FREEZINGPOINTS, OSMOTIC COEFFICIENTS, AND ACTIVITYCOEFFICIENTS OF SALTS
2319
Freezing Points, Osmotic Coefficients, and Activity Coefficients of Salts in N-Methylacetamide. 11.
Tetraalkylamrnonium Halides and
Some Alkali Metal Formates, Acetates, and Propionates1
by R. W. Kreis and R. H. Wood* Department of Chemistry, University of Delaware, Newark, Delaware
10711
(Received J u n e 2 , 1070)
Publicatian costs assisted by the A'ational Science Foundation
The freezing points of N-methylacetamide solutions of the acetates and propionates of lithium, sodium, and potassium, the formates of lithium and sodium, and the chlorides, bromides and iodides of some n-tetraalkylammonium ions have been measured at concentrations from 0.1 to 0.8 m. Osmotic and activity coefficients were calculated from the freezing points. The similarity of the order of osmotic coefficients in water and W-methylacetamide, observed for the alkali metal halides and nitrates, also holds for the alkali metal formates, acetates, and propionates. It is unlikely that "localized solvolysis" is an important factor in determining the order of osmotic coefficients. At low concentrations, the order of osmotic coefficients of the n-tetraalkylammonium halides, C1- > Br- > I-, is the same as in water. With the smaller ions the order is BuhN+ > Pr4N+ > EtiN+ > MedN+ in both water and N-methylacetamide. As the anion increases in size the order reverses in water and becomes less pronounced in N-methylacetamide. In both solvents the osmotic coefficients of the iodides of the larger cations are below the Debye-Huckel limiting law. The similarity in trends shows that the water-structure enhancing properties of the larger tetraalkylammonium ions are not responsible for the trends. The results in water and NMA can be explained by the penetration of the larger, weakly solvated anions into the hydrocarbon portion of the cation. Very small distances of closest approach are possible and the effective dielectric constant should be small. For aqueous solutions at higher concentrations,the effects of the water structure enhancement around the larger tetraalkylammonium ions become apparent.
Introduction The previous paper2 showed that order of the osmotic coefficients of alkali metal halides and nitrates in water and N-methylacetamide were similar. This could be explained by the relative ease with which oppositely charged ions displace solvent from the primary coordination sphere of an ion. The results also showed that solvent structure breaking is not responsible for the similarity of the order of osmotic coefficients. This paper extends the measurements to the osmotic coeficients of a variety of salts in order to see if the similarity to aqueous solutions is still present. Gopal and Siddiqi3have measured the apparent molal volumes of a series of tetraalkylammonium iodides as a function of concentration and temperature. Their results show a great similarity between aqueous solutions and KMA solutions. On this basis, Gopal and Siddiqi concluded that the behavior could not be due to lyophopic structure making. The present paper reports measurements of the osmotic coefficients of some tetraalkylammonium halides which show the same similarity between aqueous and NMA solutions.
Experimental Section The details of the experimental procedure have been reported previously. 2 , 4 Lithium formate, lithium acetate, and lithium propionate were prepared by reacting
the appropriate metal carbonate with either formic, acetic, or propionic acid. The resulting solutions were recrystallized from the appropriate pure acid and then from water. Sodium formate, sodium acetate, sodium propionate, and potassium acetate were obtained commercially and used without further purification. These salts were dried under vacuum for 24 hr, the formates a t 130" and the acetates and propionates at 180". As a rough check on purity, 1 M solutions of the acetates and propionates were titrated with 1 M HC1. The results were accurate to about 1% and showed purities from 98.6 to 99.1%. The initial pH's of 1 M aqueous solutions were : lithium acetate 8.60, sodium acetate 9.60, potassium acetate 8.78, lithium propionate, 8.48, sodium propionate 8.40, and potassium propionate 7.88. These p H values indicate that residual weak acid in the sample is less than 0.2%. The results of a carbon analysis of the formates were: lithium formate 23.12 calcd, 22.71 found; sodium formate 17.60 calcd, 17.52 found. (1) Presented at the 5th Middle Atlantic Meeting of the American Chemical Society, Newark, Del., April 1970. (2) R. H. Wood, R. K. Wicker, and R. W. Kreis, J . Phys. Chem., 75, 2313 (1971). (3) R. Gopal and M. A. Siddiqi, ibid., 73, 3390 (1969). (4) R. W. Kreis, Ph.D. Thesis, University of Delaware, Newark, Del., June 1969.
