Linear Solvation Energy Relationships. Standard...

J. Phys. Chem. 1988, 92, 3613-3622 3613

Linear Solvation Energy Relationships. Standard Molar Gibbs Free Energies and Enthalpies of Transfer of Ions from Water into Nonaqueous Solvents

Y. Marcus,*,+ M. J. Kamlet,t and R. W. Tafts

Department of Inorganic & Analytical Chemistry, The Hebrew University of Jerusalem, 91 904 Jerusalem, Israel, Naval Surface Weapons Center, White Oak Laboratory, Silver Springs, Maryland 2091 0, and Department of Chemistry, University of California at Irvine, Irvine, California 9271 7 (Received: July 28, 1987; In Final Form: January 2, 1988)

Data from the literature on the standard molar Gibbs free energies and enthalpies of transfer of ions from water into nonaqueous solvents have been subjected to multiparameter correlations with solvatochromic and other properties of the solvents and with suitable properties of the ions. Three parameters, a*, a, and p for small univalent or divalent cations and a*, a, and V/100 for anions, are adequate for expressing the dependence of AtrGo or AtrHo on the properties of the solvents. Four further (normalized) properties, z , O, l / r , u, and lOOu, are required for the dependence of the properties of the ions. The first two of these occur only in the combinations zz X O.l/r and z X O.l /r for small cations (for the anions z is unimportant, since only univalent ones are considered). For the large, hydrophobic tetraalkylammonium cations only two solvent properties, a* and 62/1000 (for AuGo) or V/lOO (for A T P ) , and two ion properties, l / r and R, or lOOu, are required. These dependencies are rationalized in terms of the interactions that take place in water and the nonaqueous solvents.

Introduction One of us has recently coauthored a paper on the relationship

of the Gibbs free energies of transfer of ions from water into nonaqueous solvents with certain properties of the solvents and the ions.' The treatment was limited to univalent ions, and the properties of the solvents considered did not include some of their solvatochromic properties,2 which are of extensive use nowadays. Additional standard molar Gibbs free-energy data on the transfer of univalent ions into further solvents and on the transfer of divalent cations have since become a ~ a i l a b l e . ~ Also, a critical compilation of standard molar enthalpies of transfer has been p~bl ished.~ It is, therefore, of interest to extend the previous work to accommodate the additional data and to reinterpret the relationships that are found in terms of the interactions that take place in water on the one hand and in the nonaqueous solvents into which the ions transfer, on the other.

The previous work' has shown that the Gibbs free energies of transfer of ions (X) from water (W) to nonaqueous solvents (S) can be described by the following linear solvation energy relationship:

The summation extends over all the products of the A,(j) properties of the ith ion X pertinent to their j-type interactions with the solvents S, and the differences between the Po') properties of the solvents S and those of water W. Of the multitude of solvent properties P(j ) that may be considered, only four took care of almost all of the variance of the Gibbs free-energy data. These are the propensity of the solvent to accept a hydrogen bond or to donate an electron pair, described by its donor number, DN,596 its propensity to donate a hydrogen bond (for protic solvents) or accept an electron pair, described by its ET value,' the reciprocal of its dielectric constant, l / c , and its cohesive energy density or the square of its solubility parameter, a2. Of these, the donor number, DN, did not play a significant role in explaining the variance of the anion transfer data, as might be expected, but unexpectedly the electron-pair-acceptance index, ET, was required for explaining the variance of the cation-transfer data.

The regression was applied in two stages, first for each ion on the properties of the solvents and then for each of the coefficients found in the first stage on the properties of the ions. Since for

*To whom correspondence should be addressed at The Hebrew University

'Work done partly a t the University of California at Irvine. 3 Naval Surface Weapons Center. 8 University of California at Irvine

of Jerusalem.

both the Gibbs free energies and the enthalpies the quantities pertain to the transfer from water, the properties of the solvents are the differences of given properties and the corresponding ones for water.

As before, it has now been endeavored to describe the extended (but still incomplete) matrix of solvents and ions by means of a multivariable linear regression involving the minimum number of variables, applying statistical criteria of the goodness of fit. These are the multiple correlation coefficient squared, R2, which describes the fraction of the variance explained by the regression, and the Fm," statistic, for m independent variables and n data, which should be larger than the 95% significance level. In view of the previous work,' the following properties Po') of the solvents have now been examined: the polarity-polarizability index,2 a*, the hydrogen-bond-donation ability,2 a, the hydrogen-bond-acceptance ability,2 f i (which is well correlated with DN6), the normalized reciprocal of the dielectric constant, lo /€ , the normalized square of the solubility parameter, d2/1000 (with expressed in J ~ m - ~ ) , and the normalized molar volume, V/100 (with Vexpressed in cm3 mol-'). Normalized properties are used, which are approximately in the range from 0 to 1, so that the relative contributions of the various variables can be more readily compared. It is realized that six variables are, indeed, not required for an adequate description of the variance, but a selection among them was left for the statistical criteria mentioned above.

