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this study, a revised value of AHfo29s[NzF4(g)]= -5.3 f 1.4 kcal mol-’ is obtained. This value differs significantly from that obtained by Armstrong et aL6 and no satisfactory explanation of the disagreement is presently available.
Acknowledgment. The support of the National Research Council of Canada is gratefully acknowledged. The authors thank Professor C. B. Colburn for a very helpful communication, Dr. H. Wieser for several informative discussions, and Dr. J. Duckett for calculating the moment of inertia of N2F4. References and Notes (1) P. J. Evans and E. TschuikowRoux, J. Chem. Phys., 65,4202 (1976). (2) D. R. Stull and H. Prophet, Natl. Stand. Ref. Data Ser., Natl. Bur. Stand., No. 37 (1971). (3) A. Kennedy and C. B. Colburn, J . Chem. Phys., 35, 1892 (1961). (4) J. T. Herron and V. H. Dibeler, J . Res. Natl. Bur. Stand., Sect. A , 85, 405 (1961); J . Chem. Phys., 35, 747 (1961). (5) A. V. Pankratov, Russ. J. Phys. Chem., 43, 214 (1969). (6) G. T. Armstrong, S. Marantz, and C. F. Coyle, Natl. Bur. Stand. Rep., No. 6584 (1959). (7) F. A. Johnson and C. B. Colburn, J. Am. Chem. SOC.,83, 3043 (196 1).
L. H. Blanco C. and N. 0. Smith (6) L. H. Piette, F. A. Johnson, K. A. Booman, and C. B. Colburn, J. Chem. Phys., 35, 1481 (1961). (9) H. E. Doorenbos and B. R. Loy, J . Chem. Phys., 39, 2393 (1963). (10) G. von Ellenrieder, E. Castellano, and H. J. Schumacher, Z. Phys. Chem., 55, 144 (1967). (11) D. A. Armstrong and J. L. Holmes, Compr. Chem. Kinet., 4, 143 (1972). (12) G. N. Lewis and M. Randall, “Thermodynamics”, McGraw-Hill, New York, N.Y., 1961, p 177. (13) J. R. Durig and R. C. Lord, Spectrochim. Acta, 19, 1877 (1963). (14) C. 8. Colburn, F. A. Johnson, and C. Haney, J . Chem. Phys., 43, 4526 (1965). (15) J. R. Durig and J. W. Clark, J . Chem. Phys., 48, 3216 (1968). (16) D. F. Koster and F. A. Miller, Spectrochim. Acta, ParfA, 24, 1487 (1968). (17) M. J. Cardillo and S. H. Bauer. Inoru. Chem.. 8. 2086 (1969). (18) A. Oskam, R. Elst, and J. C. Dulnker, Spectrochlm. Acta, b a r t i , 28, 2021 (1970). (19) M. M.Gilbert, G. Gundersen, and K. Hedberg, J . Chem. Phys., 58, 1691 (1972). (20) J. R. Durig and R. W. MacNamee, J . Raman Spectrosc., 2, 635 (1974). (21) H. Selig and J. H. Holloway, J. Inorg. Nucl. Chem., 33, 3169 (1971). (22) J. R. Durig, B. M. Gimarc, and J. D. Odom in “Vibrational Spectra and Structure”, Vol. 2, J. R. Durig, Ed., Marcel Dekker, New York, N.Y.. 1975. D 35. (23) G. N.’ Makee;, V. F. Sinyanskii, and B. M. Smirnov, b k l . Akad. Nauk USSR, 222, 452 (1975).
The High Pressure Solubility of Methane in Aqueous Calcium Chloride and Aqueous Tetraethylammonium Bromide. Partial Molar Properties of Dissolved Methane and Nitrogen in Relation to Water Structure‘ LUISH. Blanco C. and Norman 0. Smlth” Department of Chemistry, Fordham University, New York, New York 10458 (Received September 6, 1977)
The solubility of methane in 1 m CaClz at 25-125 “ C , and in 1 m Et4NBr at 25-71 “C, from 100 to 600 atm, has been measured using a direct sampling technique. Methane is salted out by the CaC12 but salted in by the Et4NBr. Salting coefficients are presented. The isobaric Henry’s law applies throughout most of the range of measurement. A more detailed study, confined to a pressure of 200 atm, was made of the methane solubility in 1m Et4NBr over the same temperature range. Henry’s law constants, partial molar volumes, and entropies and heat capacities of solution were derived from the solubility data and interpreted in terms of the structure-making qualities of methane. Similar data are presented for nitrogen. Hepler’s suggested criteria of structure are examined and applied to the present results. Methane appears making and breaking based on (acp0/aP)~ to be a better structure maker in the presence of dissolved NaCl than in water alone, and a poorer structure maker in the presence of dissolved CaC12 or Et4NBr.