The Journal of Physical Chemistry, Vol. 76, N o . 16, 1971
2320
R. W. KREISAND R. H. WOOD
Samples of these solutions in equilibrium with solid N N A were analyzed for salt by evaporating t o dryness at 140”)and weighed. Synthetic solutions of the salts analyzed in the same way showed that the procedure was accurate to =kO.5% for the acetates and propionates and =k 1.0 for the formates. The n-tetraalkylammonium salts were obtained commercially, purified and dried according to Unni, Elias, and Schiff.6 The per cent purity of the individual salts based on an analysis for halide was: (CH3)4YC1, 100.13; (CzH6)4NC1, 100.26; (C3H7)4NClj 99.94; (C4Hs)4n’Cl, 99.99; (CH3)4NBr, 99.70; (C2H&NBr, 99.97; (CaH7)4NBr, 99.95; (C4H9)4YBr,100.12; (CZH6)4NI, 100.30; (C3H,)&I, 99.95; and (C4!&)$1, 100.12. All samples were stored in a drybox (dewpoint, -50”) until transferred to the salt pistol of the freezing point apparatus. Samples taken from the freezing point cell were analyzed for halide by adding 2-5 ml of water and titrating with silver nitrate solution using dichlorofluorescein as an indicator and a few drops of Triton CF21 polyethyl eneoxide6 as an anticoagulant. Titration of known amounts of tetraalkylammonium halides under similar conditions were accurate to 0.3% or better. This is true even for the iodides which are known to form mixed salts with silver iodide. The all-glass cell was used for all measurements. Based on the variation of the initial freezing points of the solvent, the total impurity was 0.001 to 0.0002 m for zone melted samples. To save time, some of the experiments were conducted using NJIA recrystallized in the drybox or a second sample of solvent from the zone melting tube. The total solvent impurity in these runs varied from 0.001 to 0.03 m. No systematic differences between the results of the two methods were detected. Zone melted solvent was normally used for the lowest concentration points where it gave more reproducible results. The temperature was measured by a thermistor calibrated against a standard platinum resistance thermometer.
Treatment of Data The treatment of the data has been described previo u s l ~ .Briefly ~ ~ ~ the measured osmotic coefficients are fit t o the equation $I = 1 - (2,303A/3)m1’2c(m1’2)
(2.303/2)Bm
+ + 2.303(5/6)Cma’/” (1)
where
+ m”2 1/(1 + m”/”)- 2 In (1 + m”/”)]
c(m”2) = (3/ma’2) [I
(2)
and B and C are determined by the method of least squares. The coefficient A is the Debye-Huckel slope ( A = 0.14128 vias used).2 The activity coefficients are then given by log
y =
Am’’2/(1
+ ml”) + Bm + Cm8/’
The Journal of Physical Chemistry, Vol. 76, N o . 16,1971
(3)
Results and Discussion I . Formates, Acetates, and Propionates. The results of the least-squares fit of the data for the formates, acetates, and propionates are given in Tables 1-111 and Figure 1. The standard deviation of both the temperature differences and the osmotic coefficients are given in Table I. The standard deviations indicate that the osmotic coefficients are accurate to about 1%.
Table I : Results of the Least-Squares Fit
Salt
Li form N a form LiOAc NaOAc KOAc LiOPr NaOPr
KOPr
B
-0.4992 -0.0321 - 0.2272 - 0,1668 0.0466 - 0.0926 0.0052 0,1776
Standarda
Standard
error of e
error of 4
0.020 0.018 0.046 0.035 0.031 0,023 0.029 0 I052
0,008
C 0.3709 - 0.3373b 0,0254 - 0,0251 - 0.0422 -0.0669 -0.1399 -0.1522
0,012 0.012 0,015
0.008 0,007 0.004 0,014
a This is the standard deviation of the freezing point depression. b If C is set equal to zero, the fit is almost as good if the B coefficient is -0.2035.