The coefficients A,(j) themselves depend on various properties of the ions, in a linear solvation energy relation of the form

A,( j ) = CAijPi i

Of the properties of the ions Pi examined, the charge, z , becomes of larger significance than before, since divalent cations were now included and not only univalent cations and anions. The electrical field strength of the ions was expressed in terms of the charge and of the reciprocal of the crystal ionic radius (in nanometers), l / r . The size of the ion was expressed as the volume occupied

(1) Glikberg, S.; Marcus, Y. J . Solution Chem. 1983, 12 , 255. (2) Kamlet, M. J.; Abboud, J.-L. M.; Abraham, M. H.; Taft, R. W. J . Org.

(3).Marcus, Y. Pure Appl. Chem. 1983, 55, 977, and additional reports

(4) Marcus, Y. Pure Appl. Chem. 1985, 57, 1103, and additional reports

( 5 ) Gutmann, V.; Wychera, E. Inorg. Nucl. Chem. Lett. 1966, 2 , 257.

(6) Marcus, Y. J . Solution Chem. 1984, 13, 599. (7) Dimroth, K.; Reichardt, C.; Siepmann, T.; Bohlmann, F. Justus Liebigs

Ann. Chem. 1963, 661, 1. Reichardt, C. Solcent Effects in Organic Chem- istry; Verlag Chemie: Weinheim, 1979.

Chem. 1983, 48, 2877.

listed In Table I .

listed in Table 11.

Gutmann, V . Coord. Chem. Reu. 1976, 18$ 225.

0022-3654/88/2092-3613$01.50/0 0 1988 American Chemical Society

3614 The Journal of Physical Chemistry, Vol. 92, No. 12, 1988 Marcus et a].

TABLE I: Standard Molar Gibbs Free Energies of Transfer of Ions from Water, in kJ mol-', on the mol dm-3 Scale at 298 K, Based on the TATB Assumption"

solventb MeOH EtOH 1-PrOH 1-BuOH TFE EG Me,CO PC

50 H+ Li+ Na+ K+ Rb+ cs+ TI+ NH4+ Ba2+ cu2+ Zn2+ Cd2+ Hg2+ Pb2+ Me4N+ Et4N+ Pr4N+ Bu4N+ Ph4As+ Pic- BPh4- F- CI- Br- 1- 1,- N ,- CN- SCN- NO,- c104- Tc04-

Ag+

CHjC02- CFqSOq-

10.4 4.4 8.2 9.6 9.6 8.9 6.6 4.1

(5) 1 6.9h 2 8 . 9 27.4h 32.9h

(48)gg 4" 6 1

-109 -2 1 -24.1

-5.7d

16 13.2 1 1 . 1 7.3

-12.6 9.1 8.6 5.6

12.5a 6.1 5.8"

16.0 -16.W

-24.1

1 1 . 1 11 14 16.4 16 15 4.9 7 7

46p 42" 2 2x

(64)gg 141 10.9 6

(-6) (-8)

-6.7d -21.2

-21.2

20.2 18.2 12.9

17.0 7

14 10 8.8"

9 1 1 17 17 19 17

1

7c

43p

1 1 5'

-6' -1 7c -25 -7d

-25

26 22 19

I7 15"

3 bb

19 20 23 19

12

12 7

-7 -12 -20

-20

29 24 22

-2d

22 17"

5 0

-2 39 -2

50 1

-2 1 -7

-2 1

-10 9 -8 7 -8 3

1

5

3.1''

1 Ohh 1 o h h 4 4 4 9 3'

49ee (83)hh (61)hh

( 2 P (78)hh

3

-32

-32

57 42 25

43 48

12.4"

