J. Phys. Chem. 1987, 91, 245-248
245
of 2 with values reported in the literature. The only experimental observation which canriot be explained is the value of the electron affinity of C6F6 determined from the endothermic charge transfer from S-.5
C-H direction. Indeed, the electron impact studies show dissociations in both directions increasing the number of low-lying u states. The decrease of 0.13 eV in the adiabatic electron affinities in going from C6Fs to C6F5H is reasonable. In summary, the potential energy curves support the ECD data obtained for the negative ions of C6F6 and indirectly support the ECD data obtained for C6F5H. Thus, it appears that the ECD results are reasonable values for the ground-state electron affinities. The values of the rate constants for thermal electron attachment determined in the ECD at 1-atm pressure agree within a factor
Acknowledgment. We thank the Robert A. Welch Foundation, Grant E-095, for financial support of this work. The helpful suggestions of the reviewers are also recognized, especially in pointing out references which had been overlooked. Registry No. C6F,, 392-56-3; C,HF,, 363-72-4.
Heats of Solution of Ethane and Propane in Water from 0 to 50 O C Hossein Naghibi: S. F. Dec,* and S. J. Gill* Department of Chemistry, University of Colorado, Boulder, Colorado 80309 (Received: August 5, 1986; In Final Form: September 8, 1986)
An extensive set of measurements of the heats of solution of ethane and propane into water has been determined by direct calorimetry over a range of temperatures from 0 to 50 OC. The temperature dependence of the heats of solution permits an accurate determination of the heat capacity change for the dissolution process as a function of temperature. These results agree with the predictions based on a simple two-state model of water molecules in the first solvation shell (Gill et al. J. Phys. Chem. 1985,89, 3758) and suggest that the unique thermodynamic properties of hydrophobic solvation are largely due to water of the first solvation shell.
Introduction In a previous paper' we carried out an extensive study of the heats of solution of methane into water over as wide a temperature range as is currently experimentally practical. Our purpose in that study was to obtain precise energetic information about a simple hydrophobic solute by direct calorimetric methods so that a critical comparison could be made with very precise van't Hoff studies.2 The results have been shown to be of particular importance in testing the predictions of a simple two-state mode that was inspired from a variety of thermodynamic results on hydrophobic molecules in water.3 Although the success of that model included data from a number of simple apolar gases dissolved in water, accurate data are lacking for larger gaseous molecules. Larger gaseous molecules might induce different solvation shell arrangements and we therefore set out to determine particularly their heat capacity changes a function of temperature. As a point of historical reference the unusually large solute heat capacity of apolar molecules in water was earlier ascribed to the formation of iceberglike clusters of water molecules about the hydrophobic s01ute.~ The nature of the solvated water has been the subject of various statistical mechanical5-* and computational dynamic9 and Monte Carlo'&'2 studies. The number of water molecules in the first solvation shell is directly correlated with various solute thermodynamic properties as noted in a set of studies on experimentally13J4and computationally12determined properties. The extensive experimental results on gaseous hydrocarbon^^^-'^^^^ which illustrate a wide range of solvation shell water numbers led to the formulation of a simple two-state model where each solvated water molecule acts independently of its neighbor^.^ This model further implied that the principal region that determines the thermodynamic properties of a dissolved hydrophibic solute is confined to the first solvation shell. In the few cases where high-precision heat capacity data e ~ i s t * , ~the ~ - model '~ is found to be adequate. However, the need exists for more extensive Chemistrv DeDartment. Universitv of Kerman. Kerman. Iran. 'Current iddre'ss: Depaitment of Chemistry, Colorado State University Ft. Collins, CO 80523.