At the highest concentrations where the measurements are the most accurate, the order of osmotic coefficients is potassium propionate > potassium acetate > sodium propionate > lithium propionate > sodium acetate > sodium formate = lithium acetate > lithium formate. This order is consistent with the cation order K + > Na+ > Li+ and the anion order propionate > acetate > formate. The osmotic coefficients of sodium formate and sodium acetate are within experimental error of each other a t all concentrations and the order changes between 0.1 and 0.2 m. The high concentration data are more accurate and these are consistent with the order of the rest of the salts. I n addition the least-squares fit for sodium formate is almost as good with the C term set equal t o zero and B = -0.2035. With this change the B coefficients of Table I and the osmotic coefficients have the order propionate > acetate > formate. Also with this change sodium formate fits better into the family of curves in Figure 1. This cation order is the reverse of the order of the alkali metal halides and nitrates in both water’ and NMA.2 Similarly the order in aqueous solutions is propionate > acetate > formate.’ Thus the similarity of the order of the osmotic coefficients in water and XMA observed for the alkali metal halides and nitrates ( 5 ) A. K. R. Unni, L. Elias, and H. I. Schiff,
J. Phys. Chem., 67, 1216 (1963). (6) Rohm and Haas Co. (7) R. A. Robinson and R. H. Stokes, “Electrolyte Solutions,” 2nd ed, Butterworths, London, 1965, Appendices 8.7 and 8.10.
FREEZING POINTS, OSMOTIC COEFFICIEK’TS, AND ACTIVITY COEFFICIENTS OF SALTS
2321
Table I1 : Osmotic Coefficients, 9 m
Li form
Na form
LiAc
NaAo
KAc
LiPr
NaPr
KPr
0.01 0.05 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80
0.985 0,959 0.936 0 903 0.881 0.867
0,990 0.975 0.959 0.923
0.988 0.969 0.952 0.923 0.897 0.872
0.989 0.972 0.957 0.931 0.906 0.882
0.991 0.984 0.981 0.978 0.976 0.974 0.973 0.970 0.968 0,965
0,989 0.976 0,964 0,943 0.922 0.902
0.990 0.980 0,972 0.956 0.940
0.992 0.990 0.991 0,995 0.996 0.996 0.994
Table 111: Activity Coefficients, yi, m
Li form
Na form
LiAc
NaAc
KAc
LiPr
NaPr
KPr
0.01
0,961 0.898 0.847 0.776 0.726 0.691
0.969 0.931 0.896 0.831
0.966 0.919 0.879 0.819 0.769 0.726
0.967 0.924 0.888 0.833 0.787 0.745
0.972 0.946 0.932 0.916 0.906 0.898 0.891 0.884 0.878 0.872
0.969 0.931 0,901
0.971 0.939 0.917 0.881 0.848
0.974 0.958 0.953 0.951 0.951 0.950 0.947
0.05 0.10 0.20
0.30 0.40
0.50 0.60 0.70
0.80
I\
1
K Pr
1%--
7------------
K Ac __z
0
OS91
-
I
Li Ac
\NaAc
Li Fr I
I
I
0.2
l
-
l
0.4
I
l
0.6
‘
I
Figure 1. Osmotic coefficients of alkali metal formates (Fr), acetates (Ac), and propionates (Pr) in NWA as a function of molality.
also holds for the alkali metal formates, acetates, and propionates. Robinson and Harneds suggested that cations polarize the coordinated solvent molecules and make them stronger acids. I n the presence of a basic anion, association can occur through the intermediacy of a solvent molecule. This “localized solvolysis” was used to explain the cation order K + > Ni+ > Li+ for the salts of weak acids in water since the smaller cations polarize the solvent more and thus cause greater association. Diamondg suggested that this same mechanism was responsible for the order I- > Br- > C1- for the smaller alkali metal cations.
0.855 0.815 0.779
The use of the “localized solvolysis” concept t o explain the present results is not very plausible for the following reason. We must compare the relative free energy of an outer sphere complex in which “localized solvolysis” is present with an inner sphere complex. Comparing the acetate ion with a solvent molecule as ligands it is clear that the acetate ion has less steric hindrance, has the same coordinating atoni (oxygen),”J-lj and is a much stronger base due to the negative charge on the oxygen. Thus, there is every reason to believe that the acetate ion would preferentially displace solvent from the primary coordination sphere of the alkali metal cations. The same arguments apply to the formate and propionate ions. It is doubtful that the stabilization through an intervening solvent molecule would be anywhere near as large an effect since one must compare the acidity of the alkali metal cation with acidity induced by the alkali metal cation in a solvent molecule. This argument receives some (8) R. A. Robinson and H. S. Harned, Chem. Rev., 2 8 , 419 (1941). (9) R. M . Diamond, J . A m e r . Chem. Soc., 80, 4808 (1958).