Introduction This study is a continuation of work already reported2i3 on measurements of the high pressure solubility of gases in water and aqueous salt solutions. Attempts were made there to interpret the thermodynamic data derived from the solubilities in terms of structural considerations. This paper extends the work on methane in water and aqueous sodium chloride2 to include calcium chloride and tetraethylammonium bromide, where interest is attached to (1) methane dissolved in natural brine (of which sodium and calcium chlorides are major components) and ( 2 ) the salting-in property of tetraalkylammonium halides. It is pertinent to inquire whether, in these solvents, Henry’s law holds for methane, whether its partial molar volume depends on the total pressure, and whether there is any relation between structure in solution and the temperature dependences of partial molar volume and solubility. With data now available for comparison from this and previous 0022-365417812082-0 186501.OO/O
studies some answers to these questions can be attempted. Earlier quantitative solubility measurements of methane in aqueous calcium chloride are surprisingly scarce. Michels, Gerver, and Bij14 reported values in 2.7 N CaC12, but only a t 25 “C. A preliminary study in this laboratory5 extended to only 60 atm, and was also limited to room temperature. No previous solubilities of methane in tetraethylammonium bromide have been published except for a 1-atm study at 5-35 “C by Wen and Hung.6 Tiepel and Gubbins7 have measured the partial molar volumes of several gases, including methane, in water and various electrolyte solutions, but their data are confined to 25 “C and do not include the systems here reported.
Experimental Section Solubilities were determined in a stirred, thermostated 1-gal stainless steel autoclave, samples of liquid phases being withdrawn into a thermostated buret system for 0 1978 American Chemical Society
High Pressure Solubility of Gases in Water and Salt Solutions
The Journal of Physical Chemistry, Vol. 82, No. 2, 1978 107
TABLE I: Solubilitv of Methane in 1.000 m CaC1, and 1.000 m (C,H.),NBF
P, atm Temp, "C 25.0 25.0 38.0 51.5 51.5 71.0 71.0 102.5 125.0 a
Solvent 1 m CaCl, 1 m Et,NBr 1 m Et,NBr 1 m CaCl, 1 m Et,NBr 1 m CaCl, 1 in Et,NBr 1 m CaCl, 1 m CaCl,
100 1.032 2.025 1.747 0.834 1.591 0.787 1.541 0.803 0.826
200 1.591 3.117 2.759 1.360 2.602 1.286 2.517 1.347 1.371
300 1.956 3.740 3.436 1.724 3.264 1.665 3.304 1.740 1.709
400 2.202 3.914b 3.994 2.004 3.817 1.963 3.880 2.018 2.034
500 2.471
600 2.720
4.451 2.232 4.274 2.215 4.350 2.281 2.252
105a 1.2293 2.6462 2.0875 0.9613 1.8972 0.8866 1.7631 0.9226 0.9497
108b -2.5011 -6.9850 -4.1892 -1.6220 -3.5513 -1.3790 -2.8433 -1.4307 -1.5556
10°C
4.496b 2.455 4.448b 2.443 4.618* 2.477 2.477 Mole fraction of dissolved gas X l o 3 and parameters in X , = UP t bP2 t cP3. Not included in curve fitting.
