecules from water-immiscible organic solvents to water. In this first paper the method is illustrated by application to the transfer of n- butyric acid from toluene to water at 25'. Distribution experiments were performed to permit evaluation of the free energy of transfer. Detailed consideration was given to the enthalpy and free-energy contributions arising from dimerization of the solute in the organic solvent. The thermodynamic parameters for the process involving monomeric solute n- C?H-COOH (toluene) = nC3H;COOH (H2O) are l G 0 2 9 8 = (-1220 f 50) cal mol-', AH198 = (-3520 f 150) cal mol-'. and lS'298 = (-7.i & 0.5) cal deg-l mol-'.
Introduction In recent years there have been many publications reporting thermochemical measurements on complex biochemical systems. It has generally proven to be impossible to present a satisfactory explanation of the thermochemical data in terms of currently recognized molecular interactions. There is, however, much evidence which indicates that important contributions to the energetics of many biochemical processes arise from the transfer of groups from nonpolar to aqueous environments, or the reverse, and considerable free-energy data for such transfers in model systems have been derived from distribution experiments, solubility determinations, or spectral observations. However. there are very few pertinent enthalpy values. This paper reports the development of a new calorimetric procedure to supply enthalpy and heat capacity data for the transfer of a wide variety of model compounds to water from waterimmiscible organic solvents, and the application of the method to the transfer of n- butyric acid from toluene to water. It is hoped that data obtained by this method will eventually aid in the recognition of a t least the hydrophobic contributions to the enthalpy changes in biochemical reactions.
Experimental Section n-Butyric acid, obtained from Fisher Scientific Co.. was redistilled. Titration with standard alkali gave a purity of 98.6%. It was assumed that the impurity was water. Toluene (Chromatoquality) was purchased from Matheson Coleman and Bell. The calorimeter utilized was a flow microcalorimeter de~ e l o p e d ' - in ~ collaboration with Beckman Instruments. Talo Alto, Calif. The calorimeter was calibrated chemically
using the neutralization of 0.001 M HCl by 0.002 M NaOH with both solutions flowing a t the same rate. The heat of formation of water was taken to be -13.34 kcal mol-] at 25°.i A typical set of 10 calibration experiments at 25' gave a mean value for the calibration constant of 1160 expressed in the arbitrary units of "integrator units" per millicalorie. with a standard error of the mean of 0.14%. In the transfer experiments, one liquid delivered to the calorimeter was a solution of n- butyric acid in toluene and the other was 0.1 S KaOH. The organic liquid was delivered at a flow rate of 0.02 ml min-1 and the aqueous alkali a t a flow rate 4 to 8 times higher. It was ascertained by varying the flow rates that extraction of the solute from the organic phase was complete within the residence time in the calorimeter. In order to minimize the heat of mixing the two solvents, which can be quite large despite the "immiscibility." the toluene and water were mutually presaturated by being vigorously shaken together in a separatory funnel and allowed to stand in contact at 25'. The remaining small heat of mixing of the presaturated solvents was determined and applied as a correction to all the transfer data. This correction also included the heat resulting from viscous flow in the calorimeter. The quantity of interest is the enthalpy of transfer of the un-ionized monomeric solute from organic solvent to water. It was therefore necessary to determine the enthalpy of ionization of the solute in water and also to deduct the heat of formation of water. The ionization enthalpy of butyric acid was determined by mixing in the flow calorimeter a solution of sodium butyrate (pH 7 ) with excess HCl. Suitable corrections for dilution heats and heats of viscous flow were applied. It was assumed that the presence of toluene in the aqueous phase had no effect on the enthalpy of ionization. It was also necessary to correct the overall enthalp) of The J o u r n a l of Physicai C h e i r i s r r f V o i . 78. No. 2 3 . 7974
K. J. Breslauer, B. Terrin, and J. M. Sturtevant
2364
