J. Phys. Chem. 1986, 90.4621-4623 but that the 1/F2 - 1 vs. l / F l - 1 plot for HMPA curved upward! Since linear polyethers are much weaker cation-binding ligands, far less Me,SO or H M P A is needed to release the resin-bound salt than with the R N l 8 C 6 resin. At these low MezSO concentrations 1:l complexes are the more stable species. Hence, by a judicious choice of the competing immobilized ligand the formation of different kinds of complexes can be studied quantitatively. It was pointed out in the Introduction that the stability of a complex such as A-CrM'S depends largely on the extent to which the cation can penetrate into the crown cavity in order to interact effectively with the molecule S.I This penetration is hindered by bulky substituents in the anion close to where the cation is located (for example, the two nitro groups in the picrate anion). Also, a more planar crown compound such as DB18C6 favors cation penetration since less stretching of the interionic ion pair distance in A-M+ is needed. Not surprisingly, more charge delocalized and planar anions such as the fluorenyl carbanion very easily form A-CrM'S complexes with additives such as THF or tetrahydropyran.6 Such additives promote the formation of crownseparated ion pairs A-CrM+ vs. that of crown-complexed tight ion pairs A-M'Cr. It would be interesting to extend our studies to the more flexible 18-crown-6 where with NaANS the A-CrM+S complex with dioxane is apparently much less stable as indicated by the complexation order shown in Figure 1. The 18C6 is probably more wrapped around the cation leaving little or no space for interaction with a dioxane molecule. Synergistic effects in macrocyclic polyether binding of cations are commonly observed when substituents with converging neutral or ionic binding sites are placed in close proximity to the crown ether c a ~ i t y . ~ - 'This ~ intramolecular effect significantly con-
4621
tributes to the stability of the complex. Reports of synergistic effects in mixtures of macrocyclic polyethers and other cationbinding ligands are far less abundant. Tributyl phosphate is believed to enhance rubidium and cesium picrate extraction into benzene by 15-crown-5 and 12-crown-4.13 The apolar liquid cation exchanger bis(2-ethylhexyl) phosphoric acid when mixed with a crown ether can also enhance the alkali metal extraction ability of the macrocyclic p01yether.I~ The complexity of extraction systems makes it more difficult to study these effects. The competition method utilizing resin-immobilized macrocyclic or linear polyethers constitutes a relatively simple and reliable procedure for acquiring quantitative information on synergistic effects of additives that contribute to the stability of crown ether complexes and which can modify the selectivities of crown ligands. Acknowledgment. We gratefully acknowledge the financial support of the National Science Foundation through its Polymers Program, Grant No. DMR 8504999. Acknowledgment is also made to the donors of the Petroleum Research Fund, administered by the American Chemical Society, for partial financial support. Registry No. THF, 109-99-9; HMPA, 680-31-9; DMF, 68-12-2; Me2S0, 67-68-5; CH3CN, 75-05-8; dioxane, 123-91-1. ~~
~
~
~~~~~~
(7) Helgeson, R. C.; Weisman, G. R.; Toner, J. L.; Tarnowski, T. L.; Chao, Y.; Mayer, J. M.; Cram, D. J. J. Am. Chem. SOC.1979, 101, 4928. (8) Lehn, J. M.; Vierling, P.; Hayward, R. C. J. Chem. Soc., Chem. Commun. 1979, 296. (9) Reinhoudt, D. N.; de Jong, F.; van de Vondervoort, E. M. Tetrahedron 1981. 37. 1753. (10) Reinhoudt, D. N.; de Jong, F.; van de Vondervoort, E. M. Tetrahedron 1981, 37, 1985. (11) Schultz, R. A.; Dishong, D. M.; Gokel, G. W. J. Am. Chem. SOC. 1982. 104. 625. (12) Bartsch, R. A.; Czech, B. P.; Kang, S. I.; Stewart, E.; Waltowiak, W.; Charewicz, H. A.; Heo, G. S.; Son, B. J. Am. Chem. Soc. 1985,107,4997. (13) Takada, Y. Bull. Chem. SOC.Jpn. 1981,526, 54. (14) Kinard, W. F.; McDowell, W. J. J. Inorg. Nucl. Chem. 1981, 43, 2947.