23.8 14.6 5.3

-1.0 -7.0 18.8 11.0

(73)m (8l)hh (70)hh ( 4 7 p 472

-1 1 -13 -22 -3 1 -36.0

-6 -36.0

56 39.8 30.0 13.7

(-17)' 27 36

7.0

-3

solvent NH,' FA NMF" DMF DMA DEA" NMPy MeCN

H+ LI+ Na+ K + Rb+ c s + Ag+ TI+ ISH4+ Ba2+ cu2+ Zn2+ Cd'+ Hg2+ Pb2+ M e 4 h + Et4N+ Pr4N+ Bu4N+ Ph4As+ PIC- BPh4- F- c1- Br- I 1 3 - N,- C I T SCN- NO,- clod- Tc04- CH,CO; CF,SO,-

-97 -35" -1 7 -12 -13 -1 5

-100

-28" -66"

-181 -149 -1 52 -228

43 33 25

-10 -8 -4.3 -5 -6.0

-15.4 -1'

-4ee

-28"

-127 2.7'

-10.1'

-23.9 -7

-23.9 25 13.7 10.7 7.3

-7 1 1 13.3 7

-12 -1.6" 20

-20" -7 -6 -8 -7

-15" -10

-4ee

-32

-33'

-33

-3 3

-18 -10

-9.6 -10.0

-9.7 -10.8 -20.8 -11.5

-2 1 .4h (-18) -29.6h -33.5h

(-44)ZP -34'

-5.3 -8.0

-17 -29 -38.5

-7 -38.5

51 48.3 36.2 20.4

-27 36 40 18.4

4 3.3"

66

-22u -12.1 -1 1.7

-8 -7"

-29.0 -13"

-27"

-22"

-36"

(-7)hh

-40

-40

54.9 44.0 21

-30 40

21

5.0" 70

-12 -10

-9 -1 1 -29 -1 2

( -45 )hh -33 -22

-34'

-38.1

-38.7

1 oii

-25 -35 -15 -1 1

-8 -10 -26 -15 -24

( -8)hh -2200

-35' -3

-40

-40

51 37 19

46

18

-12

46.4 25 15.1 8.1 6.3 6 0

8.0

57.4h 6 8 O,*

68.7h 42.2h

(42)gg 64"

3 -7

-1 3 (-32)k -32.8

-4 -32.8

71 42.1 31.3 16.8

-1 5 37 35 14.4 21

2 6.87''

61 -23'

-23.2

Energetics of Ion Transfer from Water to Solvents

TABLE I (Continued)

The Journal of Physical Chemistry, Vol. 92, No. 12, 1988 3615

solvent MeNO, P h N 0 2 PyY 2-CNPy" DMSO T M S HMPT 1,l-DCIE 1,2-DCIE

H + Li+ Na+ K+ Rb+ CS+

TI+ NH4+ Ba2+ C U 2 + Zn2+ Cd?' Hg2+ Pb2+ Me4N+ Et4N+ Pr4N+

Ph4As+ Pic- BPh4- F- c1- Br- I- 13- N3- CN- SCN- NO,- c lod- T c O i CH3COY C F j S O c

Ag+

B u ~ N '

9 sii 48 31.6' 15.4' 1l.W 5.6'

21 (16)'

9 Yj

(31)gg

-4.6' - 1 0 9 -2O.N

-32.6'

-32.6'

37.7' 29.W 18.91

28 3 I d 15

4.7J

5 6'j

33 -28 38 3 6' 21e 19 18'

(15) 27

4 -5

-16 -3 1 -36

-3e -36

35 29 18

(44)'

-23

(6Im 24d 10' 5ii

16 6

13 (35) -57

-1

-50

-79

-38 -5

-38

34 21 19

20

16

-14

-19.4 40'/ -1 5

24 -13.4 14 -1 3.0

-10.4 -13.0 -34.8 -21.4

-26.6h -43"

(-45)ee (-58) (-48)gg (-52)'

-2 -2 (-9)

-39 -37.4

-39 -37.4 -6

40.3 31 27.4

10.4

25.8 35 9.1

(-4 1

24 -5 (-Ilk

(50 )

(6Ihh -3 -4 -9

-10 -4

(-1 2)hh

62ee (76)hh (39)hh

(29)hh

-36

-36

47 35 21

(-14)' 41

22

- 1 7"' 29 25 -16 30 26 - 1 0"" 29 25

-7aM 28 24 -44 -26""

(-52)hh -86"" -36""

-38'"

