RELATIVE ENTHALPIES OF SOLVATION OF ALKALIMETALIONS
501
Heats of Solution of Some Trifluoroacetates, Tetraphenylborates, Iodides, and
Perchlorates in Water and in Propylene Carbonate and the Relative
Enthalpies of Solvation of the Alkali Metal Ions in Propylene Carbonate
by Yung-Chi Wu and Harold L. Friedman' IBM Watson Reeearch Center, Yorktown Heights, New York (Received August 80,1966)
The enthalpies of transfer of the alkali metal ions from water to propylene carbonate (dielectric constant 65.1) a t 25' have been determined calorimetrically with the following results for the AH relative to that for Na+: Li+, 3.17; Na+, 0; K+, -2.80; Rb+, -3.43; Cs+, -3.96 kcal./mole. Each of these values has been derived from two independent sets of data with the disparity between independently determined values being, at most, 0.26 kcal./mole. The solvation enthalpies and their correlation, by means of the theory of Latimer, Pitzer, and Slansky, are derived and discussed. Lithium trifluoroacetate is a very weak electrolyte in propylene carbonate, A/Ao being only 0.6 in 0,001 M solution. The association produces not only ion pairs but also a large proportion of a larger aggregate.
1. Introduction The energetics of ion solvation processes are poorly known in solvents other than water although these quantities are of fundamental importance. The situation is somewhat worse for solvation enthalpies than free energies, and it seems of value to determine these enthalpies, at least for some series of ions and some solvents that are of special interest. A calorimeter for this purpose has recently been constructedJ2and the first measurements are reported here. Recently, Held and Criss3 have reported some measurements with similar objectives, although on different systems. Propylene carbonate was chosen for our initial study because its high dielectric constant tends to minimize difficulties due to ion association and because in the anhydrous state it is resistant to reduction by alkali metalsa4 On the basis of these observations, it seems likely that the standard potentials of the alkali metals may easily be determined in this solvent. The reSUlting data would lead to the free energies of S o h tion and, with the present data, to solvation entropies. There have been only a few studies made of propylene carbonate as a solvent for ionic solutions. Harris4 has measured several properties of the pure liquid and Of ionic solutions in propylene carbonate and other
cyclic carbonates. Watanabe and FuossS have made some precise conductivity studies in propylene carbonate, and Kempa and Lee6 have made extensive dielectric measurements on various cyclic carbonates a t 40". From various sources, we have collected the list of solvent properties given in Table I. I n the present work the procedure is to determine the heat of solution of a salt MX in propylene carbonate and in water, extrapolate each of these values to infinite dilution of the final solution, and then, by difference, obtain the standard enthalpy of transfer of M X from water to propylene carbonate. The standard enthalpy is, of course, the sum of the separate enthalpies of transfer of M + and X- from water to propylene carbonate. The determination is made for a number of salts of the same anion, and the relative heats of transfer of the metal ions are obtained by difference. (1) Department of Chemistry, State University of New York at Stony Brook, Stony Brook, N. y. (2) H. L. Friedman and Y. c. wu, Rev. sci.In&., 36,1236 (1965). (3) R. P.Held and C . M. Criss, J . Phys. Chem., 69,2611 (1965). (4) W. S. Harris, Ph.D. Thesis, University of California, Berkeley, Calif., 1958, UCRL Report 8381. (5) A$, Watanabe and R. M. Fuoss, J . Am. Chem. Soc., 78, 527 (1956). (6) R.Kempa and W. H. Lee, J . Chem. SOC.,1936 (1958).
Volume 70, Number 2 February 1966
502
YUNG-CHIWu
Table 1: Physical Properties of Propylene Carbonate a t 25‘ Property
Units
el dielectric
...
constant d In e/dT pl density d In p/dT 7, viscosity d In W/dT
deg. g./cm.a deg.-l CP. deg.-l
“Best” value
65.1
-0.0037 1.198 -1 x 10-3 2.530 -0.018
Ref.