(6) Takaki, U.; Hogen Esch, T. E.; Smid, J. J. Am. Chem. SOC.1971,93, 6760.
Heat of Solution of Methane in Water from 0 to 50 O C Hossein Naghibi,+S. F. h c , t and S. J. Gill* Department of Chemistry, University of Colorado, Boulder, Colorado 80309 (Received: February 7, 1986; In Final Form: May 10, 1986)
Heats of solution of methane into water have been determined by direct calorimetric measurement over a range of temperature from 0 to 50 O C . The results allow the determination of the heat capacity change and the temperature dependence of the heat capacity change. A favorable comparison is found with the high-precisionvan't Hoff study of Rettich et al. The observed temperature dependence of the solute heat capacity supports the predictions of Gill et al. based on a simple two-state model of water molecules in the first solvation shell.
Introduction The large solute heat capacity - - ofamlar molecules in water has been ascribed to the formation of iceberg-like clusters of water molecules about the hydrophobic solute.' The nature of this iceberg cluster has been the subject of various statistical mechanica12-' and computational dynamic6 and Monte C a r 1 0 ~ - ~ studies. A direct correlation between the number of water molecules in the first solvation shell and various solute thermodynamic properties was noted in a set of studies on experimentallylO~*' and comp~tationally~ determined properties. The results based on gaseous h y d r o c a r b ~ n s ~ Jcover ' * ~ ~ the largest range of solvation shell water numbers and have led to the formulation of Chemistry Department, University of Kerman, Kerman, Iran. 'Current address: Department of Chemistry, Colorado State University, Ft. Collins, CO 80523.
0022-3654/86/2090-4621$01.50/0
a two-state model where each solvated water molecule acts independently of its neighbor^.'^ A critical test of such a model (1) Frank, H. S.; Evans, M. W. J . Chem. Phys. 1945, 13, 507.
(2) Frank, H. S.;Wen, W.-Y. Discuss. Faraday SOC.1957, 24, 133. (3) Miller, K. W.; Hildebrand, J. H. J. Am. Chem. SOC.1968, 90, 3001. (4) Nemethy, G.; Scheraga, H. A. J . Chem. Phys. 1962, 36, 3401. ( 5 ) Ben-Naim, A. Hydrophobic Interactions; Plenum: New York, 1980. (6) Rossky, P. J.; Karplus, M. J . Am. Chem. Soc. 1979, 101, 1913. (7) Swaminathan, S.;Harrison, S.W.; Beveridge, D. L. J. Am. Chem. Soc. 1978, 100, 5705. (8) Alagona, G.; Tani, A. J. Chem. Phys. 1980, 72, 580. (9) Jorgonsen, W. L.; Gao, J.; Ravimohan, C. J . Phys. Chem. 1985, 89, 3470. (10) Dec, S. F.; Gill, S. J. J. Solution Chem. 1985, 14, 417. (11) Dec, S. F.; Gill, S.J. J . Solution Chem. 1985, 14, 827. (12) Olofsson, G.; Oshodi, A. A.; Qvarnstrbm, E.; Wadsb, I. J. Chem. Thermodyn. 1984, 16, 1041.
0 1986 American Chemical Society
4622 The Journal of Physical Chemistry, Vol. 90, No. 19, 1986 TABLE I: Heat of Solution of Methane in Water from 0 to 50 "C AHo f 2a, no. of temp, K kJ mol-' determinations 7 273.24 -18.53 f 0.10 10 274.00 -18.16 f 0.14 0.10 8 -17.74 276.29 20 -17.56 f 0.06 278.15 5 -16.34 f 0.16 283.15 8 -15.43 f 0.05 288.15" 11 -14.29 f 0.07 293.17 -13.18 f 0.07 10 298.15b -1 1.78 f 0.03 6 303.39 -10.70 f 0.07 6 308.17 4 -9.88 f 0.05 313.20 5 318.28 -9.04 f 0.14 5 -8.43 f 0.06 323.17
*
" Reference
1 1. *Reference 27.