2.0231 7.7333 3.6007 1.1727 2.9404 0.9704 2.1206 0.9807 1.1049
*
TABLE 11: Salting Coefficients for Methane
P,atm Temp, "C 25.0 38.0 51.5 71.0 102.5 125.0
Solvent 1m 1m 1m 1m 1m 1m 1m 1m 1m
CaCl, Et,NBr Et,NBr CaCl, Et,NBr CaCl, Et,NBr CaCl, CaCl,
100
200
300
400
500
0.244 -0.056 -0.046 0.224 -0.056 0.204 -0.085 0.211 0.222
0.225 -0.055 -0.067 0.197 -0.077 0.182 -0.105 0.187 0.199
0.225 -0.044 -0.056 0.197 -0.073 0.182 -0.105 0.190 0.203
0.235
0.247
-0.047 0.201 -0.070 0.185 -0.102 0.198 0.212
-0.054 0.203 -0.077 0.187 -0.104 0.203 0.217
analysis when equilibrium had been reached. The apparatus employed and the procedures used were those described in earlier ~ o r k The . ~ ~Heise ~ pressure gauges were calibrated periodically with a dead-weight tester, and the thermocouple which determined the temperature of the autoclave was calibrated on several occasions against a thermometer certified by the National Bureau of Standards. The methane was the Golden Label ultrapure product of the Matheson Co., Inc., with a stated purity of 99.97%. Fisher Certified calcium chloride hexahydrate was used without further purification. The tetraethylammonium bromide, from Eastman Kodak Co., was recrystallized by the method of Unni, Elias, and SchifP and its purity confirmed by bromide analysis according to the Fajans method. The water for the solubility measurements was distilled and boiled, and then cooled while bubbling methane through it. The salt concentrations were determined by halide analysis. Equilibrium was attained in a few hours, but stirring was usually continued overnight before sampling. Measurements were made approaching the equilibrium from different directions. Suitable corrections were made for the curvature of the menisci in the buret^.^ The procedure was checked by measuring the solubility of methane and nitrogen in water at 51.5 "C and 100 atm. Agreement with earlier values2 was within experimental error. In order to express the measured gas solubilities in terms of mole fraction it was necessary to convert the liquid volumes (as observed in the burets) to mass. For this purpose the density of the aqueous calcium chloride was available in the l i t e r a t ~ r e . ~The J ~ density of the aqueous tetraethylammonium bromide was determined pycnometrically. After subtracting the partial pressure of water over the salt solutionsgJ1 from the total pressure in the burets, the gas volumes were converted to moles using tables of molar volume.12
Results and Discussion Table I presents the methane solubilities in the two salt solutions a t various total pressures and temperatures, as mole fractions of dissolved gas. In computing the latter,
600
0.199 0.184 0.201 0.215
both salts were treated as completely dissociated into their ions. Each value quoted is the average of at least three independent samplings. The average deviation for each set of samples was less than 0.3% for the CaC12and about 0.4% for the Et4NBr solutions. The accuracy of the solubilities is estimated to be about 1%. Two additional solubility measurements at 25.0 "C and 53.5 atm gave methane mole fractions of 0.635 and 1.273 X low3in 1 m CaC12 and 1 m Et4NBr, respectively. The second of these figures seems to be out of line with the others, and was not included in the curve fitting referred to below. (It may be noted that the experimental accuracy is poorer at low pressures because of an unfavorable volume ratio of liquid-to-gas in the analytical procedure.) A t 25 "C and pressures of 400 atm and greater, the solubilities in aqueous Et4NBr were unexpectedly small and poorer precision was found. This is possibly caused by proximity to the conditions (462 atm at 25 "C) under which a gas hydrate forms.13 Even a t the higher temperatures the solubilities in the bromide solutions for pressures of 600 atm, despite their reproducibility, appear to be affected by an unknown factor. Several attempts were made to determine values at 102.5 "C, but the quality of the data was poor above 200 atm, perhaps because of some critical phenomenon in this region. The data, with the exception of those indicated, were fitted by least squares to the form X2 = aP bP2 cP, where X2 is mole fraction of dissolved methane. The values of the resulting parameters are included in the table. They reproduce the fitted experimental mole fractions with for the chloride and an average deviation of 0.017 X 0.011 X for the bromide solutions. Comparison with the solubility of methane in water under the same conditions2J3shows that the gas is salted out extensively by the CaC1, and salted in by the Et4NBr. Salting coefficients, k = (l/m) log (So/S),where m is salt molality, and Soand S are the solubilities of the methane in water and salt solution, respectively, are presented in Table 11. For this purpose the methane concentrations were converted to moles per 1000 g of water. The values of S were taken from the smoothed solubilities of this work,
+
+
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I
'
I
I
I
L. H.
I
12.0
7
Y
g
11.5
4
I1 0
11.0 10.5
L
0
I 100
I 200
I 300
Blanco C. and N. 0. Smith
I
I
I
400
500
600
P,atm Flgure 1. Solubility of methane: (0)in water at 25.0 and 51.5 O C (ref 13);(0)in 1 m CaCI, at 25.0, 51.5, and 71.0 O C ; ( 0 )in 1 m Et4NBr at 25.0, 38.0, and 51.5 O C .
,/
o
100
200
1''s
ljl,.o
71.0"
, 400
300
SCO
600
F: atm
Figure 2. Solubility of methane: (0)in 1 mCaCI2 at 102.5 and 125.0 OC; ( 0 )in 1 mEt,NBr at 71.0 O C .
