175
Solvophobic interaction
this work are correct and manifest the corresponding trends that one would have measured in real processes, i.e., when the final configuration of the particles is more realistic than the one employed in the model.
(3) (4) (5) (6) (7) (8)
Acknowledgment. This work has been partially supported by the Israel commission for basic research for which the authors are very grateful. References and Notes (1) Present address, National Institutes of Health, NIAMDD. LMB. Bethesda, Md 20014. (2) (a) C. Tanford. Advan. Protein Chem., 23, 121 (1968); (b) 24, 1 (1970).
(9) (10) (11) (12) (13) (14) (15) (16)
W. Kauzmann, Advan. Protein Chem., 14, 1 (1959). A. Ben-Naim, J. Chem. Phys., 54,1367,3696 (1971). A. Ben-Naim. J. Chem. Phys., 57, 5257, 5266 (1972). J. F. Brandts and L. Hunt, J. Amer. Chem SOC.,89.4826 (1967). Z. Priel and A. Siiberberg, J. Polym. Sci., Part A-2, 8, 689. 705, 713 (1970). I. M. Klotz, Fed. Proc., Fed. Amer. SOC. Exp. Bioi.. Part 1 1 1 , 24, S-24 (1965). S. Y. Gerlsma, J. Biol. Chem., 243,957 (1968). A. Ben-Naim, “An Introduction to a Molecular Theory of Water and Aqueous Solutions,” Plenum Press, New York, N. Y., in press. A. Ben-Naim and S. Baer, Trans. Faraday Soc., 59,2735 (1963). Wen-Yang Wen and J. H . Hung, J. Phys. Chem., 74,170 (1970). T. J . Morrison and F. Billet, J. Chem. Soc.. 3819 (1952). D. B. Wetlaufer. S. K. Malik, L. Stoller, and R L. Coffin, J. Amer. Chem. SOC., 86,508 ( 1964). A. Ben-Naim, J. Wilf. and M . Yaacobi. J . Phys. Chem.. 77, 95 (1973). M. Yaacobi and A. Ben-Naim, J. Solution Chem., 2, 425 (1973).
Solvophobic Interaction M. Yaacobi and A. Ben-Naim*’ Department of lnorganic and Analytical Chemistry, The Hebrew Unwersfty of Jerusalem, Jerusalem, lsrael (RecewedJuiy 72, 7973)
The solubilities of methane and ethane were measured in the following solvents: water, methanol, ethanol, 1-propanol, 1-butanol, I-pentanol, 1-hexanol, l,&-dioxane, and cyclohexane. The standard free energies, entropies, and enthalpies of solution of methane and ethane in these solvents were computed. From these data the strength of the “solvophobic interaction” is estimated in these solvents. It is found that the strength of solvophobic interaction is distinctly larger in water as compared with the other nonaqueous solvents. The entropy and enthalpy associated with the process of bringing two solutes from infinite separation to a short distance is also amonalous in water as compared with other solvents.
I. Introduction The term “hydrophobic interaction” (HI) has been used in previous articles2 to describe the indirect part of the work required to bring two solutes from infinite separation to a final configuration RI,R2 (the process being carried out within the solvent a t constant temperature T and pressure P ) .