is given by the predicted temperature dependence of the solute heat capacity. In the few cases where such high-precision heat capacity existslel* the model was found to be adequate. However, the need for more extensive accurate heat capacity information was apparent. Three general approaches are available: (1) precise van't Hoff determination solubility as a function of temperature, (2) direct solute heat capacity evaluations, and (3) accurate measurements of heats of dissolution over a range of temperature. A highly precise van't Hoff approach has been employed by Rettich et aLI4 The second approach has been utilized by Biggerstaff et aLzoin a study of argon in water from 306 to 578 K. The third method is employed in this paper. In general it is found that these more extensive determinations support the predictions of the two-state solvation model.
Experimental Section The microcalorimeter and its method of operation have been Methane was obtained from Matheson Gas Products with a purity of 99.99%. The partial pressure of water vapor was calculated from the results of Ambrose and LawrensonZZand the virial coefficient of methane was obtained from the compilation of Dymond and Smith.z3 The highest temperature that could be employed in our experiments was 50 OC since it was found that nonreproducible results were obtained a t higher temperatures, presumably due to high water vapor pressures and condensation in the connecting lines to the calorimeter. These problems were not encountered in the lower temperature studies. Results Values of AHo, the standard enthalpy change upon dissolution of methane into water, are given in Table I at the various temperatures used. Twice the standard error (2a) is noted along with the number of experimental determinations at each temperature. The data were analyzed by using a Taylor series expansion in terms of the temperature T about an arbitrary reference temperature denoted by 0. This approach is analogous to the Clarke and GlewZ4 (13) Gill, S. J.; Dee, S. F.; Olofsson, G.; Wadso, I. J . Phys. Chem. 1985, 89, 3758. ( 1 4 ) Rettich, T. R.; Handa, Y . P.; Battino, R.; Wilhelm, E. J. Phys. Chem. 1981,85, 3230.
(15) Rettich, T. R.; Battino, R.;Wilhelm, E. Ber. Bunsenges. Phys. Chem.
1982,86, 1128.
(16) Rettich, T. R.; Battino, R.; Wilhelm, E. J . Solution Chem. 1984, 13. 335.
(17) Benson, B. B.; Krause, Jr., D.; Peterson, M. A. J . Solution Chem. 1979, 8, 655. (18) Bergstrom, S.; Olofsson, G. J . Solution Chem. 1975, 4 , 535. (19) Crovetto, R.; Fernandez-Prini, R.; Japas, M. L. J. Chem. Phys. 1982, .76 -, 11-177 - - . .. (20) Biggerstaff, D. R.; White, D. E.; Wood, R. H. J . Phys. Chem. 1985, 89, 4378. (21) Dee, S. F.; Gill, S. J. Rev.Sci. Instrum. 1984, 55, 765. (22) Ambrose, D.; Lawrenson, I. J. J . Chem. Thermodyn. 1972, 4, 7 5 5 . (23) Dymond, J. H.; Smith, E. B. The Virial Coefficients of Pure Gases and Mixtures. A Critical Compilation; Clarendon: Oxford, U.K., 1980.
Naghibi et al.
--IO
.