TABLE 111: Henry's Law Constants and Partial Molar
calculated by means of the parameters given in Table I. It may be noted that the salting coefficients exaggerate the experimental errors: a 1% error in both S and So, for example, can alter k by nearly 0.01. Thus it can be said that, for a given salt at a given temperature, the salting coefficients are nearly independent of the methane pressure. Clearly, the salting-out action of 1 m CaC12 is more effective than the salting-in action of 1 m Et4NBr. The cause of the salting-in has been discussed in some detail by Wen and Hung,S whose solubility data for 0.183 m Et4NBr at 25 "C yield k = -0.074, in essential agreement with our values at higher pressures. The salting-out effect of CaC12appears to be independent of temperature except for the lowest temperature where it is somewhat larger. For Et4NBr the salting-in effect increases with the temperature. Following our earlier procedure2s3 the KrichevskyKasarnovsky equation,14In ( f 2 / X 2= ) In @ (PV?/RT), was applied to the original data, where f zis the methane fugacity, V,O its partial molar volume, and KO the Henry's law constant in the limit of zero pressure. If In ( f 2 / X 2 ) varies linearly with P down to zero pressure, the isobaric form of Henry's law, fi = K X 2 (P, T constant), must apply, and P,O must be independent of P as well as of concentration. Such linearity is evident in the graphs of the data shown in Figures 1 and 2. (Figure 1 includes, for comparison, the results for methane in water, interpolated from data of ref 13.) The data were therefore fitted to In ( f 2 / X 2 ) = a'+ b'P by least squares, and V?-and KO computed from a'and b'using a ' = In @ and b'= V,O/RT. They are listed in Table 111, which includes values for pure water for comparison. For consistency, the quantities given are confined to those determined indirectly from high pressure solubility measurements in the authors' laboratory. There was found to be no statistical basis for a nonlinear variation in the plots of Figures 1 and 2, as had been the case for h e l i ~ mnitr~gen,~B ,~ and methane2B in water and aqueous salt solutions under some conditions. The fugacities were found from tables,12 it being assumed that total pressure and methane pressure are virtually identical, except at
+
Volumes of Methane Temp, C
Solvent
KO, atm X 10-4
25.0
1rn CaCl, 1 rn Et,NBr 1 m Et,NBr Water 1 rn CaC1, 1 m Et4NBr 1 m CaCI, 1 m Et,NBr Water 1 rn CaC1, Water 1 rn CaCl,
7.12 3.57 4.34 5.44a 9.24 4.84 10.24 5.23 5.99' 10.07 5.66' 9.83
O
38.0 51.5 71.0 102.5 125.0 a
V;, cm3 mol- ' 35.3 37.6 35.3 37.1' 36.0 36.3 36.8 36.4 50.8' 44.0 62.2a 51.0
Calculated from data of ref 2.
102.5 and 125 "C where the above assumption is probably not valid. In the latter cases fugacities were corrected for the presence of water vapor by use of the Lewis and Randall rule and the experimental vapor compositions of Olds, Sage, and Lacey15 for methane in water. The correction has the effect of increasing V 2 0 and decreasing @ by 1% at 102.5 "C and 2 t o 3% at 125 "C. For the solvents water and 1m CaC12,@ is seen to pass through a maximum with rise in temperature. For 1 m Et4NBr the existence of such a maximum at higher temperatures is also suggested by the data. Thus the solubility at 1 atm in all three solvents passes through a minimum, a common phenomenon. The temperatures of these minima are estimated to be 93 "C for both water and 1 m CaC12 and 75 OC for 1 m Et4NBr. The variation of the solubility of methane with temperature at higher pressures is more complicated. Examination of Table I shows that, as the temperature increases, the solubility in aqueous CaC12at all pressures up to 600 atm passes through a minimum in the neighborhood of 65 "C, the temperature of the minimum decreasing with increase in pressure. There are also indications of a solubility maximum at somewhat higher temperatures. This pattern is similar to that found for methane in
High Pressure Solubility of Gases in Water and Salt Solutions
TABLE IV: Solubility of Methane in 1m (C,H,),NBr at 200 atm 103X, Temp, "C Temp, "C 3.117 80.0 25.0 2.759 85.0 38.0 2.602 89.5 51.5 2.580 95.0 55.0 60.0 2.550 100.0 2.527 102.5 65.0 2.517 115.0 71.0 2.533 75.0
103X, 2.549 2.579 2.595 2.625 2.659 2.636 2.676