5 5, 6 4
4 4 4
These may be combined with the relative hydration enthalpies of the same ions to obtain the relative solvation enthalpies in propylene carbonate. The principal problem in this work is to find salts that dissolve fast enough so that our instrument gives a heat measurement of useful accuracy. We work a t final electrolyte concentrations of a few millimolal, and our requirement is that the finely ground solid electrolyte dissolve to give a solution of this concentration in less than 20 min. with moderate stirring. We find it to be commonplace that many electrolytes, whose solubility is 10 mm or more, do not meet this condition, not only in propylene carbonate but also in other organic solvents as well.’ The salts studied here are exceptional in this respect. A second requirement for salts to be used in this work is that the anion be the conjugate base of a strong acid. This is to minimize the tendency of the anion to associate with the alkali metal ion. This consideration is based on the assumption that strongly basic anions can bind even alkali metal ions covalently. At any rate, in the work reported here the only difficulty with ion association occurs with lithium trifluoroacetate, and trifluoroacetate is the most basic anion studied. 2. Experimental Section
The calorimeter and sample handling have been described elsewhere.2 In all of the measurements of heats of solution in water, the final concentration is less than 10 mm, and the measured heats are corrected to standard heats by assuming that the excess enthalpy of the dilute solution is the same as that of a KCl solution of the same total concentration. The error in this procedure is less than 5 cal./moIe, judging by the known excess enthalpies of solutions of single electrolytess and known heats of mixing at constant ionic ~ t r e n g t hlo. ~ ~Similarly, in reducing measurements of the heats of precipitation in water, the heat of mixing at constant ionic strength was assumed to be negligible. The Journal of Physical Chemistry
AND
HAROLD L. FRIEDMAN
Conductivity water was used for all of the measurements in aqueous solutions and in the preparation of various salts. Propylene carbonate (Eastman Kodak, White Label) was purified by distillation at 1.5 torr in a five-plate Oldershaw column. The middle cut, which had a specific conductivity K of 2 X 10-s/ohmcm. was used immediately after collection. The conductivity increased on standing at a rate of about 10-g/ohm-cm. hr.-l. This increase in K on standing was observed to be about the same for wet (40 mm HzO) propylene carbonate as for dry. Water also enhances the conductivity of propylene carbonate, roughly 10-g/ohm-cm. per increment of 1 mm water, but this dependence does not seem to be very linear. By Karl Fischer titration the water content of a sample of purified propylene carbonate was found to be less than 0.6 mm? Finally, a sample of propylene carbonate to which water had been added to a level of 2.43 mm was used for calorimetric experiments like those described in section 3. Two samples of sodium trifluoroacetate were dissolved. For the first, giving a final salt concentration of 0.446 mm, AH = 2.95 kcal./mole while for the second, giving an increase in salt concentration of 0.500 mm, AH = 3.41 kcal./mole. These were some of the first calorimetric experiments we did in propylene carbonate and are of lower accuracy than the later work, but they do serve to indicate that accidental water in the solvent in the millimolal range would lead to greater concentration dependence of the heat of solution than we actually observed except in the case of LiC104 and LiOZCCFs. The alkali metal trifluoroacetates” were prepared by treating reagent grade carbonates with an equivalent amount of trifluoroacetic acid and drying in vacuo at 70 to 100”. In some cases, treatment with trifluoroacetic anhydride was used to facilitate the drying process, but this treatment did not work as well as expected because of a tendency for compound formation between the salts and either trifluoroacetic anhydride or acid. One effect of this sort has been studied by Klemperer and Pimentel.12 For analysis, samples of these salts were converted to sulfates and weighed with the results (weight of (7) J. L. Hawes and R. L. Kay, J. Phys. Chem., 69, 2420 (1965). (8) V. B. Parker, “Thermal Properties of Aqueous Uni-Univalent Electrolytes,” U. S. National Bureau of Standards NSRDSNBSZ, Washington, D. C., 1965. (9) R. H.Wood and R. W. Smith, J . Phys. Chem., 69,2974 (1965). (10) Y. C. Wu, M. B. Smith, and T. F. Young, ibid., 69, 1873 (1965). (11) R. Hara and G. H. Cady, J. Am. Chem. SOC.,76, 4285 (1954). (12) W. Klemperer and G . C. Pimentel, J . Chem. Phys., 2 2 , 1399 ( 1954).