One of the central questions in the study of the role of water in biological systems is to what extent the properties of water are unique as compared with other nonaqueous solvents. The purpose of this article is to compare the strength of the HI in water with the corresponding quantity, which may be referred to as “solvophobic interaction” (SI), in other solvents. The latter term has been suggested earlier2a for the quantity GGH1(R1,R2)defined in (1.1) for any solvent (we shall use the superscript HI for water and the superscript SI for the same quantity in a nonaqueous system). The approximate measure of the SI developed in previous articles2 is given by
6GS’(R = 1.533 A)
= ApKto
- 2ApMr0
(1.2)
where &lro is the standard free energy of solution of the solute cy in the appropriate solvent ( E t represents ethane and Me methane). A different estimate of the SI using the quantity 6 C S 1 ( R = 0) has been suggested earlierZa and was studied in some details by Wilhelm and Battino3 (for a review of this topic see ref 4). In this paper we use the quantity 6 P defined in (1.2) as a probe for the strength of SI. This has an obvious advantage over GGS1(R = 0). The reason is that GGsl is based on the measurements of experimental quantities ApELoand ApMen,whereas the estimation of GGS1(R = 0) is based on the scaled particle theory, the application of which to a complex liquid such as water is doubtw . 4
In order to compute the values of 6Gs1 in water and in some nonaqueous solvent we have measured the solubilities of methane and ethane in a series of solvents. These data furnish the required information necessary for estimating the solvophobic interaction through (1.2). Although we have used only a limited number of solvents, one can safely conclude that water is indeed an outstanding liquid as far as we are concerned with both the values and the temperature dependence of O G S 1 . The Journal of Physical Chemistry, Vol. 78, No. 2, 7974
176
M.Yaacobi and A. Ben-Naim 760
- 1.25 740
Methaml
560
I - Propanol
Ethanol
540
I-Pentanol l-But0nol
- 1.50
1-Hexanal 520
Ethanol Methanol I-propanol
CI
500 h
480
I-butanol
I-penlanol
I-hexanol
H20
10
I5
20
25
30
t'C
Figure 1. Ostwald absorption coefficients perature for methane in various solvents.
as a function of tem-
TABLE I: Polynomial Coeficients in (2.2) a n d t h e S t a n d a r d Deviation for E a c h Set of Measurements .
SolvenL
1
c
IJ
SLandnrd doviaLion
Methanol Ethanol 1-Propanol 1-Butanol 1-Pentanol 1-Hexanol 1,4-Dioxane Cyclohexane
Methane 0.03729 -18.546 2,604.5 0 ,01024 - 2 ,636 255.3 - 0 ,04361 29.028 -4,378.1 4,090.4 0.05623 - 29 ,065 390 , 8 0.01169 -3.230 - 0.02895 20.591 - 3,087.6 1,099.8 0 ,00988 - 4 ,781 -0.01791 12.053 - 1,822.9
1.137 0.912 1.977 1.760 2.233 1.753 3.997 1.678
Methanol Ethanol 1-Propanol 1-Butanol 1-Pentanol 1-Hcxanol 1,4-Dioxane Cyclohexane
Ethane 25 ,237 30 .439 2 ,606 51 ,627 -0.02155 12.817 - 0,02364 19.124 0.20190 -115.36 0,05878 - 29.932
1.135 1.800 1.182 1.585 3.505 3.824 3.056 2.970
- 0,03440 - 0 ,04241 0 ,00607 - 0 ,07884
-4,979.8 -5.901 .o - 1,928. O - 9 ,001 ,o - 3,395.6 -4,183.0 15,942.3 2,712.0
The solubilities of methane and ethane were determined as described in the preceeding article.2 The solvents 1-propanol, 1-hexanol, and cyclohexane were CP whereas all other solvents were of analytical grade. The Ostwald absorption coefficients y for methane and ethane in water, methanol, ethanol, 1-propanol, l-hutanol, I-pentanol, 1-hexanol, 1,4-dioxane, and cyclohexane were calculated directly from the volume of gas dissolved in a given volume ofthe solvent. A comparison of the values of y of methane and ethane in alcoholic solutions measured in this work with those of Boyer and 13ircher5 shows that our results are about 0-6% lower than theirs. It is difficult, however, to trace the source of the discrepancies between the two sets of results.
DC
Figure 2. The temperature dependence of the solvophobic interaction 6GS1 in kcal/mole computed from (3.4) for water and nonaqueous solvents.