transfer for the existence of dimers in the organic phase and the enthalpy of their dissociation. The extent of dimerization was inferred from the variation of the apparent distribution coefficient (see below) with solute concentration, and the enthalpy of dissociation of dimers from heats of dilution of butyric acid solutions in toluene. Details of the calculation of the transfer enthalpy will be given below. I t may be remarked here that much the largest contribution to the observed transfer heat is the heat of formation of water, and that the accuracy of the final result is severely limited by the fact that it is obtained as the small difference between two relatively large numbers. It may be asked why we have restricted our attention to systems involving immiscible solvents. The answer is that we were unable to find a suitable miscible solvent system, with one solvent being water, where the heats of solvent mixing were not so large as to introduce unacceptable uncertainties in the derived transfer enthalpies. Free-energy changes for the transfer process were evaluated from distribution coefficients. A known quantity of the solute was distributed between known equal volumes of water and toluene by vigorous stirring over a period of 10 hr. After complete separation of the phases, an aliquot of the aqueous phase was removed and titrated using a micrometer syringe and a Radiometer pH meter to establish the end point. The concentration in the organic phase was calculated from material balance. Distribution coefficients were determined in a room thermostatted a t 25 f 0.5". The small heat of transfer makes it clear that small temperature variations have no significant effect; temperature variations of f 1 ° introduce errors of only f O . O 1 kcal mol-' in 1 G " . Throughout this paper the approximation is made of setting activities equal to molarities. Results
The enthalpy of ionization of n-butyric acid was determined to be -0.64 and -1.08 kcal mol-' a t 25 and 40", respectively. These values compare well with those reported by Christensen, et ~ l . -0.64 , ~ and -1.12 kcal mol-', and give a value of -29 cal deg-l mol-' for the heat capacity of ionization. If it is assumed that butyric acid forms dimers in toluene but is entirely in monomeric form at low concentrations in water, then the apparent distribution constant Kapp is given by the expression6
In this expression, c s and c, are the total concentrations of solute in toluene and water. respectively, a is the degree of ionization of butyric acid in water, K1 is the true distribution coefficient, and Kd is the dissociation constant of the butyric acid dimers in toluene. Values of cy were calculated using an ionization constant of 1.55 X 10-5 M . Figure 1 gives a plot of Kappus. c,(l - a ) , The leastsquares straight line leads to the values K 1 = 0.127 f 0.009 and Kd = (0.0036 f 0.0002) M . The corresponding changes in free energy are AGO1 = (-1220 f 50) cal mol-l and X ' d = (-3330 f 50) cal mol-'. The enthalpy of dissociation of the butyric acid dimers in toluene was evaluated from dilution experiments run in the flow calorimeter. Since in the distribution experiments the organic phase was toluene saturated with water, the same solvent was used in the dilution experiments. It was The Journai o t Physical Chemistry. Voi. 78. N o . 23. 7974
TABLE I: Enthalpy of Dissociation of Dimers of n-Butyric Acid i n Toluene at 25" a No. of
diluci, M tion ratios Minimum Maximum
Ci, M 0.0850 0.0584 0.0184 0.00804
14 9 8 8
0.0036 0.0034 0.00079 0.00034
0.068 0,029 0.0092 0.0040
Weighted mean
L H d , kcal (mol dimer) - l
6.04 6.20 6.44 6.76 6.31
i 0.10 f
0.12
i 0.16 f 0.08 i 0.16
a See text for definitions of symbols. The uncertainty limits given for LHd are standard errors of the mean values calculated using eq 2.
t 0
0 02
0 04
0.06 cwlI-al
008
0.10
2
Figure 1. The distribution of n-butyric acid between toluene and water at 25". The apparent distribution constant, c,/c,(l - a), is plotted against t h e concentration of un-ionized acid in the aqueous phase, c,(l - a). cs is the concentration of acid (monomers plus dimers) in the organic phase: 0, series 1; A , series 2. The line was obtained by an unweighted least-squares calculation.
assumed that the solubility of water in toluene is not significantly affected by the presence of as much as 0.13 M butyric acid, the highest concentration encountered in the distribution experiments. Four series of experiments with stock solutions ranging in concentration from 0.008 to 0.085 M were employed. In each series the stock solution and diluting solvent were mixed in eight or more different ratios, covering dilution ratios up to 1:24. Calorimetric dilution data can in principle be used to obtain dissociation constants as well as heats of dilution.' However, if reliable equilibrium constants can be obtained from noncalorimetric experiments, it is usually preferable to use the calorimetric data only for the evaluation of heats of d i l u t i ~ n In . ~the ~ ~ present case, the distribution experiments lead to a more accurate value for Kd than can be obtained from the dilution data, and this value was used in evaluating the dimer dissociation heat. If butyric acid a t a total concentration of c = c, 2Cd, where c, and c d are respectively the concentrations of mo-
+
Thermodynamics of Transfer between Solvents
2365
TABLE 11: Enthalpy of Transfer of n-Butyric Acid from Toluene t o Water a t 2 6 " "
Concn of acid in toluene, M
No. of determinations
JQobsd,
LQd,
kcal mol - 1
kcal mol - 1
0.0638 0.0558 0.0393 0.0305 0.0178 0,00299
7 11 12 8 47 15
-15.21 + 0.06 -15.36 =t0.11 -15.35 & 0 . 1 0 -14.85 i. 0 . 1 0 - 1 5 . 0 3 =k 0 . 0 7 -15.78 zt 0 . 2 1
2.67 2.64 2.55 2.48 2.30 1.45
~ H tin-, r kcal mol-'
Weighted mean '1
-3.90 -4.02 -3.92 -3.35 -3.35 -3.25 -3.52
*
0.11 0.14 + 0.13 i 0.13 =t 0 . 1 1 + 0.22 i 0.15 =k
See text for meaning of symbols.