(10) R. A. Y. Jones and A . R. Katritzky, Chem. I n d . (London), 772 (1961). (11) R . J. Gillespie and T. Birchall, Can. J . Chem., 41, 148 (1963). (12) S. J. Kuhn and J. S.McIntyre, ibid.,43, 375, 995 (1965). (13) J. Bello and H. R. Bello, Nature, 194, 681 (1962). (14) P. Piret, L. Rodrique, Y . Gobellin, and M . van Meerssche, Acta Crystalloor., 20, 482 (1966). (15) R. A. Mackay and E. J. Poziomeck, Inorg. Chem., 7 , 1454 (1968). The Journal of Physical Chemistry, Vol. ‘76,>Vo.16, 1971
2322
R. W. KREISAND R. H.WOOD
confirmation from the observation that all of the lithium and sodium salts in this study have osmotic coefficients that fall on or below the Debye-Huckel limiting slope. This is just what would be expected if cation-anion contact was favored. FranklG and P r ~ e ” , ’have ~ explained the order of activity coefficients in water on the basis of the ease with which ions displace solvent molecules and come into contact. This model was able to account for the order of the osmotic coefficients of the alkali metal halides and nitrates in NMA.2 The previous discussion has shown that formate, acetate, and propionate anions should displace solvent molecules from the inner coordination sphere of the alkali metal cations. The strongest interaction should occur with the smallest alkali metal cation, Li+, so the order of osmotic coefficients Li+ < N a + < E(+ is expected. The anion order is not easily predicted. Data on aqueous solutions show that propionate ion is the strongest base but it also has the highest steric requirements. The present results indicate that the steric requirement is the more important in this case. It is expected that for much stronger bases steric requirements will have less relative influence. II. TetraalkylammoniumHalides. The results of the least-squares fit of the data for the tetraalkylammonium halides are given in Tables IV-VI and Figure 2. The standard deviations of both the temperature differences and the osmotic coefficients are given in Table IV. The standard deviations indicate that the osmotic coefficients are accurate to about 1%. I n the final leastsquares fit two experimental points, one for MerNBr and one for Et4NBr,were rejected because their deviations from the best fit were more than twice the standard deviation. Tetramethylammonium iodide was too insoluble to permit accurate measurements. Tetraethylammonium iodide and tetramethylammonium bromide have limited solubilities and only the B term in eq 1was necessary to fit the data.
Table IV
Salt
B
C
Me4NC1
0.0153 0.1212 0.1401 0.2043 - 0.2341 -0.0875 - 0.1427 - 0.1064 - 0.4082 - 0.4981 - 0.5182
-0.1249
Et4NC1 Pr4NC1 Bu4NC1 Me4NBrt EtaNBr PrrNBr Bu4NBr EtdNIb Pr4NI Bu~NI
- 0.0835
- 0.0629 - 0.0963
- 0.0302
Standarda error of e
Standard
0.020 0.031 0.025 0.055
0.007
0.0511 0.0481
0.051 0.035 0.044
0.2042 0.2419
0.028 0.044
error of
+
0.010 0.007 0.010 0.004 0.009 0.007 0.009 0.007 0.006 0.010
a This is the standard deviation of the freezing point depression. For these salts C was set equal to zero and only B calculat,ed.
T h e Journal of Physical Chemistry, Vol. 76, N o . 16,1971
0 0.9
0.8
Figure 2.
Osmotic coefficients in NMA
VS.
molality.