RELATIVEENTHALPIES OF SOLVATION OF ALKALIMETALIONS
sulfate/weight calculated from weight of trifluoroacetate): Li, 0.9998; Na, 0.9999; K, 0.9997; Rb, 0.9952; Cs, 0.9998. As another check on the composition, samples of the trifluoroacetates were dissolved in water to form solutions in the range 2 to 15 mm, and the conductivities were measured a t 25.00". The limiting ionic conductivity of CF3C02- was taken as 40.00,13while values for Li+, Ka+, and K + were taken from Robinson and Stokes,14 Rbf from Kunze, FUOSS, and Owen,15and Cs+ from Justice and Fuoss.16 Equivalent conductivities at infinite dilution were estimated from the measured conductivities by the s+/[I empirical equation14 iioestd = Arnea8d &] where S is the Onsager slope and c is the molarity. This equation usually gives Ao within 0.2% for 1-1 electrolytes in this concentration range. Our observations for Aoestc/Aolit for the various trifluoroacetates follow: Li, 1.0095; Na, 1.017; K, 1.011; Rb, 1.017; Cs, 1.015. Each of these is the average of three measurements which differ among themselves by, a t most, 0.3%. Our tentative conclusion is that Xo for CF3C02- is about 41.0. Then only the conductance of the rubidium salt is off by more than 0.5%. The rubidium salt was also analyzed for metallic impurities by arc and flame spectroscopy. The chief impurity was found to be Ca, but its amount, compared to Rb, was less than 5 atoms/1000. A second sample of rubidium trifluoroacetate was later prepared having substantially less Ca impurity. It gave the same heat of solution in water as the first but a different heat in propylene carbonate, as noted below. Sodium and potassium tetraphenylborates were purified as described by Kunze and Fuoss." Rubidium and cesium tetraphenylborates were precipitated from aqueous solutions of the sodium salt and recrystallized from acetone by adding petroleum ether or from propylene carbonate by adding water. These salts were all dried under vacuum at 100" before use. LiC1, KC1, NaI, and KI, of reagent grade, were dried at 350" and used without further purification. LiClOI was prepared from lithium carbonate and perchloric acid and dried at 100" in vacuo for 2 days. A sample was converted to sulfate, dried, and weighed with the result: weight of sulfate/weight calculated = 0.9993. LiI was prepared from reagent grade LiI .3H20 by dehydrating a t 240" in a stream of nitrogen and then purified by zone-refining in a stream of forming gas containing a little Iz vapor. A sample converted to sulfate and weighed gave 0.9993 of the calculated weight. As anoi,her check on the purity the heat of solution in water was measured and compared with earlier worksa l8 (Table 11).
+
+
503
Table 11: Heats of Solution in Water a t 25' A H o , kcal./mole
Salt
LiI RbCl CsCl
This researcha
-14.95 4.04 4.15, 4.16
Lit.
-15.13,* -14.47' 4.13,b 4.17d 4.25,b 4.14"
Each entry is the result of a single measurement in which the final concentration is less than 10 mm, and the correction See for the heat of dilution is made as described in section 2. ref. 8. Lange and Martin18 value combined with estimated heat of dilutions ( A H = - 124 cal./mole) from 0.20 m. Lange and Martin18 value combined with estimated heat of dilutions ( A H = -67 cal./rnole) from 0.157 m. ' Lange and Martinla value combined with heat of dilutions ( A H = -24 cal./mole) from 0.267 m.
RbCl and CsCl were prepared from 99.9% carbonates (supplied by Eastern Chemical Co.) by treatment with HC1, drying, and fusing in platinum. The equivalent conductivity of aqueous solutions, estimated from measurements on our preparations as described above for the trifluoroacetates, were ( h o e , t d / i i O ~ i t ) 0.9955 and 0.9969 for RbCl and CsC1, r e s p e c t i ~ e l y . ~ ~The . ~ ~heats of solution of these materials in water were measured and compared with earlier work (Table 11). The heat of dilution of aqueous RbCl was also measured for this work; the results will be reported elsewhere.
3. Trifluoroacetates The heats of solution in water are reported in Table 111. Each individual value in the "present work" column is the result of a separate experiment. Replicate determinations were only made in cases where there was disagreement with the earlier work. These differences seem to be due to impurities in the samples investigated earlier. It is remarkable that the results are so sensitive to impurities. The heats of solution in propylene carbonate are reported in Table IV. To get AH" of solution from these data we require the heats of dilution from the final concentration to zero concentration. From the temperature coefficient of the dielectric constant and the density of the solvent (Table I) we estimate that the Debye-Huckel limiting law contribution to the (13) A. L. Henne and C. J. Fox, J . Am. Chem. Soc., 73,2321 (1951). (14) R. A. Robinson and R. H. Stokes, "Electrolyte Solutions," Butterworths Scientific Publications, London, 1959. (15) R. W. Kunze, R. M. Fuoss, and B. B. Owen, J . Phys. Chem., 67, 1719 (1963). (16) J.-C. Justice and R. M. Fuoss, ibid., 67,1707 (1963). (17) R. W. Kunze and R. M. Fuoss, ibid., 67, 385 (1963). (18) E. Lange and W. Martin, Z . Elektrochem., 42, 667 (1936).