water.13 For aqueous Et4NBr the table also indicates a temperature of minimum solubility a t all pressures, and a similar shift of the minimum with increase in pressure. These shifts to lower temperatures are consistent with the expectation that pressure increase favors the destruction of the water structure and the onset of more "normal" behavior (positive temperature coefficient of solubility for sparingly soluble gases) a t lower temperatures. A more detailed study of the temperature dependence of the methane solubility in 1 m Et4NBr at a total pressure of 200 atm was undertaken, giving the results in Table IV. The data, exluding those for the two highest temperatures, were fitted to In ( f 2 / X 2 )= A B T 1 C In T giving the parameters A = 154.8978,B = -7445.408, and C = -20.909, which reproduce the experimental values of In ( f i / X 2 )with an average deviation of 0.005. By assuming, as above, that Henry's law is valid, and that ACp" is independent of T , the parameters lead to the following quantities for the transfer of 1 mol of gas at unit fugacity to the hypothetical dissolved state ( X , = 1) where Henry's law holds, at a total pressure of 200 atm: ACpo = 41.6 cal deg-l, A H 0 2 9 8 = -2.41 kcal, = -29.5 eu, and AGO298 = 6.39 kcal, all at 200 atm. Similarly, fitting the data to In X 2 = A B Y 1 + C. In T gives A = -135.2291, B = 650.371, and C = 18.892, and a calculated minimum solubility at 200 atm of X 2 = 2.532 X a t 71 "C. The analogous computation was made using the data in Table I for methane in aqueous CaC12up to 102.5 "C, but the accuracy of the derived thermodynamic parameters is poorer because only four data points are available. The following values for the transfer of 1 mol of methane into 1 m CaCl, a t a total pressure of 200 atm were thus obtained: ACp" = 34.3 cal deg-l, = -2.26 kcal, = -30.4 eu, and =_ 6.79 kcal. Table I11 shows that V2' is generally smaller in 1 m CaClz than in water. In 1 m Et4NBr it is larger than in water at 25 "C but smaller at higher temperatures. (Tiepel and Gubbins7 found the presence of tetraalkylammonium bromides to cause an increaje at 25 'C.) Further, the temperature dependence of V2"in each solvent indicates that it passes through a minimum. HepleP has suggested that the thermodynamic relation (aCp,"/aP)T = -T(a2V2"/aT2)p may be used as a criterion of structure making and breaking for the solute, methane in this case. He proposed that the partial molar heat capacity, CP,", of a solute at infinite dilution might be expected to decrease with increase in pressur! if the solute were a structure maker. In this event (a2V2"/aP)p would be positive. For structure breaking solutes it would be negative. This second derivative was therefore calculated, not only for methane but for nitrogen, in several systems for which V2" is now available for a t least three temperatures. After fitting the V2"values to a polynomial in T , (a2V20/aT2)p was computed for a temperature of 75 "C, approximately the average temperature of measurement for most of the data, although just beyond the range of the data for aqueous Et4NBr. The results are recorded in Table V.
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The Journal of Physical Chemistry, Vol. 82,
No. 2,
TABLE V: Values of ( a 2 V " / a X 2 l p at 7 5 o c for Dissolved Gases in Various Solvents from High Pressure Solubility Data ( a 2 v ; / a T 2 ) p , No. of Gas Solvent cm3 mol-' deg-' data points CH, Water 0.0065 3 1 m NaCl 0.015 3 4 m NaCl 0.031 3 1 m CaCl, 0,0042 5 1 m Et,NBr 0.0049 4 N, Water 0.0098 3 1m NaCl 0.014 3 4 m NaCl 0.038 3
1978
189
Data source Ref 2 Ref 2 Ref 2 Table I11 Table I11 Ref 2 Ref 2 Ref 2
f 4
BOC
60
+
+
40 3o 2 5
Water 50
75
100
125
T,'C Figure 3. Temperature dependence of partial molar volume of methane at infinite dilution in aqueous solvents.
They are semiquantitative at best. The differences in the tabulated values of (a2V20/a79pfor methane are evident in the curvatures of the lines in Figure 3, which is a plot of the data in Table 111. In spite of the uncertainty in the values of the second derivative the application of Hepler's ideas to these data invites the following interpretation. The appearance of only positive values of (a2V20/aP)p indicates that, in the neighborhood of 75 "C, methane and nitrogen are structure makers in all the systems listed. In the presence of NaCl, however, both gases are better structure makers than in its absence. One may say that since some water structure has been destroyed by the NaCl there is "more structure for the methane to make". Increase in the NaCl concentration amplifies this situation. With Et4NBr present, however, the derivative is decreased. Since this salt is generally accepted as a structure maker17 the indication is that when it is present there is "less structure left for the methane to make", or that methane is then less successful at making structure. The presence of CaClz is seen to have an effect in the same direction as the Et4NBr, implying that CaC12is, on balance, a structure maker too. There is evidence elsewhere in the literaturela of this, the results of the stronger electric field of the divalent calcium ion. Since C1- and Br- are thought of as breakers,19s20one may regard both Ca2+ and Et4N+ as makers, competing with the methane for the water in their efforts to impose structure on it. Further evidence, based on entropy and heat capacity data will be presented below. Hepler's use of the sign of (a2V2"/aP)p as a criterion of structure making/ breaking deserves closer examination.
