J. Phys. Chem. 1987, 91, 241-245 A
v+ T
0
-
-0.6 -0.4
-0.2 0.0
E (VOLTS vs.SCE) Figure 10. Cyclic voltammograms at 0.1 V.S-' in 0.1 M Na2S04for (A) Pt/Nafion, NBS; (B) Pt/Nafion, NBS/SPS (0.25 mg.cm-2Nafion; 0.50 mg.cm-2SPS). The first two cycles (A) and three cycles (B) are shown.
for obtaining useful measurements by using homopolar bilayer arrangements, i.e., applying an outer layer of a highly permselective polymer of the same polarity. This idea is demonstrated in Figure 10 for the electrochemical reduction of the anionic NBS21 in Nafion films on Pt. The NBS was incorporated into Nafion by the "one-step" method: Le., by dissolving a quantity of NBS (sodium salt) in the Nafion casting solution, equivalent to 0.09 mequiv/g, before applying the film. As shown in Figure 10, unlike the case of a single layer where practically no NBS peaks are observable (Figure lOA), with the homopolar bilayer arrangement Pt/Nafion, NBS/SPS (Figure 10B) some retention of NBS in the Nafion layer is obtaiwd, sufficient to observe clearly the NBS reduction peak. As expected, rapid ejection of NBS occurs upon its reduction to the dianion. If however the NBS is not reduced, (21) Rubinstein, I. J . Electroanal. Chem. 1985,183, 379. (22) Pickup, P. G.; Kutner, W.; Leidner, C. R.;Murray, R. W. J . Am. Chem. SOC.1984,106, 1991.
24 1
it slowly leaks out on the time scale of several minutes.
Conclusion Bipolar polymer films on electrodes are of interest due to possible considerable improvement in the retention of electroactive counterions at the electrode surface but also in the general framework of the construction of complex microstructures on electrodes for obtaining desired properties.22 Bipolar polymeric layers on electrodes in which electroactive ions are incorporated were thus analyzed both theoretically and experimentally. Approximate expressions for the rate of leakage of electroactive ions in electrolyte solutions due to ion-exchange and Faradaic reactions were derived, predicting a possible improvement of several orders of magnitude in the stability with respect to single layers (simple electrostatic binding). It was experimentally demonstrated that such a stabilization can indeed be obtained with bipolar films, for electroactive anions as well as cations. It was verified that the rate of leakage can be controlled by changing experimental conditions, such as electrolyte concentration and film thickness, in a theoretically predictable manner. Added benefits of such systems in enabling the use of soluble ion-exchange polymers for electrode surface modification, as well as co-ions retention in ion-exchange polymer films on electrodes, were also demonstrated. It is becoming increasingly evident that obtaining specific long-term desired properties with chemically modified electrodes requires the synergistic application of a number of operational principles in a single electrode system. Bipolar arrangements on electrodes, allowing for the combined exploitation of equilibrium as well as transport properties of ion-exchange polymers, may well constitute important components of such systems. Registry No. PXV, 32168-10-8; Fe(CN)?-, 13408-62-3;Fe, 743989-6; NBS, 127-68-4;Pt, 7440-06-4; Fe(CN)64-,13408-63-4; NaCIO,, 7601-89-0; H2S04, 7664-93-9;Na2S04,7757-82-6; Nafion EW 1100, 63496-24-2.
Electron Aff lnltles of Hexafluorobenzene and Pentafluorobenzene W. E. Wentworth,* Thomas Limero, University of Houston-University Park, Houston, Texas 77005
and Edward C. M. Chen University of Houston-Clear Lake, Houston, Texas 77058 (Received: April 30, 1986)
The attachment of thermal electrons to hexafluorobenzeneand pentafluorobenzenehas been studied as a function of temperature with an electron capture detector. The electron affinities, the rate constants for thermal electron attachment, and the activation energies for the rate constants for thermal electron attachment have been determined from the data. The values for these properties are as follows: For CsF6, EA = 0.86 0.03 eV, kl = 2 X lo-' cm3/(molecule s) at 300 K, and El* = 0 eV. For C6FSH,EA = 0.73 f 0.08 eV, kL = 1 X 1O-Io cm3/(molecules) at 300 K, and El* = 0.1 eV. The results have been compared with other values reported in the literature. The negative ion states of hexafluorobenzene have been described by "pseudo-two-dimensional" Morse potential energy curves which have been estimated from experimental data.