0 \
i
t
270
200
290
300 T
310
3.20
330
(K)
Figure 1. Enthalpy change, AH', as a function of temperature for the dissolution of methane into water. Ranges of experimental results at a given temperature are indicated by vertical boxes. The theoretical line was calculated by least-squares analysis of all points using eq 1. TABLE 11: Comparison of Calorimetric and van't Hoff Heats of Solution of Methane in Water at Different Temperatures AHo. kJ mol-' calorimetric van't Hoff, T, K this work" ref 1 2 ~ ref 14c 273.15 -18.56 f 0.08 -19.43 f 0.19 -18.13 f 0.12 278.15 -17.44 f 0.05 -16.85 f 0.06 283.15 -16.33 f 0.05 288.15 -15.24 f 0.06 -15.53 f 0.09 -15.60 f 0.04 -14.38 f 0.04 293.15 -14.17 f 0.07 298.15 -13.12 f 0.07 -13.06 f 0.15 -13.18 f 0.04 -12.01 f 0.05 303.15 -12.08 f 0.07 -10.70 f 0.09 -10.87 f 0.04 308.15 -11.06 f 0.07 -9.75 f 0.04 313.15 -10.06 f 0.08 318.15 -9.08 f 0.10 -8.66 f 0.07 -7.59 f 0.13 323.15 -8.12 f 0.14 'Uncertainty is twice the standard deviation as calculated by using an equal temperature interval data set based on eq 1. buncertainty as reported. CUncertainty is twice the standard deviation as calculated according to the method of Clark and Glew.
TABLE 111: Comparison of Calorimetric and van't Hoff ACO, and d(AC".)/dT in Water at Different Temperatures calorimetric' van't Hoffb T, K ACO, (dACo,/dT) ACO, dACop/dT) 273.15 226.9 f 9.8 -0.72 f 0.20 262.7 f 16.1 -1.04 f 0.58 278.15 223.3 f 7.5 -0.72 f 0.20 257.5 f 13.2 -1.04 f 0.58 283.15 219.7 f 5.7 -0.72 f 0.20 252.3 f 10.4 -1.04 f 0.58 288.15 216.1 f 4.0 -0.72 f 0.20 247.1 f 7.6 -1.04 f 0.58 293.15 212.5 f 2.9 -0.72 f 0.20 241.9 f 4.6 -1.04 f 0.58 298.15 209.0 f 2.9 -0.72 f 0.20 236.7 f 3.0 -1.04 f 0.58 303.15 205.4 f 4.2 -0.72 f 0.20 231.5 f 3.2 -1.04 f 0.58 308.15 201.8 f 5.8 -0.72 f 0.20 226.3 f 5.3 -1.04 f 0.58 313.15 198.2 f 7.7 -0.72 f 0.20 221.0 f 8.0 -1.04 f 0.58 318.15 194.6 f 9.6 -0.72 f 0.20 215.8 f 10.8 -1.04 f 0.58 323.15 191.0 f 11.5 -0.72 f 0.20 210.6 f 13.6 -1.04 f 0.58 "This work. Uncertainty is twice the standard deviation as calculated by using an equal temperature interval data set based on eq 1. bRettich et a]. (ref 14). Uncertainty is twice the standard deviation as calculated according to the method of Clark and Glew.
procedure for estimation of thermodynamic parameters and their errors from solubility data. The relevant equation for our data is expressed as follows: AHo(T) =
Higher order terms reflect the temperature-dependent higher derivatives of the standard-state heat capacity change ACo,(B). (24) Clarke, E. C. W.; Glew, D. N. Trans. Faraday SOC.1966, 62, 539.
Heat of Solution of Methane in Water A least-squares fit of eq 1, using an arbitrary temperature 19, provides the best estimate of the thermodynamics parameters of the system. This is illustrated in Figure 1 by the theoretical line determined by the three-parameter eq 1 with the reference temperature of 298.1 5 K. The inclusion of a fourth term in the fitting equation was not considered to be significant when examined by the variance ratio F test. The results of the least-squares analysis of the data at selected reference temperatures with 5-deg intervals from 273.15 to 333.15 K are summarized in Table 11. Also included in this table are the calorimetric determinations of Olofsson et a1.I2 and the van’t Hoff results of Rettich et a1.I4 as analyzedz5by employment of the Clarke and Glew method. The general agreement of the enthalpies of dissolution of methane into water at these temperatures by direct and van’t Hoff analysis is gratifying. This agreement carries over as well to the heat capacity change and its temperature derivative within reasonably expected error limits as shown in Table 111. This is the first case where it has been possible to make such a detailed comparison between direct calorimetric and van’t Hoff values.