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The Journal of Physical Chemistry, Vol. 82, No. 2, 7978
TABLE VI: Standard H e a t Capacity a n d Entropy D a t a for D i s s o l u t i o n of M e t h a n e a t 7 5 " C (cal deg-' mol-') A Cp"
AS"
ACp'
AS"
(200a t m ) (200a t m ) (1 a t m ) (1 a t m ) Water (7)= 52.7 -24.0 64 -33 1 m NaCl(6) 46.3 -24.1 71 -34 4 m NaCl(7) 18.5 -26.0 71 -36 1 m CaC1, (4) -25.0 42 -35 34.3 1 m Et,NBr (13) 41.6 -23.1 50 -33 a T h e numbers in parentheses are t h e n u m b e r of data p o i n t s used in f i t t i n g t h e In ( f , / X , )vs. T data. Solvent
It was his suggestion that, even for pure liquids, (a2V/aTL)p bears a relationship to structure. For practically all liquids (including water) this second derivative is positive. The values for water, carbon tetrachloride, n-pentane, and diethyl ether, for example, are 1.60, 3.22, 9.07, and 9.59 X cm3 molW1deg-2, respectively at 20 "C, yielding (aCp/aP)~= -1.13, -2.29, -6.44, and -6.81 X cal deg-l mol-l atm-l for the four liquids at the same temperature. Hepler's concept implies, however, that water, doubtless the most structured of the four, should have the most, not the least, negative value. He has suggestedz1that for this purpose liquids should possibly be compared, not as above for equal numbers of molecules, but on some other basis, such as for equal volumes or equal reduced temperatures. Conversion of the above figures to equal volumes gives (aCp/aP)~= -6.28, -2.37, -5.59, and -6.56 X cal deg-l cm-3 atm-l, respectively, suggesting that ether is more structured than water, an unlikely event. Comparison of the liquids at equal reduced temperatures did not appear useful. The present authors suggest that, although comparison of liquids with one another does not appear to be fruitful, the comparison of the values for a given liquid under varying conditions might be more productive. A second part of Hepler's concept16was its extension to solutes through (aCp,O/aP)T = -T(a2V2"/aT2)p,referred to earlier as it applies to the data presented in Table V. As Hepler rightly pointed out, there can be ambiguity about what kind of "structure" is being made or broken. For solutes such as methane, for which (a2V2"/aP)p and C p z o are both positive by experiment, increase in P would make Cp: less positive, presumably by causing partial collapse of the cages of water molecules which comprise the structure. However, salts with small or multiply charged ions such as LiCl are also called structure makerslg because they orient and immobilize water molecules, decreasing the heat capacity of the solution. Since (a2V2"/aT2)p is negativez2and so is CPzo,a t least for LiC1,lg the value of Cpz" mu@ become less negative with rise in P. Thus it would appear that the immobilization process occurs with greater difficulty under higher pressures. Finally, there are the salts such as CsCl and, in our view, NaC1, called structure breakers. For these (a2Vzo/a?"")p and C p z o are also negative, so the latter must also become less negative with increase in P. The breaking of the water structure (by whatever means) must occur with greater difficulty at higher pressures. The interpretation of the data in Table V, made above, is partly substantiated for methane by calculations of ACp" and ASo at 75 "C for the solution of the gas in various solvents, using the 200-atm data presented in Table IV for 1 m Et4NBr, Table I for 1m CaC12, and earlier data from this laboratory2for water, 1 m NaC1, and 4 m NaC1. Values for ACpo and AS" at 200 atm were first found as described earlier. These were then converted to the corresponding quantities for 1atm using (aACp0/aP), = -T(a2V"/aT2)p and (aASo/aP), = -(aAVo/aT)p, the necessary temperature coefficients of volume being obtained from the ideal gas