0022-3654/87/2091-0245$01.50/0
TABLE I: Heat of Solution of Ethane into Water from 0 to 50 ' C T,K A H o f 20, kJ mol-' no. of determinations 273.24 278.15 283.15 288.15 293.15 298.15' 303.15 308.15 313.15 318.15 323.15
-26.59 -25.16 -23.84 -22.52 -20.59 -19.52 -18.30 -16.59 -15.28 -13.98 -13.38
f 0.10
6 5
f 0.22
5 3 4 12 5 5 5 3 5
+ 0.10
f 0.32 f 0.21
f 0.12 f 0.23 f 0.24 f 0.26 f 0.16 f 0.16
'Reference 29. TABLE 11: Heat of Solution of Propane into Water from 0 to 50 OC T,K A H o f 2a, kJ mol-' no. of determinations 273.24 278.15 283.15 288.15 293.15 298.15' 303.15 308.15 313.15 318.15 323.15
-31.19 -29.83 -27.93 -26.25 -24.42 -23.27 -21.72 -19.72 -18.60 -16.57 -15.58
f 0.26 f 0.17
f 0.22 f 0.25 f 0.24 f 0.26 f 0.01 f 0.20 f 0.12 f 0.23 f 0.19
3 6 5 5 4 13 3 3 5 5 4
'Reference 29. accurate heat capacity information in order to test the validity of the model and its consequences. (1) Naghibi, H.; Dec, S. F.; Gill, S. J . J . Phys. Chem. 1986, 90, 4621. (2) Rettich, T. R.; Handa, Y .P.; Battino, R.; Wilhelm, E. J . Pys. Chem. 1981, 85, 3230. (3) Gill, S. J.; Dec, S. F.; Olofsson, G.; Wadso, I. J. Phys. Chem. 1985, 89. 3758.
0 1987 American Chemical Society
The Journal of Physical Chemistry, Vol. 91, No. 1, 1987
246
-10
/I Ethane
-
n
Y
-2s
-35
270
280
290
300 310 T (K)
320
330
Figure 1. Enthalpy change, A H o , as a function of temperature for the dissolution of ethane and propane into water. Range of experimental results at a given temperature are indicated by vertical boxes. Theoretical line calculated by least-squares analysis of all points using eq 1.
Experimental Section The microcalorimeter and its method of operation have been given.20 Ethane (Matheson Gas Products) and propane (Scientific Gas Products) h a d specified purities of 99.99%. The partial pressure of water vapor was calculated from the results of Ambrose and Lowenson21and t h e virial coefficients of ethane and propane were obtained from t h e compilation of Dymond and Smith.z2
TABLE 111: Comparison of Calorimetric and van't Hoff Heats of Solution (kJ mol-') of Ethane in Water at Different Temperatures calorimetric T, K AHo" AHob van't Hoff AHoc 273.15 -26.70 f 0.18 -26.38 f 0.29 278.15 -25.19 f 0.13 -25.06 f 0.17 283.15 -23.69 f 0.10 -23.72 f 0.08 288.15 -22.23 f 0.10 -22.56 f 0.09 -22.34 f 0.05 293.15 -20.81 fO.10 -20.94 i 0.07 298.15 -19.43 f 0.10 -19.30 f 0.12 -19.51 f 0.08 303.15 -18.09 f 0.10 -18.05 f 0.07 308.15 -16.78 f 0.10 -16.21 f 0.12 -16.58 f 0.05 313.15 -15.51 f 0.10 -15.05 f 0.08 318.15 -14.28 f 0.14 -13.51 f 0.16 323.15 -13.09 f 0.20 -1 1.94 f 0.28 "This work. Uncertainty is twice the standard deviation as calculated by using an equal temperature interval data set based on eq 1. bOlofssen et aLis Uncertainty as reported. cRettich et a1.2 Uncertainty is twice the standard deviation as calculated according to the method of Clark and Glew.
TABLE I V Comparison of Calorimetric and van't Hoff ACpo (J K-I mol-') and d(ACpo)/dTof Ethane into Water at Different Temperatures calorimetric" van't Hoffb ACpo (dACpo/dT) T. K ACpo (dACpo/d7') 273.15 310.5 f 8.0 -0.76 f 0.16 260.7 f 27.6 1.13 f 1.09 278.15 303.0 f 6.6 -0.76 f 0.16 266.3 f 22.3 1.13 f 1.09 283.15 295.4 + 5.1 -0.76 f 0.16 271.9 f 17.0 1.13 f 1.09 288.15 287.8 f 3.8 -0.76 0.16 277.6 f 11.8 1.13 f 1.09 293.15 280.2 f 2.8 -0.76 f 0.16 283.2 f 6.8 1.13 f 1.09 298.15 272.6 f 2.4 -0.76 f 0.16 288.6 i 4.1 1.13 f 1.09 303.15 265.0 f 3.0 -0.76 f 0.16 294.5 i 6.8 1.13 f 1.09 308.15 257.4 f 4.2 -0.76 + 0.16 300.1 f 11.6 1.13 i 1.09 313.15 249.8 f 5.5 -0.76 f 0.16 305.8 f 16.8 1.13 f 1.09 318.15 242.2 f 7.0 -0.76 f 0.16 311.4 f 22.1 1.13 f 1.09 323.15 234.6 f 8.5 -0.76 f 0.16 317.1 f 27.5 1.13 f 1.09
+
Results F r o m t h e heat of dissolution of the hydrocarbon gases at n e a r atmospheric pressure conditions, values of AH', t h e standard enthalpy c h a n g e upon dissolution of the hydrocarbon gases into water, were determined. The results of the numerous experiments are summarized in T a b l e s I and 11. Twice the standard error (20.) is given along with t h e number of experimental determinations a t each temperature. The t e m p e r a t u r e dependence of the results may be exprrssed in terms of a standard Taylor's expansion of t h e enthalpy change a n d its derivatives as follows:
AH'(Tl = \
Naghibi e t al.