-39

-39

58 46 30

49

20

-7

18 16 11 5

(-23)5 -27 -33

-27 -33

58 52 43 38 31 25

(65Y

7 22 16

OUnless otherwise noted, data are from ref 3 (the data for ammonia are a t 240 K, those for tetramethylene sulfone and for 2-cyanopyridine are at 303 K). bThe abbreviations stand for the following names of the solvents: MeOH = methanol, EtOH = ethanol, 1-PrOH = 1-propanol, 1-BuOH = 1-butanol, TFE = 2,2,2-trifluoroethanoI, EG = 1,2-ethanediol, Me,CO = acetone, PC = propylene carbonate, FA = formamide, N M F f N- methylformamide, D M F = N,N-dimethylformamide, DMA = N,N-dimethylacetamide, DEA = N,N-diethylacetamide, NMPy = N-methyl- pyrrolidinone, MeCN = acetonitrile, MeNOz = nitromethane, PhNO, = nitrobenzene, Py = pyridine, 2-CNPy = 2-cyanopyridine, DMSO = di- methyl sulfoxide, TMS = tetramethylene sulfone, HMPT = hexamethylphosphoric triamide, 1,l-DCIE = 1,l-dichloroethane, 1,2-DCIE = 1,2-dichloroethane. CDanil de Namor, A. F.; Contreras, E.; Sigstad, E. J . Chem. Soc., Faraday Trans. 1 1983, 79, 1001. dHundhammer, B.; Solomon, T.; Alemu, H . J . Electroanal. Chem. 1983, 149, 179. eDanil de Namor, A. F.; Contreras, E.; Sigstad, E. J . Chem. Soc., Faraday Trans. 1 1983, 79, 2713. ILewandowski, A. Electrochim. Acta 1984, 29, 547. EAbraham, M. H.; Danil de Namor, A. F.; Schulz, R. A. J . Chem. SOC., Faraday Trans. 1 1980, 76, 869. *Hedwig, G. R.; Owensby, D. A.; Parker, A. J. J . Am. Chem. SOC. 1975, 97, 3888. 'Cox, B. G.; Waghorne, W. E. Chem. SOC. Reu. 1980, 9, 38 1. JDanil de Namor, A. F.; Ghousseini, L. J . Chem. Soc., Faraday Trans. 1 1984, 80, 2843. Ahrland, S . ; Ishiguro, S . ; Portanova, R. Aust. J . Chem. 1983, 36, 1805. 'Benoit, R. L.; Wilson, M. F.; Lam, S.-Y. Can. J . Chem. 1977, 55, 792. "'Vanysek, P. J . Electroanal. Chem. 1981, 121, 149. "Lemire, R. J.; Sears, P. G . J . Solution Chem. 1981, 10, 511. "Singh, P.; McLeod, I. D.; Parker, A. J. J . Solution Chem. 1982, 1 1 , 495. PCoetzee, J. F.; Istone, W. K. Anal. Chem. 1980, 52, 53. qKolling, S. Trans. Kans. Acad. Sei. 1962, 85, 61. 'Hundhammer, B.; Solomon, T.; Alemayu, B. J . Electroanal. Chem. 1982, 135, 301. 'Czapkiewicz, J.; Czapkiewicz-Tutaj, B.; Struck, D. Pol. J . Chem. 1978, 52, 2203. 'Gritzner, G. Inorg. Chim. Acta 1977, 24, 5. UGsaller, G.; Gritzner, G. 2. Phys. Chem. 1983, 130, 137. uGritzner, G. J . Electroanal. Chem. 1983, 144, 259. "Boeck, J.; Gritzner, G. 2. Phys. Chem. (Neue Fulge) 1982, 130, 181. "Case, B.; Parsons, R. Trans. Faraday SOC. 1967, 63, 1224; data for lead chloride minus twice the chloride value given in this table. YPersson, I. Pure Appl. Chem. 1986, 58, 1153. IGritzner, G.; Geyer, E. Z . Phys. Chem. (Neue Fulge) 1981, 125, 7; adjusted with the value for transfer from water into acetonitrile, given by the linear relation found there to the K+ value. ""Kraml, G.; Gritzner, G . J . Chem. SOC., Faraday Trans. 1 1985,81, 2875. "*Value for HCI from H . D. Wehle (quoted by: Schwabe, K.; Queck, C. Abhandl. Saechs. Akad. Wissen. 1979, 53, No. 3, and for CI- from this table. CCSchindewolf, U. Ber. Bunsen-Ges. Phys. Chem. 1982, 86, 887. ddChantooni, M. K.; Kolthoff, I. M. J . Phys. Chem. 1978, 82, 994. "Lewandowski, A. Electrochim. Acta 1985, 30, 311; 1986, 31, 59; negligible liquid junction assumption. ffGomaa, E. A. Thermochim. Acta 1985, 91, 235. EtBalyatinskaya, L. N . Russ. Chem. Reu. 1979, 48, 418; adjusted for the use of the ferrocene assumption by data obtained for Ag+ on this assumption by Badoz-Lambling, J.; Bardin, J. C. Electrochim. Acta 1974, 19, 725; and the Ag+ data from the present table. hh Calculated from the data of Gritzner, G. J . Phys. Chem. 1986, 90, 5478; relative to his data for transfer into MeCN and his data for Ag+ and the present data for transfer from water to MeCN and those for Ag'. "Neck, V.; Kanellakopulos, B.; Kim, J. I. Kernforschungszentrum Report KfK 1985, 3998. "Badoz-Lambling, J.; Bardin, J. C. Electrochim. Acta 1974, 19, 725; adjusted for fic+/foc reference value with the CI- value from this table.