V o l u m e 70,N u m b e r d
February 1966
504
YUNG-CHIWu
AND
HAROLD L. FRIEDMAN
30
I
Table 111: Heats of Solution of Trifluoroacetates in Water AH', kcal./mole
Present work
Earlier work"
Best value
-6.32, -6.34, - 6 . 2 6 -2.00 1.24 1.84, 1.92, 1 . 9 0 1.52
- 5 . 5 5 f0 . 0 5 -1.96f0.12 1 . 2 4 f0 . 0 3 1 . 3 6 f0 . 0 3 1.56 f 0 . 0 3
-6.33 -1.99 1.24 1.89 1.53
Metal
Li
Na K Rb
cs
A
20
K. H. Hu and H. L. Friedman, unpublished results with an earlier version of the calorimeter used in the present work. The unoertainties indicate the maximum deviation from the average of three or more determinations. Analysis of the materials used after the calorimetry was completed, revealed over 1% impurity in the Li, Rb, and Cs salts. IO
heat of dilution is AHDHLL= - 9 O G cal./mole. The magnitude of this effect is only 7 cal./mole a t 6 mm, the highest concentration in this work, and this is negligible compared to the experimental errors.
Table IV : Heats of Solution of Trifluoroacetates in Propylene Carbonate AH,
AH',
kcal./ mole
kcal./mole, best value
2.36 f 0 . 4
Metal
mm
Final oonon., mm
Li
0 1.29 2.78 0 0.95 2.60
1.29 2.78 5.36 0.95 2.60 4.80
-0.09 -1.75 -2.14 0.17 -1.66 -2.10
0 0.90
0.90 2.01
3.32 3.33
3.32
0 0.91 2.08
0.91 2.08 3.44
3.76 3.73 3.51
3.73
0 0.93
0.93 4.59
2.84 2.93
0.63 1.21
1.21 2.10
3.79 3.76
3.78
0 0.75 2.36
0.75 2.36 6.24
3.11 2.97 3.03
3.04
Initial conon.,
Na
K
Rb
cs
Therefore, for strong electrolytes we expect AH of solution to be independent of concentration within the accuracy of the present work, and this is consistent with the observations for all the trifluoroacetates but that of lithium. The JournaE of Phgsical Chemistry
0
5
10
100&
Figure 1. Phoreograms for various salts in propylene carbonate a t 25". Here c is the molar concentration. The straight lines are calculated Onsager slopes for the various salts. The curved lines serve only to connect data for the same salts and are without theoretical significance.
The strong concentration dependence of the heat of solution of the lithium salt suggests that an ion association process with a substantial heat effect is contributing to the heat. Attempts to fit the concentration dependence of AH on the basis of an ion association equilibrium led to the tentative conclusion that an association complex of jour ions was involved. I n order to elucidate this, the electrical conductivities of some of the solutions were measured with the results shown in Figure 1. Ao for LiCOzCF3 cannot be determined by extrapolating the phoreogram, and at lower concentrations than those investigated the solvent conductance interferes. The conductivities of the other salts shown in Figure 1 were determined to get Ao for LiC02CF3by Kohlrausch's law, with the result shown on Figure 1. Apparently, NaC02CFa is also a weak electrolyte in propylene carbonate, but its association is not very significant in the concentration range of the calorimetric measurements. It was found to be impossible to calculate the phoreogram for LiCOzCFa on the basis of association to form either an ion pair or an ion-pair dimer. Presumably, both association processes are occurring in this concentration range, which would be consistent with the concentration dependence of A H . If we make the approximation that only one (un-
RELATIVE ENTHALPIES OF SOLVATION OF ALKALI METALIONS
505
specified) association process is occurring and if the degree of dissociation at molality m be designated a ( m ) , then the molar heat of solution of the salt to form a final solution of concentration m is of the form
AH(m) = AH"
+ [l - a(m)]AH,
(3.1)
where AHa is the molar enthalpy increase in the association process. I n this equation, as in the preceding discussion of this problem, we have neglected the longrange interionic effects that determine the DebyeHuckel and Debye-Huckel-Onsager limiting laws. That this is reasonable may be seen from Figure 1, where the limiting-law contributions to the conductances of the perchlorates are seen to be only a moderate fraction of the total conductance. These long-range interionic effects will, of course, be even smaller for the weak electrolytes a t a given stoichiometric concentration. If we neglect the long-range interionic effects, then in any given solution a(m) = A/Ao. Thus, according to eq. 3.1, a plot of AH as a function of A/Ao should yield a straight line whose intercept is AH" and whose slope is A€€*. This is demonstrated in Figure 2. The observed small curvature of the data when plotted is presumably due to the fact that there are two association processes playing a role in this concentration range, and they do not have the same AH,. The linear extrapolation is regarded as yielding a provisional value of AH" for this system. The two sets of values for rubidium trifluoroacetate in Table IV were obtained from the two different preparations of the material described in the Experimental Section. The second set is much more in accord with the rest of the data, and, on this basis, it is presumed that the first set reflects a sizeable heat effect due to some impurity. This illustrates again the sensitivity of these heats to impurities and the need for independent checks in this work. The AH" values from Tables 111 and IV may be combined to obtain the standard enthalpies of transfer of the trifluoroacetates from water to propylene carbonate (Table V). These heats of transfer are composed of additive ionic contributions, and this affords an opportunity to test their accuracy by investigating other salts as described in the following sections.