*
Introduction The reaction of hexafluorobenzene with thermal electrons is known to rapidly at rOOmtemperature. nerate constant for this process has been determined experimentally with good agreement a t pressures less than 5 Torr and is 1.06 X lo-' cm3/(molecule s).'-~ Unfortunately, the same consistency has (1) Davis, F. J.; Compton, R. N.; Nelson, D. R. J. Chem. Phys. 1973,59,
2324.
(2) Spyrou, S. M.; Christophorou, L. G. J . Chem. Phys. 1985,82, 1048. (3) Adams, N. G.;Smith, D.; Alge, E.; Burdon, J. Chem. Phys. Lett. 1985,
116, 460.
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not been obtained for the energetics of the reaction. The exFfimental values of the electron affinity for C6F6 range from 0.52 to 7 1.8 eV.4-'0 In order to clarify the situation, we would like (4) Page, F. M.; Goode, G. C. Negative Ions and the Magnetron; WileyInterscience: New York, 1969. ( 5 ) Lifschitz, C.; Tiernan, T. 0.;Hughes, B. M. J. Chem. Phys. 1973,59, 3182. (6) McDonald, R. N.; Chmdhury, A. K.; Setser, D. W. J. Am. Chem. Soc. 1981,103, 7588. (7) Sowada, U.; Holroyd, R. A. J . Phys. Chem. 1980,84, 1150. (8) Rains, L. J.; Moore, H. W.; McIver, R. J . J . Chem. Phys. 1W8,68, 3309.
0 1987 American Chemical Society
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The Journal of Physical Chemistry, Vol. 91, No. 1 , 1987
Wentworth et al.
to publish the results of the temperature dependence of the re(6) sponse of the electron capture detector (ECD) to C6F6 and C6FSH, which were obtained several years ago before much of the new data were available. For both molecules, the electron affinity, (7) EA, the rate constant for thermal electron attachment, k l , and the activation energy for thermal electron attachment, E l * , can In the linear region, the response is given by be obtained from the ECD data. The use of the ECD for the determination of electron affinities b-e lim = Koa was first proposed by Wentworth and Becker1’s’2in 1961. The a-0 b proposal was subsequently verified experimentally by Wentworth, Chen, and Love10ck.I~ There were very few molecular electron (9) affinities available at the time for comparison purposes. Recently, Chen and WentworthI4 have made favorable comparisons of the where b is the electron concentration in the absence of a capturing absolute values of the electron affinities obtained in the ECD and other literature values. Kebarle, Grimsrud, and ~ o - w o r k e r s ~ ~ species ~ ~ ~ while e is the electron concentration in the presence of AB. The term [e] is the positive ion concentration, and a is the have referenced the relative values of electron affinities obtained concentration of AB. by equilibrium charge-transfer experiments in the gas phase to A comparison of eq 7 and 9 shows that a common constant K, the absolute value of the electron affinity of SO2 and obtained can be obtained by simply multiplying K , by 2kD’[e] and KOby a good comparison with the absolute values of the electron affinities 2/tp. The pulse time can be accurately measured with an osfrom the ECD and other procedures. Also, the relative values cilloscope, but the rate constant term is more difficult to measure of the electron affinities measured by Fukuda and McIver” using because of the effect of impurities. Thus, the “short” time data the equilibrium charge-transfer procedure in an ICR mass will be more consistent. However, both solutions depend upon spectrometer are in agreement with the values reported by the steady-state concentration of the positive ions. Grimsrud, Caldwell, Chowdhury, and Kebarle,16,17although Two temperature regions can be defined for K, based on the different absolute values are given because a different reference point was used. relative values of k-, and kNI’[$]. In the a region, >> kNI’[$], and K , = kNl’[$]kl/k-,. Using the quantum mechanical exSince the ECD procedure is a direct, absolute determination pression for the equilibrium constant, K = k , / k - , , gives of the electron affinities, it is suggested that the current results are the “best” values. The only other absolute value was obtained In K,T3I2 = In A In kh,’[e] E A / R T (10) from the magnetron m e t h ~ d .The ~ different values will be discussed in detail. There is no literature value for the adiabatic The term A is made up of fundamental constants and the ratio electron affinity of C6F5H. of the partition function of the negative ion to that of the neutral. The negative ion states of C6F6 will be described by “pseudoIf the recombination term is temperature independent, then the two-dimensional” Morse potential energy curves using a procedure electron affinity can be obtained from the slope of a graph of In which has been applied to the negative ion states of the halogens.I8 K,T3I2vs. 1/T. In the p region, k-, 1.80 f 0.3 ( 5 ) 1.1 x 10-7 (3)
*
* C1.79 * 0.02 ( 6 )
’This work.