law and curve fittings leading to Table V. The results are listed in Table VI. (Unfortunately, the temperatures of measurement of most of the data do not extend down to 25 "C so values of ACpO and AS" for that temperature could not be computed.) They are at best semiquantitative because the number of data points on which the volume data are based is small (see Table V). Moreover, it has been assumed that ACp" is independent of T, since the introduction of a fourth parameter in fitting the data to In ( f z / X z = ) f(T) was hardly warranted. In spite of these shortcomings it is of interest to note from the 1-atm results that, if the magnitude of ACpo be taken as an index of structure making, methane makes structure in all five solvents, is a better "maker" in 1 m NaCl and 4 m NaC1, and is a worse "maker" in 1m CaC12 and 1 m Et4NBr, the same result as found by applying Hepler's ideas above in interpreting Table V. Similarly, if loss in entropy can be interpreted in terms of making structure the 1-atm values of AS" lead one to approximately the same conclusions, except for methane in 1 m CaClz where the error is expected to be greatest. At 200 atm the absolute values of ACpo and AS" are all less than those at 1 atm, so that the structure making effects of methane are less extensive at the higher pressure. However, the values are in a different numerical order and suggest that the relative structure making ability of methane in the five solvents is quite different. In contrast to the 1-atm results, therefore, the 200-atm ones do not support the conclusions reached by the Hepler approach. It is possible that any agreement between conclusions based on ACp" and AS",and conclusions based on (a2 V2"/aTL)p is fortuitous because there is a contradiction in principle here: Since V2 for methane is independent of P in systems where In v2/X2)varies linearly with P (as in most of the work reported) Hepler's use of (a2V20/aT2)p as an index of structure making should, if valid, lead to conclusions that are independent of pressure, and so should be the same at 200 atm as at 1 atm. On the other hand, it is the marked differences in (a2Vz0/aT2)p which cause the order of the ACp" values to be different at the two pressures. In 4 m NaC1, for example, it is the large positive (a2Vz0/aP)pthat causes ACp", which is the smallest value at 200 atm, to be the largest at 1 atm. Thus the relative order of "structure making" in the various solvents will, as judged by ACpo, be strongly pressure dependent. It appears to the present authors that the relative magnitudes of the ACpo and AS" values are more immediately associated with structure making/breaking, and that the use of (a2V20/aTL)p alone is of doubtful value for this purpose.
Acknowledgment. It is a pleasure to acknowledge the assistance of a grant from the National Science Foundation. References and Notes (1) Taken, in part, from the Ph.D. Dissertation of L.H.B. Portions of this paper were presented before the 165th and 173rd National Meetings of the American Chemical Society, Dallas, Tex., April 1973 and New Orleans, La., March 1977, and the Fifth International Conference on Chemical Thermodynamics, Ronneby, Sweden, Aug 1977. (2) T. D. O'Sullivan and N. 0. Smith, J . Phys. Chem., 74, 1460 (1970). (3) G. E. Gardiner and N. 0. Smith, J . Phys. Chem., 76, 1195 (1972); 77, 2928 (1973). (4) A. Michels, J. Gerver, and A. Bijl, Physica, 3, 797 (1936). (5) J. R. Duffy, N. 0. Smith, and B. Nagy, Geochim. Cosmochim. Acta, 24, 23 (1961). (6) W. Wen and J. H. Hung, J . Phys. Chem., 74, 170 (1970). (7) E. W. Tiepel and K. E. Gubbins, J . Phys. Chem., 76, 3044 (1972). (8) A. K. R. Unni, L. Elias, and H. I. Schlff, J . Phys. Chem., 67, 1216 (1963). (9) B.M. Fabuss and A. Korosi, Office of Saline Water Research Review Progress Report No. 384, 1968. ( I O ) "International Critical Tables", Vol. 3, McGraw-Hill, New York, N.Y., 1928.
Solvation of
Ions
The Journal of Physical Chemistry, Vol. 82, No. 2, 1978
(11) S. Lindenbaum and G. E. Boyd, J. Phys. Chem., 68, 911 (1964). (12) F. Din, "Thermodynamic Functions of Gases", Vol. 3, Butterworths, London, 1961. t . Mech. Eng., (13) 0. L. Culberson and J. J. McKetta, Jr., Trans 192, 223 (1951); J . Petrol. Techno/., 2, : 9. em. Soc., 57, (14) I. R. Krichevsky and J. S. Kasarnovsky, J 2168 (1935). (15) R. H.Olds, 0. H. Sage, and W.N. Lacey, Ind. Eng. Chem., 34, 1223 (1942).