Discussion Our principal motivation in determining the higher temperature derivatives of the heats of solution of methane in water was to provide independent evidence of the temperature dependence of the heat capacity change of hydrophobic solutes. Such results provide a test of a simple two-state modelL3which attributes the anomalously large heat capacity of hydrophobic solutes to N independently behaving water molecules in the first solvation shell. The excess heat capacity for this system is
The Journal of Physical Chemistry, Vol. 90, No. 19, 1986 4623
300
200
100
0 100
200
300
400
500
600
400
500
600
T (K)
300
200
100
0 100
200
300
T (K) Figure 2. Heat capacity change vs. T for methane in water. The theoretical lines were calculated by using eq 2 with N = 17, AH = 6.5 kJ/mol, T, = 1/370: (a) this work (Table 111) with vertical lines equal to 2u; (b) Crovetto et al. (ref 19) with 2u error range as calculated by the Clarke and Glew method at selected temperatures from the wide-
Here C, is taken as the heat capacity of water molecules in the solvation process, Cop,the heat capacity of these molecules in the ground-state configuration. The excess heat capacity of the solvation process, C, - Cop,is assumed to be independent of the intrinsic heat capacity of the solute and is determined by the measured values, ACp The reciprocal temperature is T (1 / 7‘) and T , is the reciprocal temperature where the concentrations of water molecules in the two states are equal; Le., the temperature dependence of the equilibrium constant between the two states of water molecules is exp[(-AH/R)(T - rm)]. This model represents a highly simplified view of the behavior of the water molecules in the solvation shell. We have estimated N by determining cavity surface area, A,, for various solutes by the method of Herman# and dividing by the effective surface area of a water molecule (9 AZ).l3 This method of computation for N agrees within 100% with those systems for which Monte Carlo results are Previous argumentsL3have suggested that AH is of the order of hydrogen-bond energies, 6.5 kJ/mol-l, and T , = 1/370 K. The temperature dependence of the heat capacity change predicted with these values, using eq 2, is shown in Figure 2a along with the experimental calorimetric determinations from 0 to 50 O C . The observed agreement with the experimental calorimetric results for methane and simple theory is over a limited temperature range. Solubility studies by Crovetto et al.,I9 though not of the accuracy of Rettich et aI.,l4 have covered a large range (300-600 K). We have fitted their results by use of the Clarke and Glew (25) Dec, S. F.; Gill, S. J. J . Chem. Educ. 1985, 62, 879. (26) Hermann, R. B. J . Phys. Chem. 1976, 76, 2754. (27) Dec, S.F.; Gill, S.J. J . Solution Chem. 1984, 13, 27.
range temperature-dependent solubility data. equations which as noted enable an estimate of the heat capacity change along with probable error. The results are shown in Figure 2b at six selected temperatures, along with the theoretical curve. The observed agreement over the extended temperature range is supportive of the general features of the proposed hydrophobic solvation model. However, the only true direct determination of solute heat capacity of a hydrophobic solute at very high temperatures is that of argon by Biggerstaff et aLZ0 Their study indicates the initial trend of a decrease in solute heat capacity with increase in temperature above room temperature, but with temperature above 400 K there is a marked increase presumably reflecting the change in water as the critical point is approached. The results of Crovetto et aI.l9 do not show this behavior, presumably due to the lower precision available in their experiments. Direct heat capacity measurements on dissolved methane in water would be helpful in further tests of the two-state solvation model. It might also be pointed out tht even though the limited heat capacity data presently available support the predictions of a simple two-state model, this does not mean that such a model will necessarily provide an adequate description of all properties attributable to hydrophobic solvation. One hopes that the present thermodynamic results which bear out the adequacy of a two-state model will prompt other investigations on the possible structural nature of these states, perhaps by means of theoretical simulations, spectroscopic, and scattering studies. Acknowledgment. We acknowledge the assistance of NSF Grant PCM8019930 and the University of Kerman for providing sabbatical to Dr. Hossein Naghibi. Registry No. Methane, 74-82-8.