TABLE 11: Values of the Ostwald Absorption Coeficient y S for M e t h a n e and E t h a n e in Various Solvents x Solvent
11. Experimental Section
The Journal of Physical Chemistry, Vol. 78, No. 2, 1974
t
150
100 ~
103
200
250
30'
~~
Water Methanol Ethanol 1-Propanol 1-Butanol 1-Pentanol 1-Hexanol 1,4-Dioxane Cyclohexane
44.8 543.7 556.7 541.7 519.4 492 , 5 472.7 384.1 760.3
Methane 40.5 37.0 536.4 527.8 546.8 537.0 528.2 517.4 511.5 501.6 484.3 476.0 462.2 453.5 387.6 390.7 752 . O 745 . O
34.2 518.0 527.2 509 . O 489.8 467.6 446.3 393.3 739.5
31.9 507.0 517.5 502.9 476.5 459.2 440.4 395.6 735.3
Water Methanol Ethanol 1-Propanol 1-Butanol 1-Pentanol 1-Hexanol 1,4-Dioxane Cyclohexane
69.1 2864 3361 3492 3491 3403 3252 2590 6470
Ethane 59.1 51.4 2678 2518 3117 2909 3241 3014 3225 3008 3155 2935 3034 2842 2548 2465 6067 5673
45.3 2379 2731 2808 2830 2740 2674 2347 5291
40.5 2258 2578 2621 2686 2566 2526 2201 4921
The standard free energy of solution of a solute s is computed by the relation Ap:
=
RT In y s
(2.1)
and the temperature dependence of Apso was fitted to a second-degree polynomial of the form Apbo = a
+ bT + c T 2
(2.2)
where T is the absolute temperature. The coefficients a, b, and c (obtained by the method of least squares) as well as the standard deviation for each set of measurements are reported in Table I.
177
SolvoDhobic Interaction
TABLE 111: Values of the Standard Energy, Entropy, and Enthalpy of Solution for Methane in Several Solventsa Solvent
t,
oc
Water
10 25
Methanol
10
Ethanol 1-Propanol 1-Butanol 1-Pentanol 1-Hexanol 1,4-Dioxane Cyclohexane
AS8'
AprO
1747 2000 343 .O 390 .O 329.7 379.4 345 .O 400.2 368.7 423 .O 398.6 450.5 421.7 478.2 538.5 553 .O 154.2 179 .O
25 10 25 10 25 10 25 10 25 10 25 10 25 10 25
- 18
- 3400 - 2600
- 15 -3 -4 -3 -3 -4 -3
- 400 - 700 - 600 - 700 - 900 - 500 - 400 - 900 - 500 - 600 - 800 - 500 300 200
-3 -4 -3 -4
-4 -3 -1
-1 -2
-1
- 400 - 200
TABLE IV: Values of the Standard Free Energy, Entropy and Enthalpy of Solution for Ethane in Several Solventsa Solvent
t,
oc
10 25
Methanol
10 25 10 25 10 25 10 25 10 25 10 25 10 25 10 25
Ethanol 1-Propanol 1-Butanol 1-Pentanol 1-Hexanol 1,4-Dioxane Cyclohexane
A&O
AS,"
1504 1833 -592.2 -513.6 -682.2 -595.4 -703.8 -611.8 -703.6 -616.6 -689.2 -597.4 -663.7 -583 .O -535.6 -505.6 -1050.8 -987.3
-24 -20 -6 -5 -6 -5 -6 -6 -7 -5 -6 -6 -6 -5
1 -5 -3 -5
AH,'
-5200 -4200 -2200 -1900 -2500 -2100 -2400 -2500 -2700 -2000 -2500 -2400 -2300 -2100 - 200 -2000 -2000 -2500
Units as in Table 111.
The smoothed values of the Ostwald coefficients for methane and ethane in the various solvents are reported in Table 11. Note that the solubility of methane (as measured by y ) in 1,4-dioxane increases with temperature. In all others the solubility decreases with temperature. This behavior is depicted in Figure 1.