0.73
* 0.08
*
0.2 (8, 15, 16) 0.52 f 0.06 (9) 0.8
C6F5H
E l * , eV ECD‘ 0.0
1
x 10-10
1
x
10-10 (3)
0.1
References are given in parentheses.
3 ~ - l { j ~ J K - ’ )
Figure 1. Graph of [In KCT3/*] vs. 1 / T for C6Fs and C6F5H.
Results The electron capture data are shown in Figure 1 as In K,T3I2 vs. 1/T. All of the C6F6 data and the high-temperature data for C6F5Hwere taken at low pulse times, 20-50 ps. Both compounds show a distinct a region, and the electron affinities, EA, have been obtained from the data in this region by using a nonlinear least-squares procedure. The rate constants for thermal electron attachment at 300 K, k , , and the activation energy, El*,for this process have been obtained from the data in the 0 region, which is also quite evident. It must be noted that the electron affinity is determined from the slope in the high-temperature region and does not depend on the magnitude of the rate constant for thermal electron attachment. These results are given in Table I with the literature values and references. The first experimental value of the rate constant for thermal cm3, was reported by Davis, electron attachment, 1.06 X Compton, and Nelson’ in 1973. The temperature dependence of the attachment of thermal electrons to C6F6 has been reported by Adams et aL3 using a flowing afterglow Langmuir probe. (falp) procedure. Spyrou and Christophorou2 have obtained similar data but at electron energies ranging from 0.1 to 0.8 eV using an electron swarm apparatus. The falp and swarm values agree with the earlier values of the rate constant which are about a factor of 2 lower than the ECD value, but it must be noted that the total pressure is 1 atm in the ECD experiment while it is 5 Torr or less in the others. None of the earlier studies report activation energies, but it has been reported that for C6F6the attachment process does not change much with temperature to about 400 K, implying a low activation en erg^.^^^ Above this temperature, the “apparent” rate of attachment drops by several orders of magnitude. This is also the temperature dependence which is observed in the ECD data. In the case of the ECD data, the drop is interpreted in terms of an enhanced detachment from the ground-state negative ion. Spyrou and Christophorou have interpreted the decrease in electron attachment in terms of a decrease in the forward rate constant, k , . A more complete discussion of these differences is in p u b l i c a t i ~ n . ~In ~ ~this ~ ~article, ~ * ~ it will be assumed that the (19) Christophorou, L. G.J . Chem. Phys. 1985, 83, 6543.