"This work. Uncertainty is twice the standard deviation as calculated by using an equal temperature interval data set based on eq 1. bOlofsson et Uncertainty as reported. cRettich et aL2 Uncertainty is twice the standard deviation as calculated according to the method of Clark and Glew.
I
AH'(6)
+ A C p o ( 0 ) ( T -0) +
i(a) d AC,,'
( T - 0)'
+ ... (1)
8
w h e r e 0 is an a r b i t r a r y reference t e m p e r a t u r e and AC,' (the standard h e a t capacity change) is t h e first derivative of the s t a n d a r d enthalpy change. H i g h e r order t e r m s reflect t h e tem-
(4) Frank, H. S.; Evans, M. W. J . Chem. Phys. 1945, 13, 507. (5) Frank, H. S.;Wen, W.-Y. Discuss. Faraday Sot. 1957, 24, 133. (6) Miller, K. W.; Hildebrand, J. H. J . Am. Chem. Sot. 1968, 90,3001. (7) Nemethy, G.; Scheraga, H. A. J . Chem. Phys. 1962, 36, 3401. (8) Ben-Naim, A. Hydrophobic Interactions; Plenum: New York, 1980. (9) Rossky, P. J.; Karplus, M. J . Am. Chem. SOC.1979, 101, 1913. (IO) Swaminathan, S.; Harrison, S.W.; Beveridge, D. L. J . Am. Chem. SOC.1978, 100,5705. (11) Alagona, G.; Tani, A. J . Chem. Phys. 1980, 72, 580. (12) Jorgonsen, W. L.; Gao, J.; Ravimohan, C. J . Phys. Chem. 1985, 89, 3470. (13) Dec, S. F.; Gill, S. J. J . Solution Chem. 1985, 14, 417. (14) Dec, S. F.; Gill, S.J. J . Sol. Chem. 1985, 14, 827. (15) Olofsson, G.; Oshodi, A. A.; Qvarnstrom, E.; Wadso, I. J . Chem. Thermodvn. 1984. 16. 1041. (16) Rettich, T. R.; Battino, R.; Wilhelm, E. Eer. Bunsen-Ges. Phys. Chem. 1982, 86, 1128. (17) Rettich, T. R.; Battino, R.; Wilhelm, E. J. Solution Chem. 1984, 13, 335.
(18) Benson, B. B.; Krause, D., Jr.; Peterson, M. A. J . Solution Chem. 1979, 8, 655. (19) Bergstrom, S.; Olofsson, G. J . Solution Chem. 1975, 4, 535. (20) Dec, S. F.; Gill, S. J. Rev. Sci. Instrum. 1984, 55, 765. (21) Ambrose, D.; Lawrenson, I . J. J . Chem. Thermodyn. 1972, 4, 755. (22) Dymond, J. H.; Smith, E. B. The Virial Coefficients of Pure Gases and Mixtures. A Critical Compilation; Claredon Press: Oxford, 1980.
TABLE V Comparison of Calorimetric and van't Hoff Heats of Solution (kJ mol-') of Gaseous Propane in Water at Different Temwratures calorimetric T, K AHoa AHob van't Hoff A H o c 273.15 -31.32 f 0.25 -3 1.7 278.15 -29.66 f 0.17 -29.9 283.15 -27.99 f 0.13 -28.0 288.15 -26.34 f 0.12 -26.62 f 0.14 -26.2 293.15 -24.72 f 0.15 -24.3 298.15 -23.11 f 0.13 -22.90 f 0.08 -22.5 303.15 -21.53 f 0.13 -20.6 308.15 -19.96 f 0.12 -18.84 f 0.12 -18.8 313.15 -18.42 f 0.13 -17.0 318.15 -16.90 f 0.17 -1 5.1 323.15 -15.39 f 0.24 -13.3 "This work. Uncertainty is twice the standard deviation as calculated by using an equal temperature interval data set based on eq 1. bOlofssen et aLi5 Uncertainty as reported. 'Wilhelm et aLZ5 No uncertainty of the enthalpy charge is available from their analysis. However, the percentage standard deviation of the fitted Henry's constant was reported as 4.6, indicative of relatively large errors. perature-dependent higher derivatives of t h e standard state h e a t capacity change. A conventional least-squares fit of t h e d a t a t o eq 1 provides the best estimates of t h e thermodynamic parameters of t h e system. This is illustrated in Figure 1 by t h e theoretical lines determined by t h e three-parameter eq 1 with a reference temperature of 298.15 K. T h e inclusion of a fourth t e r m in t h e fitting equation was not considered t o b e significant.