111. Solvophobic Interaction (SI) In order to compute the SI and its temperature dependence we need the standard free energy, entropy, and enthalpy of solution of methane and of ethane in the various solvents. These are computed from the relations
Ap:
=
- RT
In y,
AS," = -[aA&"/aT] AH," = ApSQ4- TAS,"
-.
gsS1
AH,O
a The units for A b o and AHso are cal/mole and for AS," are cal/rnole degree.
Water
TABLE V: Solvophobic Interaction and the Corresponding Entropy and Enthalpy Values for the Reaction 2(Methane) Ethane i n Several Solventw
(3.1)
(3.2) (3.3)
Note that these quantities refer to the process of transfer-
t, "C
Solvent
Water
10 25 10 25 10 25
Methanol Ethanol 1-Propanol
10 25 10 25 10 25 10 25 10 25 10 25
1-Butanol 1-Pentanol 1-Hexanol 1,4-Dioxane Cyclohexane a
*@I
(10")
6HS' (10')
11
+ 1500
0
- 1400
0
- 1300
2
- 600
-1
- 1900
0
- 1500
2
- 700
3
- 800
1
- 1200
- 1990 - 2168 -1278.2 -1293.6 - 1341 . 6 -1354.2 -1393.8 -1412.2 -1441.0 -1462.6 -1486.4 -1498.4 -1507.1 - 1539.4 -1612.6 -1611.6 - 1359.2 -1345.3
Units aa in Table 111.
ring a solute s from a fixed position in the gas to a fixed position in the liquid. The process being carried out a t constant temperature and pressure (for more details see ref 4). The computed values of Apso, ASSo,and AHs" are reported in Tables I11 and IV. Note that the entropy of solution of methane and ethane in water is between -20 and -24 eu whereas in organic solvents the corresponding values range between - 1 and -6 eu. The outstanding low and negative enthalpy of solution of these gases in water is also clear from Tables I11 and IV, The strength of the SI and the corresponding entropy and enthalpy associated with the process of bringing two methane molecules to a short distance are computed by the approximate relations
6G'I
=
6s''
= ASEL"
APE,'
-
2ASweo
(3.4)
- 2ASweQ 6HS' = AHEL" - 2AHM,O
(3.5) (3.6)
Values of 6GS1, 6Ss1, and 6 W are reported in Table V and the temperature dependence of 6GsI is exhibited in Figure 2. From Figure 2 it is clear that both the values of 6GSI and its temperature dependence in water are markedly different from the corresponding behavior in nonaqueous solvents. The significance of the strong HI in water to biological systems has long been recognized.6-8 Various processes such as conformational changes of biopolymers, adsorption of a substrate on an enzyme, etc. are all affected by the strength of the HI. We should like to conclude this article by pointing out that the temperature dependence of HI is also of important biological ~ignificance.~ Consider, for example, the helix coil transition in proteins or any process of denaturation of a biopolymer. One expects that as the temperature increases, the system would tend to break its structure. The fact that the HI strengthened with the increase of temperature may be considered as a counteraction to the tendency of randomization, and aids t o maintain the stable conformation of the polymer. The Journal of Physical Chemistry, Vol. 78, No. 2, 7974
I 78
G . N. Papatheodorou and 0. J. Kleppa
Acknowledgment. This work has been supported in part by the Israel for Basic Research, for which the authors are very grateful. References and Notes (1) Present address, National Institutes of Health, N I A M D D , LMB, Bethesda, Md. 20014.
(2) (a) Ben-Nairn. J. Chem. Phvs., 54. 1387. 3696 (19711; (b) A. BenNairn and M. Yaacobi, J. Phys. Chem., 78, 170 (1974). (3) E. Wilhelm and R. Battino, J. Chem. Phys., 56, 563 (1972). (4) A. Ben-Naim, “An Introduction to a Molecular Theory of Water and Aqueous Solutions,” Plenum Press, New York, N. Y . , in press. ( 5 ) F. L. Boyer and L. J. Bircher, J. Phys. Chem., 64, 1330 (1960). (6) W. Kauzmann.Advan. Protein Chem., 14, 1 1959). (7) G. Nernethy and H. L. Scheraga, J. Phys. Ahem., 66, 1773 (1962). (8) C. Tanford, Advan. Protein Chem., 23, 121 (1968). (9) ti. L. Scheraga, G. Nernethy, and I. 2 . Steinberg, J. Biol. Chem., 237, 2506 (1962).