nomeric and dimeric solute, is present in toluene, the fraction of the total solute present which is in monomeric form is given by
(1
-
.t)HA(org) =
H'(aq)
-
1
- 1-
(HA),(org) 2 A- (aq) = HA (aq) ~
H 2 0 = H*(aq) - OH-(aq) Summing these equations gives where a = Kd/c. If A x is the change in x resulting from the dilution, the enthalpy of dissociation, expressed in kilocalories per mole of dimer, is obtained from the expressions -1Q = A q / c , , where Aq is the enthalpy change in kilocalories per liter of stock solution and c , is the stock concentration, and V I d = 2 A Q / A x . I t is assumed that there is no significant volume change on mixing. The results of the dilution experiments are given in Table I. The concentrations of the stock solutions are given in column 1, and the number of different dilution ratios used in column 2. In most cases several determinations were performed a t each dilution ratio. The range of dilution ratios employed can be inferred from the final concentrations given in columns 3 and 4. The mean calculated enthalpies of dissociation are listed in column 5 together with the standard errors of the mean. The values for f l d in Table I appear to increase significantly with decreasing initial concentration. However, we have ignored this apparent dependence on concentration since no such trends appear in the individual series of dilution experiments, and no indications of nonideality can be seen in the distribution data. The mean value, U d = 6.31 f 0.16 kcal (mol of dimer)-', calculated weighting the individual values in proportion t o the number of dilution ratios used, was used in evaluating enthalpies of transfer as outlined below. Stock solutions for transfer experiments were prepared by equilibrating a known amount of n- butyric acid with known amounts of water and toluene. The concentration of butyric acid in the organic phase was evaluated, as in the distribution experiments, by titration of aliquots of the aqueous phase with standard alkali. Appropriate corrections to the transfer heats were based on blank experiments in which water-saturated toluene was flowed against an NaOH solution. Six stock solutions were employed ranging in concentration from 0.003 to 0.064 M The results of the transfer experiments are listed in Table 11. The concentrations of the stock solutions in toluene are listed in column 1, the number of transfer experiments run in column 2, and the corrected observed heat effect in column 3. Several processes are involved in each transfer experiment, as shown in eq 3-6. 1
-
\
\HA(org) - __ (HAI2(org) 2
-
OH'(aq) =
HA(org) = HA(aq)
AHtrans =
AQobsd - AQd - A H , - AHw (7 ) where the enthalpy of transfer is VItrans. The quantity x in eq 3 and 4 is calculated from the equilibrium constant Kd and the stock concentration by means of eq 2; AQd = [( 1 - x )/2] w d ; fl] is the molar heat of ionization of butyric acid; and AH, is the heat of formation of water. The fourth column in Table I1 gives the calculated corrections, @ d , based on the dissociation heat in Table I, and the fifth column the final heats of transfer, UTtranSr calculated according to eq 7 . The uncertainty limits are based on the standard errors of the means for LQobsd and VI&and uncertainties of fO.05 kcal mol-' in AH, and f O . O 1 kcal mol-' in AH-.It appears that within experimental uncertainty AH trans is independent of concentration as expected. The mean of the values in the table, AH,,,,, = -3.52 kcal mol-' with a standard error of the mean of f0.15 kcal mol-' (f4%), was calculated assigning weights to the individual values equal t o the numbers in column 2.
Discussion Goodman'O studied the distribution of straight-chain fatty acids between heptane and water, and his data were reinterpreted by Smith and Tanford.'' Extrapolation of the values for the free energy of transfer of octanoic and higher acids to butyric acid gives -1.0 kcal mol-', as compared with our value of -1.2 kcal mol-' for transfer between toluene and water. Literature values for the free energies of dissociation of acetic and butyric acid dimers are given in Table 111. It appears that there is little or no change in going from acetic to butyric acid in either the aliphatic or the aromatic solvents, and that our value in toluene is thus intermediate between that of Pohl, et a1 , 1 2 and the value Davies, et al., would probably have found for butyric acid in benzene if they had studied that system. In making intercomparisons of the values in Table 111, it should be noted that the data of Pohl, e t al., are for anhydrous solvents while all the other data are for water-saturated solvents. The influence of dissolved water on the dimerization of the fatty acid is unknown. The enthalpy of dissociation of the dimeric form of nbutyric acid, 6.3 kcal mol-', corresponds to a hydrogen bond energy of 3.2 kcal mol-'. The Journal of Physical Chemistry Vol. 78. No. 23. 1974