The osmotic coefficients of the iodides are below the Debye-Huckel limiting law [+(DH) = 0.957 at 0.2 m]. The same salts are below the limiting law in ~ a t e r . ~ ~ ~ The order of osmotic coefficients in Table I1 is Bu4NC1 > Pr4NC1 > Et4NC1 > R!te4NC1> Bu4NBr > PrdNBr > Et4NBr > Me4NBr > Bu4NI > Pr4NI. The Pr4NBr-EtrNBr order is reversed below 0.3 m where the data are not as accurate. Similarly the Pr4NI-Bu4NI order is reversed below 0.2 m, and the position of EthNI is not certain. The anion order is C1- > Br- > Iand this is exactly the same as the low concentration order of aqueous tetraalkylammonium solutions. It is also the reverse of the anion order of the alkali metals in water and NMA. I n NMA the order is Bu4Nf > Pr4N+ > Et4N+ > Me4N+ and this order is less pronounced as the anion size increases. I n the case of aqueous solutions the order is the same for the fluorides21 and reverses with the chlorides21$22 and bromides.’g The same trend seems to be present in both water and NNlA but while the iodide is apparently not big enough to cause a reversal in NMA, the reversal (16) H. 8. Frank, J . A m e r . Chem. Soc., 63, 1789 (1941). (17) J. E. Prue, “Chemical Physics of Ionic Solutions,” B. E. Conway and R. G. Barradas, Ed., Wiley, New York, N. Y., 1966, p 163; (b) J. E. Prue, “Ionic Equilibria,” Pergamon Press, Oxford, 1966, Chapter 10. (18) J. E. Prue, A. J. Read, and G. Romeo, “Hydrogen Bonded Solvent Systems,” A. K. Covington and P. Jones, Ed., Taylor and Francis, London, 1968, p 155. (19) S. Lindenbaum and G . E. Boyd, J. Phys. Chem., 68,911 (1964). (20) S. Lindenbaum, L. Leifer, G. E. Boyd, and J. W. Chase, ibid., 74, 761 (1970). (21) W. Y. Wen, S. Saito, and C. M. Lee, ibid., 70, 1244 (1966). (22) J. P. Rupert and H. 5 . Frank, Abstracts, 5th Middle Atlantic Regional Meeting of the American Chemical Society, Newark, Del., April 1970.
2323
FREEZING POINTS, OSMOTIC COEFFICIENTS, AND ACTIVITY COEFFICIENTS OF SALTS Table V : Osmotic Coefficients, 6 m
0.01 0.05 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 1.oo
MerNCl
EtaNCl
PsNCl
BuNCl
MetNBr
EtrNBr
PraNBr
BuaNBr
EtaNI
PraNI
BuiNI
0.991 0.981 0.974 0.961 0.947 0.931 0.914
0.992 0.988 0.988 0.990 0.993 0.994 0.995 0.995 0,996 0.993
0.992 0.989 0.991 0.997 1.004 1.010 1.016 1.022 1.027 1.031 1.034
0.993 0.992 0.997
0.988 0.969
0,990 0.977 0.966 0.949 0.932 0.917 0.901 0.885 0.870 0.853 0.837
0.989 0.975 0.963 0.946 0.932 0.920 0.909 0.900 0.891 0.883 0.876 0.869
0.989 0.977 0.967 0.954 0.944 0.936 0.929 0,923 0.918 0.913 0.910 0,907
0.986 0,959 0.930
0.985 0.957 0.929 0.883 0.844
0.985 0.956 0.928 0.883 0.846 0.814 0.786 0.763 0.743 0.726 0.712 0.701
EtaNBr
PraNBr
BuNBr
EtaNI
PraNI
BurNI
0.969 0.932 0.904 0.863 0.829 0.799 0.771 0.744 0.719 0.694 0.671
0.968 0.928 0.898 0.856 0.823 0.796 0.773 0.752 0.734 0.717 0.702 0.688
0.969 0.932 0.906 0.870 0.843 0.822 0.804 0.788 0.775 0.763 0.752 0.743
0.962 0.899 0.842
0,960 0.894 0.837 0.750 0.683 0.628 0.582
0.959 0.893 0.835 0.749 0.683 0.630 0.586 0.549 0.518 0.492 0.469 0.450
Table VI : Activity Coefficients, m
0.01 0.05
0.10 0.20 0.30 0.40 0.50 0.60 0.70
0.80 0.90
MerNCl
0.971 0.941 0.920
0.888 0.859 0.831 0.803
EtaNCl
0.973 0.953 0.945 0.940 0.939 0.939 0.939 0.938 0.937 0.934
1.008 1.018 1.028 1.037 I . 044 1.051 1.057 1.061
0.810 0.779
yi PraNCl
0.974 0.956 0.951 0.952 0.959 0.967 0.976 0.984 0.993
1.001 1.008
BuaNC1
0.975 0.962 0.963 0.974 0.990 1.006 1,022 1.038 1.052 1.066 1.078
MeaNBr
0.967 0.917
1.00
occurs with at least two of the chlorides in water.22 The reversal of the cation order in water and the low osmotic coefficients of the iodides have been ascribed to the unique structural properties of the water in the hydration spheres of the ions. 19-21,23 I n the case of the iodides an increased structure-enforced ion pairing as the cation increases in size was p o ~ t u l a t e d . ~For ~ the fluorides an increased structural salting-out was assumedZ1because of the incompatability of the kinds of structure making occurring in the ions. The unique structural properties of aqueous solutions are not present in NMA since nonpolar molecules do not enforce solvent structure in NMA.24 I n addition, the conduct a n ~ e and ~ ~ surface r ~ ~ tensionz6of the larger tetraalkylammonium ions in NMA do not show effects attributed to water-structure enhancement in aqueous solutions. 