ECD model, which has yielded absolute EA’S and accurate k l values for many other compounds, is also applicable to these two molecules. The EA values for C6F6 in the literature cover a wide range (0.52 to > 1.8 eV). The value from the ECD data can be reconciled with all but one of these, that being the lower limit of 1.8 f 0.3 eV obtained from the threshold for endothermic charge transfer from S- to C6F6.5 The EA value obtained from the magnetron method is 1.2 f 0.07 eV. This is considerably larger than the ECD value. However, the limits represent precision rather than accuracy. When the electron affinities determined by the direct capture process in the magnetron method (eight m01ecules)~J~ are compared with those obtained by other techniques, the standard deviation is f0.35 eV. By the same token, the errors given for the ECD value represent the precision of this specific measurement. A more representative value would be f0.1 eV. Thus, the difference in the two values is within these accuracies. The solution photodetachment value of 1.09 f 0.04 eV7 is also greater than the ECD value, but the difference of 0.23 eV is less significant when it is noted that few molecular electron affinities have been determined with this technique. The original results of Rains, Moore, and McIver,8 obtained by measuring the position for the equilibrium charge transfer for various anions in an ICR mass spectrometer, placed the electron affinity of C6F6 between that of benzophenone and nitrobenzene. At the time, it was believed that the electron affinity of benzophenone was greater than that for the methoxy radical, 1.57 eV. Subsequently, it has been shown that the electron affinity of benzophenone is 0.64 eV9914and that of nitrobenzene is 1.02 eV.9 Using these values to establish the absolute scale for the ICR results, we estimated a value of 0.8 eV for the electron affinity of hexafluorobenzene, in agreement with the ECD value. The most recent value of the electron affinity of C6F6 was obtained from the determination of the temperature dependence of the thermal charge-transfer reactions in a “high-pressure” mass spectrometer. Both the enthalpy and the entropy of the reactions were ~ b t a i n e d .The ~ value is 0.52 f 0.06, which does not overlap the ECD value. This is especially important since many of the other values obtained with this technique overlap electron affinities obtained by using the ECD and other techniq~es.’~J~ One possible explanation for this result is that the mass spectrometric experiments refer to an excited state and the ECD results refer to the ground state. This is likely since the mass spectrometric experiments are still carried out at relatively low pressures, 5-10 Torr, while the ECD experiments are carried out at atmospheric pressure. This is also attractive from the standpoint of negative ion states which will be discussed shortly. Although the dissociative reaction of thermal electrons with c6F6 is highly endothermic, we have investigated the negative ions formed in an atmospheric pressure ionization source of a quadrupole mass spectrometer in the presence of hexafluorobenzene. In the absence of oxygen, the only ion found is the parent negative ion, C6F6-. Semiempirical Morse potential energy curves containing three dimensionless parameters have been found to be very valuable in (20) Hernandez-Gil, N.; Wentworth, W. E.; Limero, T.; Chen, E. C. M. J . Chromatogr. 1984, 312, 31.
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Wentworth et al.
TABLE II: Morse Potential Parameters and Properties of Negative Ion States of C,F, kA kR kB DAB-, eV vAB-, cm-’ re,AB-, A 0.886 0.860 0.562 0.560
1.468 1.447 1.619 1.579
-2t
0.68 0.68 0.55* 0.61*
2.96 2.83 1.08 1.10
567 535 267 299
1.83 1.84 2.52 2.39
I\\ I
Figure 2. Morse potential energy curves for the negative ion states of C6F6.
describing the negative ion states of the halogens and hence consolidate data from many diverse sources.I8 Therefore, a similar approach has been used for C6F6. The Morse potential referenced to zero energy at infinite separation of the ground-state atoms is given by WX2) = -2Dx2 exp(-P(r - re))
+ Dx, exp(-W(r
- re))
(12)
where Dx2is the spectroscopic bond dissociation energy, r is the X-X separation, and re = r at the minimum of U(X,).The constant, 0,is defined by
0 = ve(2x2p/D)’Iz where v, is the fundamental vibrational frequency and p is the reduced mass. The parametrized Morse potential for the negative ions is given by U(X,-) = -2kADxz exp(-kBP(r - re)) + kRDxz eXP(-zk~P(r - re)) - EAx (13) where the parameters kA. kB, and kR are constants, and EAx is the electron affinity of X. This is also a Morse potential, and the relationships between the negative ion properties and the neutral properties have been given.” The Morse potential energy curves for four negative ion states of c6F6 calculated from eq 13 are shown in Figure 2. Also shown are the calculated distributions for the formation of the various ions and the experimental distributions.21 The parameters, the experimental data used in the calculations, and the properties of the negative ions calculated from these parameters are given in Table 11. The Morse properties for the neutral potential energy curve were taken to be those for a typical aromatic C-F band and are D = 5.5 eV, ve = 1100 cm-’, and re = 1.4 A. The electron affinity of the F atom is well established at 3.4 eV. The electron affinity of the C6F5radical is less well established but can be estimated from the electron beam studies of the pentafluorophenyl halides to be between that of the I atom, 3.08 eV, and the Br atom, 3.37 eV.z2 This gives a value of 3.2 eV, which is consistent with the (21) Fenzlaff, H.; Illenberger, E. Int. J . Mass Spectrom. Ion Phys. 1984, 32, 185. (22) Naff, W. T.; Compton, R. N.; Cooper, C. D. J . Chem. Phys. 1971, 54, 212.