4. Tetraphenylborates The heat of solution of sodium tetraphenylborate in water was measured directly, while the salts of K, Rb, and Cs were studied by measuring the heat of the precipitation reaction which ensues when a solution of NaB(CeHJ4 is mixed with, respectively, KC1 solu-
5.20
kcal/mole
-2
I
I
'
I
'
t
'
'
l
'
t
'
0 A/A, OF FINAL SOLUTION 0.5
Figure 2. Integral AH of solution of LiCOZCF3 in propylene carbonate. The plain and barred circles represent two series of determinations.
Table V : Standard Heats of Transfer from Water to Propylene Carbonate
Metal
AH"(MX), kcal./mole
AH"(MX) AHo(NaX), kcal./mole
Trifluoroacetates 8.69 5.35 2.52 1.89 1.52
-2.83 -3.46 -3.83
cs
Tetraphenylborates -5.93 -8.67 -9.32 -10.02
0 -2.74 -3.39 -4.09
Li Na
Perchlorates -3.16 -6.37
3.21 0
Iodides -0.10
3.12
-3.22
0
Li
Na K Rb cs Na
K Rb
Li Na
3.34 0
tion, RbCl solution, or crystalline CsCl. Further details and the results are given in Table VI. Volume YO, Number B February 1966
YUNC~CHI Wu AND HAROLD L. FRIEDMAN
506
~~~~
Table VI:
~
Heats of Solution of Tetraphenylborates in Water Kcal./mole Initial M C1 concn., m
Metal
Initial B(CsH6)dconcn., mm
Final B(CsHd4concn., mm
0
AHa precip.
901.6 cor.
DiLE cor.
aoln.
-4.79 -4.80 -4.75
-4.79
AHo
0.82 1.53
0.82 1.53 2.06
3.06 1.99 1.99
2.06 21.64 20.65
1.32 20.65 18.38
-8.79 -9.32 -9.27
-0.19 -0.02 -0.01
-0.29 -0.17 -0.17
9.27 9.51 9.46
9.41
3.37 3.37
18.38 17.27
17.27 15.61
-11.17 -11.49
0 0
-0.40 -0.40
11.57 11.89
11.73
Crystal Crystal Crystal
10.70 9.51 7.38
9.51 7.38 4.83
-8.13 -8.30 -8.29
0 0 0
-4.16 -4.16 -4.16
12.29 12.46 12.45
12.40
Na
K
Rb
cs
AHo
soln., best value
0.010 0.005 0.002
" This is the molar heat of the precipitation reaction, corrected for the heat of breaking the sample bulb. This is the correction to allow for the incomplete precipitation of MB(CeH6)a. The estimate for KB(CaH6)d is based on a value of 3.3 X 10-8 for the solubility product (W. Rudoff and H. Zaunier, Z. Naturforsch., 8b, 611 (1953)). The solubility products for RbB(C&)4 and CsB(C&)r This is a correction to standard states. I n the case of KCl (ref. 8) and RbCl (Wu and are assumed to be, a t most, half this value. Friedman, unpublished results), it is the molar heat of dilution of the initial MCl solution. In the case of CsCl it is the standard heat of solution of the crystal in water.