27-29 This means that the previous explanations for the low-concentration data in water are probably not correct since they fail to explain the similarity of the results in NMA. At higher concentrations, the osmotic coefficients of some of the tetraalkylammonium halides in water show very irregular behavior.'$ This is quite probably due to the unique properties of aqueous solutions since the effects are not evident in NMA solutions. It is well known that cation-cation interactions have very large effects on the excess heats, entropies, and volumes of
tetraalkylammonium i o n ~ , ~ Obut - ~ ~ relatively small effects on the free energies. l 9 FranklGhas shown that the effects of dielectric saturation near an ion in water would greatly increase the attraction between ions so that cation-anion contacts would be common. I n order to explain the activity coefficients of the alkali halides in water, it was neces(23) R. M. Diamond, J . Phys. Chem., 67,2513 (1963). (24) R. H. Wood and D. E. Delaney, ibid., 72, 4651 (1968). (25) C. M. French and K. H. Glover, Trans. Faraday SOC., 51, 1427 (1955). (26) (a) R. E. Singh, P. P. Rastogi, and R. Copal, Can. J . Chem., 46, 3525 (1968); (b) R. Gopal and 0. N. Bhatnagar, J . I n d i a n Chem. Soc., 44, 1082 (1967). (27) D. F. Evans and R. L. Kay, J . Phys. Chem., 70, 366 (1966). (28) R. L. Kay and D. F. Evans, ibid., 70, 2325 (1966). (29) R. L. Kay, T. Vituccio, C. Zawoyski, and D. F. Evans, ibid., 70, 2336 (1966). (30) W. Y. Wen and S.Saito, ibid., 68, 2639 (1964). (31) S. Lindenbaum, ibid., 70, 814 (1966). (32) R. H. Wood and H. L. Anderson, ibid., 71, 1871 (1967). (33) R. H. Wood, H. L. Anderson, J. D. Beck, J. R. France, W. E. DeVry, and L. J. Soltzberg, ibid., 71, 2149 (1967). (34) W. Y. Wen andK. Nara, ibid., 71,3907 (1967); 72,1137 (1968). (35) W. Y. Wen, K. Nara, and R. H. Wood, ibid., 71, 3048 (1967). (36) It also should be noted that the cation-anion interactions proposed in this paper cannot explain the large heat and volume changes observed on mixing tetradkylammonium halides with the corresponding alkali metal halidell-21 because there is no change in the cation-anion interaction during the mixing process. The Journal of Physical Chemistry, Vol. 76, N o . 16, 1971
R. W. KREISAND R. H. WOOD sary to postulate that the hydration of the alkali metals ena and that the effective radius of th,e tetraalliylamresulted in a decreased tendency for cation-anion conmonium ions could be as low as 1.7 A. Adams and tacts. The balance between these two forces then Laidler44 showed that the pressure and temperature accounts for the experimental results in water. These dependence of the conductivity of some tetraalkylsame effects will explain the present results. Models ammonium halides in acetone indicated the presence of show that a halide ion can bury itself in the hydrocarbon the two kinds of ion pairs. The authors concluded that portion of the n-tetraalkylammonium cation and that solvent-shared and solvent-separated ion pairs were when this happens the radius of closest approach of the present. However, the ion size parameters derived in tetraalkylammonium ion is about 1.7 A (this is the this study are more consistent with the conclusion radius of the Cs+ ion). This distance does not vary that one of the two kinds of ion pairs that are formed is much as the alkyl groups increase in length. I n conthe contact ion pair postulated here. More recently trast the average radius of the Bu&+ ion is about 4.9 Darbari and Petrucci46 reported ultrasonic absorption This means that from some angles of approach data which support the conclusion that two kinds of this ion will have a very large radius while from other ion pairs are present in acetone solutions. angles of approach it will be much smaller.38 ,4t a It is interesting to note that the behavior of the distance of 3.7 A, the effective dielectric constant would tetraalkylammonium halides dissolved in water,46some be expected to be very low because of the very low a l ~ o h o l s and , ~ ~f ~ r~m~ a m i d e ~ show ~ - ~ l some similarities dielectric constant of the hydrocarbon chains in the to the present results. The amount of association