K. J. Breslauer, B. Terrin, and J.
2366
TABLE 111: Free Energies of Dissociation of F a t t y Acid Dimers in Organic Solvents at Approximately 25 AG",i, kcal mol-'
Substance Acetic acid n-Butyric acid
In hexane or heptane
In benzene or toluene
-4.8 -3.9 -5.9 -4.9
-2.8 -3.6
Ref a b C
a
-3.3
d
-3.6
C
Goodman. lo Obtained by linear extrapolation of values for octanoic through myristic acids derived from measurements of the distribution between heptane and water a t 23'. Davies, et aZ.6 Derived from measurements of distribution between hexane and water and between benzene and water a t 25". cPohl, et a1.12 Derived from measurements of dielectric polarization of solutes in anhydrous heptane or benzene a t 30". This paper. TABLE 1V: T h e r m o d y n a m i c P a r a m e t e r s for Transfer of Related C o m p o u n d s f r o m Nonpolar to Aqueous M e d i u m ~
~~
~
AGO,
n-Butanea 1-Butanolb n-Butyiic acidc
~
M. Sturtevant
change and a decrease in entropy resulting from the ordering of water molecules around the nonpolar groups.13 The substantial decrease in enthalpy observed in the case of n- butyric acid is undoubtedly largely due to the interaction of the polar carboxyl group with water. Further indication of this is indicated by the c o m p a r i ~ o n ,given '~ in Table IV, of data for the transfer of n- butane and 1-butanol from the respective pure liquids to water with the data for the transfer of n- butyric acid from toluene to water. It appears that immersing a carboxyl group in water is about 3 kcal mol-' more exothermic than immersing a methyl group, and that the entropy change is also much more favorable in the case of the carboxyl group. It may be conjectured that the enthalpy difference arises from more energetic hydrogen bonding between carboxyl groups and water molecules than between water molecules, and that the entropy difference reflects less structuring of water molecules around a carboxyl group than around a methyl group.
Acknowledgments. The authors thank Mr. Roy Wiener for his expert assistance. This research was aided by grants from the U. S. Public Health Service, No. GM-04'725, and from the National Science Foundation, No. GB 36346X.
~~
*",
kcal mol-'
kcal mol-'
$6060 +2400 - 1220
- 800 - 2250 - 3520
AS",cal mol-l
deg-1
- 23 -15.6 -7.7
a Data for transfer from the pure organic liquid a t 20°, Tanford. l5 Data for transfer from the pure organic liquid a t 25'; Tanford.15 c Data for transfer from toluene a t 25"; this paper.
We find for the transfer of n- butyric acid from toluene to water a t 25' the thermodynamic parameters AGO = (1220 f 50) cal mol-', A H = (-3520 f 150) cal mol-', and ASo = (-7.7 f 0.5) cal deg-' mol-'. I t is usually considered that the transfer of nonpolar groups from organic to aqueous medium is accompanied by little if any enthalpy
The Journal of Physical Chemistry. Voi. 78. No. 23. 1974
References and Notes (1) J M. Sturtevant. Fractions, No. l(1969). (2) J. M. Sturtevant and P. A. Lyons, J. Chem. Thermodyn., 1, 201 (1969). (3) J. M. Sturtevant, "Methods in Enzymology," VoI. 26, C. H. W. Hirs and S. N. Timasheff, Ed., Academic Press, New York, N.Y., Chapter 11, 1972. (4) I. Grenthe, H. Ots, and 0. Ginstrup, Acta Chem. Scand., 24, 1067 (1970). (5)J. J. Christensen, J. L. Oscarson, and R. M. Izatt, J. Amer. Chem. SOC., 90, 5949 (1968). (6) M. Davies. P. Jones, D. Patnaik, and E. A. Moelwyn-Hughes, J. Chem. Soc., 1249 (1951). (7) R. Stoesser and S. J. Gill, J. phys. Chem., 71, 564 (1967). ( 8 ) S. J. Gill, M. Downing, and G. F. Sheats, Biochemistry, 6, 272 (1967). (9) S. Cabani and P. Gianni, Anal. Chem., 44, 253 (1972). (10) D. S. Goodman, J. Amer. Chem. SOC., 80, 3887 (1958). (11) R. Smith and C. Tanford, Roc. Nat. Acad. Sci US..70, 289 (1973). (12) H. A. Pohl. M. E. Hobbs, and P. M. Gross, J. Chem. Phys., 9, 408 (1941). (13)'W. Kauzmann. Advan. Protein Chem., 14, 1 (1959). (14) This comparison was brought to our attention by one of the reviewers of this paper. (15) C. Tanford, "The Hydrophobic Effect," Wiley, New York, N.Y., 1973, pp l a , 20.