(16) L. G. Hepler, Can. J . Chem., 47, 4613 (1969). (17) See, for example, T. S. Sarma, R. K. Mohanty, and J. C. Ahluwalia, Trans. Faraday Soc., 65, 2333 (1969). (18) E. C. Bingham, J. Phys. Chem., 45, 885 (1941). (19) H. S.Frank and M. W. Evans, J . Chem. Phys., 13, 507 (1945). (20) H. S. Frank and W. Wen, Discuss. Faraday Soc., 24, 133 (1957). (21) L. G. Hepler, personal communication. (22) A. J. Ellis, J. Chem. SOC.A , 1579 (1966), 660 (1967); L. A. Dunn, Trans. faraday Soc., 64, 2951 (1968).
Preferential
Single
191
Preferential Solvation of Single Ions. A Critical Study of the Ph4AsPh4BAssumption for Single Ion Thermodynamics in Amphiprotic and Dipolar-Aprotic Solvents J. I. Kim Institut fur Radiochemie, TU Munchen, 8046 Garching, Federal Republic of Germany (Received May 18, 1977) Publicailon costs assisted by the Institut fur Radlochemie, TU Munchen
A critical study has been made in order to verify the Ph4AsPh4Belectrolyte assumption, in which the standard free energies of transfer for the electrolyte from one solvent to another, AlG", are divided equally between the cation and the anion. Discussion is made on the basis of a model treating the solvation energy of an ion being a composite of the electrostatic and nonelectrostatic contributions. The electrostatic parts of standard free energies of transfer, which account for interactions between the charges of ions and multipoles of solvent molecules, are calculated by the Buckingham theory, whereas the nonelectrostatic parts are replaced by the experimental values of AfGo(Ph4Ge)and AfGo(Ph4C),where the neutral molecules, Ph4Ge and Ph4C, are proved to be, by their sizes and structures, the neutral analogues of the reference ions Ph4Ast and Ph4B-, respectively. The sums of these two energy contributions are then compared with the corresponding experimental values of Af Go(Ph4AsPh4B)in various organic solvents and reasonable agreements between the values are observed. In the procedure, the molecular volumes of different physical natures for the tetraphenyl molecules are determined and they are correlated to standard free energies of transfer in an effort to support the postulation that the AfGo(Ph4Ge)and AfGo(Ph4C)values are equal to the AfGo(neut)values of the Ph4As+ and Ph4B- ions, respectively. The partition of the values for the reference cation and anion has revealed some differences in standard free energies of transfer, in most cases, slightly greater for the cation than for the anion. However, the differences do not exceed the relative error assigned to each value. The results from the present study support strongly the Ph4AsPh4Bassumption which enables the determination of thermodynamic values for single ions.
1. Introduction
A thermodynamic approach to the evaluation of ionsolvent interactions involves the determination of the standard free energy of transfer for single ions from one solvent (index 1)to another (index 2), A:Go. The related quantity is often expressed as the medium effect log of the ion. However, the estimation of energetic quantities for single ions requires extrathermodynamic assumptions, for which a wide variety of methods have been introduced by a number of authors since the first experimental method proposed by Bjerrum and Larsson in 1927.l The existing methods have been continuously discussed by a number of authars2-l0and most extensively by Popovych5 and Parker.4 The method most widely practiced by different a ~ t h o r s l l is - ~based ~ on the assumption that the medium effect for a large reference cation can be equated to that of a reference anion of molecular similarity. The method was originally introduced by Grunwald et using the reference electrolyte PbPPh4B. Different pairs of large reference ions were later suggested by other authors, Le., TABPh4B (TAB, triisoamyl-n-butylammoniand Ph4AsPh4B." The latter electrolyte has been used to estimate the partial molar volume^,^^^^^ the solvation e n t h a l p i e ~ , ~and ~ - ~ other ~ thermodynamic quantities14 for single ions. 0022-3654/78/2082-0191$01.00/0
The criteria which make the use of such reference electrolytes plausible are based on the following assumptions: (1)the electrostatic parts of the standard free energies of transfer for the reference ions are relatively smaller than their neutral parts, because of their large and symmetrical size; (2) the molecular volumes or average radii of the reference ions are almost equal, as the contribution of the central atom size to the molecular volume might not be so large; (3) the standard free energies of transfer for the cation and anion from one solvent to another can therefore be considered almost identical. As mentioned in the original work of Grunwald et al., the solvation of a large ion with very low density of surface charge may closely resemble that of an uncharged molecule of equal size and structure. Their logical choice for the neutral molecule was Ph4C and its value was compared with that of Ph4PPh4Bin a water-dioxane mixture (50 wt %), such that d(Gih4F"
+ Gh4B-)
dX1
)
(1)
which equaled 29.4 f 1.3 and 32.2 f 1.2 kcal/mol, where X1 is the mole fraction of the solvent component 1and t the dielectric constant of the medium. The last term on 0 1978 American
Chemical Society