cation as well as the effect of dielectric saturation. increases as the size of the halide increases. This has This would result in very high attractive forces between been explained by Evans and Gardam47by the increase the oppositely charged ions. Add t o this the fact that in solvation of the lower halides that is expected in the tetraalkylammonium ions are not strongly solvated hydrogen-bonding solvents like water, N MA, and the and it is easy to account for an appreciable decrease in alcohols. In addition, the amount of association is osmotic coefficients due t o >he occasional penetration relatively independent of cation size. In some cases of the anion t o within 1.7 A of the positively charged the larger cations even have higher association connitrogen atom.39 Another way of saying this is that stants. For instance the association constant for these effects make the effective Bjerrum radius40 much tetraheptylammonium iodide is larger than that for larger than what would be expected on the basis of the tetrabutylammonium iodide in ethanol, 1-propanol, and macroscopic dielectric constant and also allow very low l - b ~ t a n o l . ~In ' 1-pentanol the association constants are distances of closest approach. The order of osmotic equal. coefficients in water can be explained by the very low effective radius of the tetraalkylammonium ions to(37) Reference 7, p 125. gether with the ion-solvent competition principle. l7' w (38) The small effective radius of the tetraalkylammonium ions postulated here explains why the trialkylsulfonium halides have It is postulated that the fluoride ion has strong enough similar properties t o the tetraalkylammonium halides in aqueous solvation t o prevent it from losing its solvation layer solutions. The structural effect of the hydrocarbon chains is similar and the distances of closest approach are similar. See 5. Lindenand coming into direct contact with the tetraalkylbaum, J . P h y s . Chem., 72, 212 (1968), and D. F. Evans a n d T . L. ammonium ions. The osmotic coefficients are high Broadwater, ibid., 72, 1037 (1968), for details. and the butyl ion is the highest because of its larger (39) It will require some force to push the hydrocarbon chains out of the way because their freedom of movement (free volume) will effective size. In the case of the bromide and iodide become somewhat more restricted. What is postulated here is that where the solvation of the anion is weaker, the effective this is a small force compared with the attraction between the cation and anion. radii of th,e tetraalkylammonium ions are reduced to (40) N . Bjerrum, Kgl. D a n . Vidensk. Selsk., 7, No. 9 (1926). about 1.7 A and appreciable cation-anion contact takes (41) Recent evidence suggests that the tetramethylammonium ion place. The iodide with its weaker solvation would have does not often come into contact with the iodide ion [D. W.Larsen, J . Phys. Chem., 74, 3380 (1970)l. the lowest osmotic coefficients. The Bu4N + ion would (42) S. R. C. Hughes and S. H . White, J . Chem. SOC.A , 1216 (1966). have the lowest osmotic coefficients because it would (43) S. R. C. Hughes and D. H. Price, ibid., 1093 (1967). have about the same distance of closest approach and a (44) W. A. Adams and K. J. Laidler, Can. J . Chem., 46, 1977, 1989, lower effective dielectric constant (because of its larger 2005 (1968). alkyl groups).41 The order of osmotic coefficients in (45) G. S. Darbari and S.Petrucci, J . P h y s . Chem., 74, 268 (1970). NMA is explained in a similar may by assuming the (46) R. L. Kay, C. Zawoyski, and D. F. Evans, ibid., 69, 4208 (1965). iodide ion still has enough solvation so that cation(47) D. F. Evans and P. Gardam, ibid., 72, 3281 (1968); 73, 158 anion contacts are about equally frequent with all of (1969). the tetraalkylammonium ions. (48) R. L. Kay, F. F. Evans, and G. P. Cunningham, ibid., 73,3322 I n a series of papers Hughes and c o ~ v o r k e r shave ~ ~ ~ ~ ~(1969). (49) R. Gopal and M. M. Husain, J . I n d i a n Chem. Soc., 43, 204 presented evidence from conductance measurements (1966). that interpenetration of anions and tetraalkylammo(50) R. Gopal and 13. A. Siddiqi, Z . P h y s . Chem. (Frankfurt a m nium cations occurs in some ketone solvents. The presM a i n ) , 67, 122 (1969). ent results indicate that this is a more general phenom(51) R. Gopal and K. Singh, ibid., 69, 81 (1970). T h e Journal of Physical Chemistry, V o l . '76, No. 16, 29'71