EA, eV
E,, eV
0.86* 0.53* -1 .o -1.2
0.38* 0.75* 4.8* 4.8*
E,*, eV -0.01 * 0.1 1.71 1.70
fwhm, eV 0.49 0.49* 0.71* 0.76*
recent electron beam studies of C6F5H.21The study of the pentafluoro halides using the magnetron4 and more recently using collisional ionization with a K beamz3gave values of 2.75 and 2.7 & 0.2 eV for this electron affinity. However, in order to extract this quantity, the C-X bond dissociation energies must be known. If one uses the most recent values of the phenyl-C1 (4.2 eV), phenyl-Br (3.5 eV), and phenyl-F (5.5 eV) bond dissociation energies,24with the reported experimental data, the electron affinity for C6F5is 3.2 eV. The lowest state leading to F is uniquely defined by the molecular electron affinity and the activation energy from the ECD measurements and the vertical energy. The dissociation limit is consistent with the lowest state being a CT state, as has been established experimentally by Wang and WilliamsZSand Yim and Woods .26 The first excited state leading to C6F5-is defined from the molecular electron affinity from thermal charge-transfer studies? the vertical energy, and the distributions from electron beam studies.2’ The second and third excited states are defined in the Franck-Condon region by the electron beam value for the vertical energy and the accompanying ion distributiom2’ The other parameter has been defined empirically. Coincidentally, this gives a molecular electron affinity between -1 and -1.2 eV, which is in agreement with an estimate obtained from the endothermic charge transfer to C6F6 from I-.5 The potential energy curves illustrate the difference between the vertical electron affinity and the adiabatic electron affinity. The electron transmission s t ~ d i e and s ~ electron ~ ~ ~ ~impact measurements give the vertical electron affinity while the thermodynamic studies give the adiabatic electron affinity. Indeed, in the case of C6F6,the vertical electron affinity is negative while the adiabatic electron affinity is positive. The photodetachment threshold is different from either the adiabatic electron affinity or the vertical electron affinity since there is a large change in geometry. In this case it is larger than the adiabatic electron affinity which could account for the difference in the ECD measurement and the solution photodetachment value.’ The potential energy curves show both u* and x* states based on the negative ion formed at the dissociation limit. It is clear that the two levels are close together. The two lowest states show a separation of about 0.4 eV, which was observed in the experimental data used to define the curves. The electron transmission studies only show one resonance at an intermediate value. Some ~ t u d i e s ~place ~ - ~ ’the a* level lower than the u* level while the most recent theoretical study considers the electron to be in a g*, a* combination orbital in which the x* component prevails.32 Compton and Reinhardtz3suggest both a bound u* and a* level to explain the results obtained for the collisional ionization of C6F5Xwith a K beam. Potential energy curves can be drawn for C ~ F S Hbut , the reaction coordinate could be either in the C-F direction or in the (23) Compton, R. N.; Reinhardt, P. W. Chem. Phys. Lett. 1982, 91, 268. (24) McMillen, D. F.; Golden, D. M . Annu. Reu. Phys. Chem. 1982, 33, 493. (25) Wang, J. T.; Williams, F. Chem. Phys. Lett. 1980, 71, 471. (26) Yim, M. B.; Wood, D. E. J . A m . Chem. Soc. 1976, 98, 2053. (27) Frazier, J. R.; Christophorou, L. G.; Carter, J. G.; Schweinler, H. C. J . Chem. Phys. 1978, 69, 3807. (28) Burrow, P. D.; Michejda, J. A,; Jordan, K. D. J . A m . Chem. SOC. 1916, 98, 6392. (29) Symons, M. C. R.; Selby, R. C.; Smith, J. G.; Bratt, S. W. Chem. Phys. Lett. 1977, 48, 100. (30) Symons, M. C . R. J . Chem. Soc., Faraday Trans. 2 1981, 77, 783. (31) Chowdhury, S.; Grimsrud, E. P.; Heinis, T.; Kebarle, P. J. Am. Chem. SOC.1986, 108, 3630. (32) Shchegoleva, L. N.; Bilkis, I. 1.; Shastner, P. Y. Chem. Phys. 1983, 82, 343.
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