The Journal of Physical Chemistry, Vol. 91, No. 1 , 1987 247
Heats of Solution of Ethane and Propane TABLE VI: Comparison of Calorimetric and van’t Hoff ACpo (J K-’ mol-‘) and d(AC,O)/dTof a Solution of Gaseous Propane into Water at afferent Temperatures T, K 273.15 278.15 283.15 288.15 293.15 298.15 303.15 308.15 313.15 318.15 323.15
calorimetrica d(AC.O)/dT
AC,O 339.8 f 11.2 335.7 f 9.2 331.6 f 7.3 327.4 f 5.4 323.2 f 3.8 319.0 f 3.1 314.9 f 3.6 310.7 f 5.1 306.5 f 6.9 302.4 f 8.9 298.2 f 10.9
-0.42 -0.42 -0.42 -0.42 -0.42 -0.42 -0.42 -0.42 -0.42 -0.42 -0.42
calorimetric* van’t HofF AC,”
f 0.21 f 0.21 f 0.21
f 0.21 f 0.21 f 0.21 f 0.21 f 0.21 f 0.21 f 0.21 f 0.21
389 f 20
AC.O 368 368 368 368 368 368 368 368 368 368 368
‘This work. Uncertainty is twice the standard deviation as calculated by using an equal temperature interval data set based on eq 1. *Olofssonet Uncertainty as reported. CWilhelmet al.25 No uncertainty estimate is available for this parameter. The results of the least-squares analysis of the data for ethane at selected reference temperatures with 5-deg intervals from 273.1 5 to 323.15 K are summarized in Tables I11 and IV. Also included in these tables are earlier calorimetric determinations of Olofsson et al.,Is obtained by a batch technique, and the precise van’t Hoff results of Rettich et a1.2 as analyzed by employment of the Clarke and Glew method.23s24 The general agreement of .the enthalpies of dissolution of ethane into water at low and near room temperatures by direct and van’t Hoff analysis is evident. However, at greater temperatures our results deviate significantly from the van’t Hoff results.z A significant difference is seen between the calorimetric and van’t Hoff determined heat capacity changes as a function of temperature. The average of both types of determinations over the 0 to 50 OC range are quite similar, but the trend with temperature is just opposite. The calorimetric values follow the expected trend in this low temperature range of decreasing with increase in temperature, as is also found with other nonpolar molecule^.^^^ It should also be noted that Olofsson et al.Is found a somewhat larger value at 25 OC of 317 f 10 J K-I mol-’ using a batch technique at three temperatures. Present and previous results obtained for propane are tabulated in Tables V and VI. There is reasonable agreement among the steady-state and batch calorimetric values of the enthalpy changes. However, the agreement with the van’t Hoff determinationsz5is probably fortuitous since the solubility studies of propane in water were made by low precision techniques with an estimated percentage standard error of 4.6% for the representation of the solubility as a function of temperature. The high precision method of Benson et a1.I8 is capable of giving determinations of solubility to better that 0.01%. The comparison of the heat capacity changes a t various temperatures is shown in Table VI. Our values are again somewhat lower than those obtained by earlier, more limited calorimetric experiment^.'^ The low-precision temperature-dependent solubility studieszs yield a constant value for the heat capacity change of 368 J K-I mol-’. In view of the large uncertainties in the solubility determinations these van’t Hoff results must contain a very large error of uncertainty. From the extensive data set collected in the present study, we find a well-defined first derivative of the heat capacity change, which has not been evaluated previously.