2325
ALKALINEEARTHHALIDES IN HIGHDIELECTRIC SOLVENTS The conductance studies also show that the distances of closest approach necessary to fit the data are very low and independent of the cation. Evans and coworkers concluded that contact as well as solvent-
separated ion pairs were involvedg7and that at least part of the particular concentration dependence of aqueous solutions was a general feature of hydrogenbonding s01vents.5~ This behavior is consistent with the very low distances of closest approach that are possible with the large tetraalkylammonium ions. Solvents which solvate cations very strongly would be expected to solvate the tetraalkylammonium ions. Models show that a low distance of closest approach is possible for at least one solvent molecule. With these solvents close cation-anion contacts might not occur and the tetraalkylammonium ions would behave as ordinary large ions. Some examples of solvents exhibiting this type of behavior are a ~ e t o n i t r i l e nitro,~~ methane,54 and n i t r o b e n ~ e n e . ~In~ order ~ ~ ~ ~to~ pre~ dict the behavior of a solvent, it mill be necessary to know more about the energy of the process
R4iS+.nS
+ X-SmS
+ R4N+X-*pS
+ (n + m - p ) S
where S denotes a solvent molecule. This equation shows that the relative ease of displacement of solvent from a tetraalkylatnmonium ion will depend on the difference between the solvation energy of the cation and the solvation energy of a solvent molecule. The normal behavior of acetonitrile, nitrobenzene, etc., could be due to a reasonably high energy of solvation of the cations together with a low energy of solvation of the solvent. In water, the alcohols, and NMA the energy of solvation of the solvent is much higher and this favors cation-anion contact.
Acknowledgments. The authors are grateful for the support of this work by the National Science Foundation. We also wish to thank Dr. John E. Prue for helpful discussions. (52) T. L. Broadwater and D. F. Evans, J . Phys. Chem., 73, 3985 (1969). (53) D. F. Evans, C. Zawoyski, and R. L. Kay, ibid., 69, 3878 (1965). (54) R . L. Kay, S. C. Blum, and H. I. Schiff, ibid., 67, 1223 (1963). (55) E. G. Taylor and C. A. Kraus, J . A m e r . Chem. Soc., 69, 1731 (1947). (56) C. T. Witschonke and C. A. Kraus, ibid., 69, 2474 (1947).
Solvation Studies. 11. Some Alkaline Earth Halides in High Dielectric Solvents by A. Finch, P. J. Gardner," and C. J. Steadman Moore Laboratory, Chemistry Department, Royal Holloway College, Surrey, United Kingdom
(Receked September 16, 1970)
Publication costs borne completely by T h e Journal of Physical Chemistry
The standard enthalpies of solution of the chlorides and bromides of calcium, strontium, and barium in formamide (F),N-methylformamide (NMF), and N,N-dimethylformamide (DRIF) are reported (excepting barium chloride in "IF' and DMF and barium bromide in DMF). Debye-Huckel limiting law slopes are compared with those obtained experimentally. Structural implications of enthalpies of transfer and combined ion solvation enthalpies are discussed. Individual ionic entropies are estimated from a correspondence principle.
Introduction In part I,l corresponding data for alkaline earth chlorates and bromates in F, NMF, and D M F were reported. Since then there have been several calorimetric studies using these2-j and ~ t h e r ~nonaqueous -~ solvents (e.y., N-methylacetamide, dimethyl sulfoxide, and propylene carbonate). Usually salts of the alkali metals or alkylammonium halides have been employed. Data for diunivalent electrolytes remain scarce.
In this work an isoperibol (constant-temperature environment) solution calorimeter was used to measure (1) A. Finch, P. J. Gardner, and C. J. Steadman, J . Phys. Chem., 71, 2996 (1967). (2) D. V. S. Jain, B. S. Lark, S. P. Kochar, and V. K. Gupta, Indian J . Chem., 7, 256 (1969). (3) L. Weeda and G. Somsen, Red. Traa. Chim. Paus-Bas, 85, 159
(1966). (4) R . P. Held and C. M. Criss, J . Phys. Chem., 71, 2487 (1967). (5) C. M.Criss and E. Luksha, ibid., 72, 2966 (1968).
The Journal of Physical Chemistry, Vol. 76, N o . 16, 1971