The heats of solution of the tetraphenylborates in propylene carbonate were measured directly, with the results given in Table VII, and used to calculate the heats of transfer from water to propylene carbonate (Table V). Table VII:
Heats of Solution of Tetraphenylborates in Propylene Carbonate
Metal
Na K Rb
cs
AH',
Initial conon., mm
Final concn., mm
kcal./mole
kcal./mole, beat value
0 0.20
0.20 0.30
-10.92 -10.52
-10.72
0 0.55
0.55 0.77
0.74 0.74
0 0.57
0.57 1.14
2.41 2.41
2.41
0 0
0.14
2.41 2.38
2.38
0.18
AH,
Table VIII: Heats of Solution in Propylene Carbonate
Salt
0.74
LiI
5. Iodides The solubility of K I in propylene carbonate is 0.23 m, but the rate of solution is not large enough to permit measurement of the heat of solution with our instrument. The same is presumably true of the R b and Cs salts, but the Li and Na salts dissolve readily and The Journal of Physical Chernktry
rapidly enough, and the heats were measured with the results given in Table VIII. It proved to be more dficult to get reproducible results with the iodides than with the other salts reported here, apparently because of heat effects due to the interaction of iodide ion with traces of impurities in propylene carbonate. Heats differing by several kilocalories per mole from those reported kere were obtained in other experiments in which less care was used in purifying the salts and handling the solvent.
Final total concn., mm
kcal./ mole
0.76
3.39 0.76 1.82
-15.04 -14.93 -15.14
3.39" 8.83 1.82" 2.76
8.83 10.58 2.76 3.79
-5.00
0
1.64 5.24 14.26
-9.33 -8.43 -6.99
Initial concn., mm
0.85"
0
NaI
LiClOh
1.64 5.24 NaCIOa a
AH,
-5.00
AH', kcal./mole, best value
-15.05
-5.04
-5.16 -5.01
See ref. 2
Initial concentration of LiI solution.
-9.51 -3.05
RELATIVE ENTHALPIES OF SOLVATION OF ALKALIMETALIONS
The heat of solution of LiI in water is given in Table I1 while for NaI the corresponding quantity is -1.8lS or -1.8218 kcal./mole. With these data and those in Table VI11 we calculate the heats of transfer given in Table V.
6. Perchlorates For these salts the solubility situation is similar to that for iodides in propylene carbonate, and heats of solution were measured only for the Li and Na salts (Table VIII). Conductance measurements (Figure 1) indicate that LiC104and NaC104in propylene carbonate are strong electrolytes in the concentration range of interest here. However, the heat data for LiC104 depend strongly on the molality, the magnitude of the concentration dependence being as large as for LiC02CF3. Frorn these data we may calculate AH(m), the enthalpy change on dissolving the salt in pure solvent to form a solution of final molality m, with the result AH(m) = -9.51 14.30m f 0.10 kcal./mole, where the uncertainty given is the maximum deviation. This differs from the concentration dependence for AH for LiC02CF3 in two important respects. First, the dependence is linear for the perchlorate, implying that, if an association process were responsible, the degree of association would be small in the experimental range and the molar heat of association would be astronomical. Second, the sign of the concentration dependence is positive here. Therefore, the predominant ion-ion interaction is endothermic, rather than exothermic as for the trifluoroacetate. For solution in water we haves AH' = -6.35 kcal./ mole for LiC104, and 3.32 kcal./mole for NaC104.18 Combining the heats in water and propylene carbonate, we obtain the heats of transfer given in Table V.
+
7. Other Attempted Studies and Miscellaneous Observations We examined several other processes which a t first seemed promising for determining heats of solution in propylene carbonate. The alkali halides are relatively easy to obtain in pure form, but for the most part they dissolve only slowly in propylene carbonate, and their solubilities are quite A possible approach seems to be to dissolve the alkali halide in the presence of an agent, previously added to the propylene carbonate, to complex the halide ion and thus compensate for the presumed poor solvating power of the solvent for these ions. FeC& is such a complexing agent for chloride,lg and it was found that FeC4 enhances the solubility of KC1 in propylene carbonate and that FeC14- is formed in the process. However, even this process proved
507
to be too slow to be investigated in our calorimeter although a measurement was obtained with LiCl and FeC13. For FeCL dissolving in propylene carbonate AH = -17.3 kcal./mole for a final concentration of 7 mm. When LiCl dissolves in this solution AH = -3.3 kcal./ mole for a final Lif concentration of 2.6 mm. An attempt was made to enhance the rate of solution of the iodides of the heavier metals by employing Iz as a complexing agent since the process II I- = Is- is expected to proceed readily. Again the equilibrium prediction was correct, but the rate of solution of K I was too small even in the presence of excess
+
12.