Discussion The availability of high-precision results on ethane and propane now permits a more extensive test of the simple model3 proposed to describe the heat capacity properties of a hydrophobic solute in water. As noted the anomalously large heat capacity is at(23) Clarke, E. C. W.; Glew, D. N. Trans. Faraday SOC.1966, 62, 539. (24) Dec, S. F.; Gill, S . J. J . Chem. Educ. 1985, 62, 879. (25) Wilhelm, E.; Battino, R.;Wilcock, R. J. Chem. Rev. 1977, 77, 219.
400
300 200 100 0
I
100
200
300
400
500
600
T (K)
500
400
300 200 100
0
I 100
200
300
400
500
600
T (K) Figure 2. Heat capacity change vs. T for (a) ethane and (b) propane in water. The solid theoretical lines were drawn by using the predictions for an independent two-state model for solvated water with the number of solvated water molecules N equal to 21 for ethane and 25 for propane.” The experimental results are represented by points with vertical lines indicating twice the estimated standard error of the point as calculated by the method of Clarke and G I ~ w . * ~
tributed to the special properties of the water molecules in the first solvation shell. The number of such molecules is denoted by N . Each solvated water molecule is assumed, as a first approximation, to exist in equilibrium between two different thermodynamic states. The excess heat capacity and its temperature dependence for such a system has been de~cribed.~ The important features of the model are that (1) the heat capacity is proportional to thee number of solvated water molecules as determined by computer (2) the two energetic states of the solvated water are separated by an energy equivalent to a hydrogen bond, and (3) a temperature (370 K) exists at which the population of the two states is equal. This model predicts a slow decrease in the partial molar heat capacity of a hydrophobic solute with increasing temperature. In Figure 2 the results of the heat capacity change upon dissolution from the gaseous state are shown for ethane and propane along with the theoretical curves generated from estimates of the number of first solvation shell water molecules (ethane 21, propane 25) and from an energy difference of 6.5 kJ mol-’ solvation water for the assumed two states. The observed agreement for ethane and propane with the predictions of this simple theory extends the number of systems for which this model has been found to be adequate. However the number is still quite small because of the limited high-precision data available. Direct heat capacity measurements on dissolved ethane and propane in water would be helpful in further tests of the two-state solvation model. It should be stressed that even though the more extensive heat capacity data presented here support the predictions of a simple two-state model, this does not mean that it will be adequate to (26) Hermann, R. B. J . Phys. Chem. 1976, 76, 2754.
248
The Journal of Physical Chemistry, Vol. 91, No. 1 , 1987
describe all properties attributable to hydrophobic solvation. A direct determination of solute heat capacity of a hydrophobic solute has been made for argon by Biggerstaff et aLZ7 Their study indicates the decrease in solute heat capacity with increase in temperature above room temperature, but at very high temperatures a marked increase occurs as the critical point is approached. Obviously, such a result cannot be accounted for by the simple two-state model presented here. A more extensive treatment of two-state concepts as they apply to particular properties of water has been formulated by Grunwald.28 The descriptive features of each water molecule are determined by the number of hydrogen (27) Biggerstaff, D. R.; White, D. E.; Wood, R. H. J . Phys. Chem. 1985, 89, 4378. (28) Grunwald, E. J . Am. Chem. SOC.1984, 106, 5414. (29) Dec, S.F.;Gill, S. J. J . Solurion Chem. 1984, 13, 27.
Naghibi et al. bonds it makes with adjacent water molecules. Inserting a hydrophobic solute into water perturbs number of solvated molecules in the different hydrogen bond states. The distribution of states is sensitive to temperature resulting in the explanation of the large heat capacity observed for hydrophobic solutes in water. One hopes that the present series of thermodynamic results will assist our understanding of the possible structural nature of the solvated water and inspire further detailed investigation by means of theoretical simulations and spectroscopic and scattering studies. Acknowledgment. We acknowledge the assistance of N S F Grant PCM8019930 and the University of Kerman for providing sabbatical to Dr. Hossein Naghibi. We thank Ernest Grunwald for making a manuscript on hydrophobic solvation available to us. Registry No. Ethane, 74-84-0; propane, 74-98-6
ADDITIONS AND CORRECTIONS 1984, Volume 88
S. Ruhman, 0. AMer, and Y. Haas*: Ground-State Photochemistry of Tetramethyldioxetane. 1. Energy Distribution among Molecules Excited by Multiple Photon Absorption. Page 6406. The correct form of eq AS is 13
C (Fn + F:) +
n=12
18
]lz(Fl4 + p14r)/[y2tF14
+ F14r) +
(Fn n=lS
+ F:)l