Thermodynamic Studies of Binary Charge Unsymmetrical Fused Salt Systems. Cerium(1I I) Chloride- Alkali Chloride Mixtures G. N. Papatheodorou* and 0 . J. Kleppa The James f r a n c k Institute and The Department of Chemistry, The University of Chicago, Chicago, lilinois 60637 (ReceivedJune 11, 1973) Publication costs assisted by the National Science foundation
The molar enthalpies of mixing (AW)in the liquid alkali chloride-cerium chloride mixtures have been measured at 845”. All the interaction parameters (AM = AHM/XlX2) are negative, increasing sharply from about -1 kcal/mol in LiC1-CeC13 to about -25 kcal/mol in CsCl-CeC13. The systems also have significant energetic asymmetries with more negative values of AM in the alkali chloride-rich than in the cerium chloride-rich regions. The results are discussed with respect to the following points: (1) comparison with the Davis conformal solution theory for the enthalpies of mixing of charge unsymmetrical fused salt mixtures; (2) “complexing” in the mixture.
Introduction
Experimental Section
While thermochemical and thermodynamic information is now available for a significant number of binary charge unsymmetrical fused salt mixtures of the type AX-BX2,I much less is known about the corresponding AX-BX3 systems. The present paper represents the first detailed thermochemical study of a system of this type, and covers the liquid systems AC1-CeCl3, where A = Li, Na, K, Rb, or cs. The thermodynamic properties of these mixtures previously were studied by equilibrium emF-4 and phase diagram5 methods. The e m F data were interpreted to indicate the formation of various complex entities such as CeC14 - and CeCl& . Strong evidence was presented for CeC14-, while the evidence for CeC163- was much less conclusive. In the present communication we report the enthalpies of mixing ( A W ) of cerium(II1) chloride with the alkali chlorides. The purpose of this work is to obtain information on the systematics of the thermodynamic behavior of unsymmetrical solution systems and to examine the possibilities of “complex” formation in these mixtures. The new data are compared with the enthalpy measurements on the LaC13-AC16 systems and are discussed in terms of the conformal solution theory of Davis.’ Finally by combining the calorimetric and emf data we have obtained the partial excess entropies of mixing of CeC13 in liquid CeC13-NaC1 and CeC13-KC1 mixtures.
The measurements of the integral enthalpies of mixing were of the “crucible-double breakoff” type, where both liquid salts were contained in fused silica containers.l.8 The calorimetric apparatus used, its calibration, and the required corrections have been described elsewhere.lVs All experiments were carried out at 845”. The cerium(II1) chloride was purchased from Alfa Inorganics Inc. The salt was first dried under vacuum by slowly increasing the temperature to 200”. At that temperature a gaseous mixture of cC14-N~ was passed over the salt and the temperature was raised slowly (-50”/hr) to 500”. Finally, the salt was melted under a Nz atmosphere. The sources and methods of purification of the alkali halides were the same as before.1 The purity of the salts was checked by passing an aqueous solution through a cation-exchange column and titrating the resulting acidic solution. The premelted salt assayed 98.8 mol 7’0 CeC13.
The Journal of Physical Chemistry, Vol. 78, No. 2, 1974
Results and Discussion All experimental results obtained in the course of the present investigation are recorded in Table 1.9 Graphs of the enthalpy interaction parameter, AM = .AHM/X1X2, us. mole fraction, X z = XCeC13,are given in Figure 1. For each system listed in Table I the values of AM were fitted, by the method of least squares, to fifth-order polynomials of Xz. The coefficients of the least-squares expressions