For H2O (1) dissolving in propylene carbonate, we find AH = 2.00 kcal./mole for a final concentration of 2.35 mm. Several solubilities in propylene carbonate were determined with the following results: LiI, 0.020 m (1.365 m); NaI, 1.10 m (1.11 m); KI, 0.23 m (0.206 m); C S B ( C ~ H ~0.016 ) ~ , m. The figures in parentheses are the results of H a r r i ~ . We ~ have not analyzed the solid phases in equilibrium with the solution, but the above results suggest that at least LiI(c) becomes solvated in equilibrium with propylene carbonate.
8. Solvation Energies The various independent determinations of the heats of transfer relative to sodium ion, listed in Table V, are considered to be in good agreement in view of the fact that each entry in the last column of the table is the combination of four separate AH" determinations, each with an uncertainty of at most 30 cal./mole for aqueous solutions and 50 cal./mole for propylene carbonate solutions. Simple averages of these determinations are taken as best values given in Table IX, except that the LiC02CF3 data have been neglected because of the uncertainty in the extrapolation in Figure 2. In Table I X we also list the standard enthalpies of hydration of the alkali metal ions. These may be combined with the heats of transfer to obtain the relative solvation enthalpies in propylene carbonate, given in the last column of the table. The range of enthalpies of solvation is smaller for these ions in propylene carbonate than in water, which implies that the magnitudes of the solvation energies are smaller as well. I n fact, they are smaller than expected on the basis of the difference in dielectric constant alone. This may be seen in the following way. ~~
(19) H.L.Friedman, J. Am. Chem. Soc., 74, 5 (1952).
Volume 70,Number I February 1966
508
YUNG-CHIWu AND HAROLD L. FRIEDMAN
Table IX: Heats of Transfer Relative to N a f (kcal./mole) AH',
Li + Na +
K+ Rb Cs
+
+
-
AH',
AHO,~
aq. + p.c.a
aq.
3.17 0 -2.80 -3.43 -3.96
P.C.-c
gas
gas
26.28 0 -20.18 -26.09 -30.61
23.11 0 -17.38 -22.66 -26.65
Calculated from the heats a P.C. = propylene carbonate. of formation of gaseous and aqueous ions tabulated in "Selected Values of Chemical Thermodynamic Properties," National Bureau of Standards Circular 500, U. S. Government Printing Office, Washington, D. C., with the following exceptions: Li+(aq), AH" = -66.706 kcal./mole from H. L. Johnson and T. W. Bauer, J. Am. Chem. Soc., 73, 1119 (1951); Cs+(aq), A H o = -62.6 kcal./mole, reported by H. L. Friedman and M. Kahlweit, J. Am. Chem. SOC.,78,243 (1956).
We begin with the Latimer, Pitzer, and Slanskya formula for the free energy of solvation of an ion of charge ei and Pauling crystal radius ri in a solvent of dielectric constant E Fi = -ei2[1 - l/e]/2[ri 61 (8.1)
+
where 6 is a parameter depending on the sign of the ion and on the solvent. This is a modification of the Born equation for the solvation energy in which the parameter 6 accommodates a number of effects suppressed in the derivation of the Born equation, where the solvent is considered only in the role of a dielectric continuum with properties independent of field strength and pressure.20,21Although it seems surprising that such diverse effects as molecular structure and pressure dependence and electric field strength dependence of solvent properties can all be accommodated by a single parameter 6, Latimer, Pitzer, and Slansky found that, for aqueous solutions, eq. 8.10gave good agreement with experiment if 6 = 0.85 A. for cations and 6 = 0.10 A. for anions.Z2 On this basis, it seems to us that the 6 parameters may be useful for characterizing and correlating the ability of various media to solvate ions.23 By differentiating eq. 8.1 we obtain the corresponding enthalpy of solvation
Lit
No+ 0.4
0.5
0.6 0.7 [ r t b]-',A-'
48
Figure 3. Ionic solvation enthalpies relative to sodium ion a t 25".
and in propylene carbonate to the abbreviated equation, with the results shown in Figure 3. The linearity of the plots in Figure 3 is about as good as for the free energy of hydration.2o It would be premature to conclude from the fact that the linearity is a little better for propylene carbonate than for water that the former is a more nearly "ideal" ionic solvent. We do conclude from the significant difference in 6 values that the former is not so good a solvent for these ions as the latter, even after allowing for the difference in dielectric properties. It seems appropriate to rest with this primitive interpretation of the data until the corresponding free energies and entropies are known.
9. Ion Association Processes In the course of this work we have found some evidence for the association process (20) W. M. Latimer, K. 5. Pitzer, and C . M. Slansky, J . Chem. Phys., 7 , 108 (1939). (21) K. J. Laidler and M. Pegis, Proc. Roy. SOC.(London), A241,
80 (1957). (22) On the other hand, it has been claimed21 that eq. 8.1 is in error because it implies that the ion has radius ri 6 in the gas phase as well as in solution. This seems to be wrong. Equation 8.1 may be derived by calculating the free energy of the electric field outside of the ion in the gas phase and in solution and taking the difference. If the ion is a spherically symmetric charge distribution with all of the charge within a radius l i < ri 6, then the electric 6 does not change when the ion field in the shell between l i and ri is solvated. The field outside of this shell is the same as the field outside of a conducting sphere having radius r i 6 and the same charge as the ion. This is all that is needed for the familiar derivation of eq. 8.1. This equation does assume that the charge distribution of the ion is the same in the gas phase as in solution. An alternative model has been investigated by R. H. Stokes, J . Am.
+
+
+
+
To the extent that &/dT is negligible this gives the same dependence on [ri 61-l as eq. 8.1 except for the slope. For the rest, we explicitly neglect bS/dT (which amounts to including a portion of its effect, if any, in 6) and fit the solvation enthalpies in water
+
The Journal of Physical Chemistry
Chem. SOC.,8 6 , 979 (1964). (23) One of the possible refinements of this equation is to apply it only to the difference of the ionic solvation energy and the solvation energy of a real or equivalent uncharged body. See H. L. Friedman and G. R. Haugen, J. Am. Chem. Soc., 7 6 , 2060 (1954), and R. M. Noyes, ibid., 86, 971 (1964).
RELATIVE ENTHALPIES OF SOLVATION OF ALKALI METALIONS
2Li+
+ 2CF3C02- +Liz(CF3COz)z
(9.1)
in propylene carbonate. It seems that the greater part of the electrolyte is associated to the ion-pair dimer at all concentrations in excess of 10 mm. A possible structure of the ionpair dimer is that of a carboxylic acid dimer with the protons in the hydrogen bonds replaced by lithium ions. As a check that these effects are not due to impurities in LiC02CF3, we have studied the change in conductivity on mixing a LiC104 solution with an equal volume of NaC02CF3 solution, both having c = 4.59 mM. The equivalent conductance of the mixture was 16.32 while that estimated from the mixing ratio and the conductivities of the end solutions, assuming linearity, was 19.62. This confirms that the lithium ion and the trifluoroacetate ion have an exceptional affinity for each other in propylene carbonate. I n another experiment small amounts of water were added to a 5 mM LiC02CFa solution. Up to 1 m water added increases the equivalent conductance only slightly. The great stability of the ion association products, especially the ion-pair dimer, seem surprising to us, but we are unable to propose an alternative interpretation of our observations. This situation implies
509
that for some reason the solvation of trifluoroacetate ion by propylene carbonate is much poorer than that of other ions in other solvents. Support for this view may be found in the fact that the heats of transfer of neutral salts from water to organic solvents are generally exothermic, but this is not so for trifluoroacetates in propylene carbonate. Some examples of the general rule may be found in Table V; others have been reported by Held and C r i ~ s . ~ The conductance data for NaC02CF3 (Figure l), although sparse, indicate that appreciable ion association occurs in this case too, but at higher concentrations than used in the calorimetry of this salt. On the other hand, the conductivity data for lithium and sodium perchlorates in propylene carbonate give no evidence for ion association although, as pointed out in section 6, the heat effect indicates a very large ionic interaction in LiC104 solutions. Acknowledgment. The authors are grateful to Miss
T. I. Sun for the preparation and analysis of the trifluoroacetates, to Mr. E. J. Petrillo for assistance in operating the calorimeter, to Dr. W. Reuter and Mr. B. L. Olsen for carrying out many of the chemical analyses, and to Dr. R. W. Dreyfus and Mr. K. W. Asai for zone-refining the lithium iodide.
Volume 70,Number 8 February 1966