by it, 1000 = (400~ /3 ) ( r /nm)~ . The polarizability of an ion was expressed in terms of its normalized molar refractivity, RD/10 (with RD given in em3 mol-'). A final property of the ions considered was its softness parameter,'^^ 0. However, for the larger ions, this was not independent of 1000 or of RD/10 and played a significant role only for smaller ions, with r E 0.25 n m or less.

~

( 8 ) Marcus, Y . Isr J Chem 1972, I O , 659. (9) Marcus, Y . Thermochim Acta 1986, 104, 389

Input Data The solvents and ions that are considered in this paper are those

for which standard molar Gibbs free energies 4,,Go(X,W-S) or enthalpies 4,,Ho(X,W-S) of transfer from water to nonaqueous solvents are available, on the basis of a reliable extrathermodynamic assumption. This is necessary for the relation of these quantities to solvation properties of individual ions. The extrathermodynamic assumption that has so far been found to be the least objectionable, and also to be applicable to both Gibbs

Marcus et al. 3616 The Journal of Physical Chemistry, Vol. 92, No. 12, 1988

TABLE 11: Standard Molar Enthalpies of Transfer of Ions from Water, in kJ mol-', Based on the TATB Assumption" solventb solventb

D 2 0 MeOH EtOH I-PrOH PC N H 3 D,O MeOH EtOH 1-PrOH PC NH, H+ -7.4' 14.6' 44 Pr4N+ -0.2 15 1 1.6c Li+ 1.9 -21.7 -20.2 -18.4 2.8 -45 B u ~ N + -1.0 20 21.3 1 8.4c Na+ 2.6 -20.7 -19.4 -18.8 -10.5 -36 Ph4As' 0.7 -1.0 0.0" 1.5 -13.1 K+ 2.8 -19.0 -19.6 -18.3 -22.5 -26 Pic- -0.9s Rb+ 2.9 -16.5 -24.9 -25 BPh4- 0.7 -1.0 0.0" 1.5 -13.1 c s + 3.0 -14.1 -11.8" -12.7 -27.5 -33 F -2.6 13.8'

NH4+ 1.3 -18.8" -26.5" -28.0 -19.8 Br- 0.4 4.5 5.5 2.5 15.2 -16 Ca2+ 5.4 -10.9 -98 1- 1.0 -1.0 -0.7 -1.5 -1.6 -29 Sr2+ 5.7 -15.1 -109 iV3- 0.5 16.7 Ba2+ 6.1 -60.6 -21.8 -102 SCN- -3.2' Zn2+ -45.6' Clod- -0.2 -3.1 -2.7 0.0 -16.3 Cd2+ -40.4e B F4- 3.6 Me4N+ 1.8 0.3 0.2 -16.3' CF3SOj- 4.6 Et4N+ 0.9 7.1 9.6 0.6'

Ag+ 2.3 -20.9 -11.1 -106 CI- -0.2 8.4 10.4 8.4 26.2 6

solvent solvent Pyk FA NMF" NEA" DMF DMAd NMPy Pyh FA NMF" NEAO DMF DMAd NMPy

Li+ -6.0 -7.1 -25.4 -26" B u ~ N + 7.9 26.V 24.6 10.9C,d 7.7' 6.4C.d Na' -30.3 -16.5 -22.5 -8.6 -32.4 -41.2' -41 Ph,As+ -22.8 -0.5 -7.6 -7.3 -17.2 -13.7" -17 K+ -24.1' -17.9 -24.0 -35.7 -47 Pic- -12.OS Rb+ -27.8' -17.8 -36.1 BPh4- -22.8 -0.5 -7.6 -7.3 -17.2 -13.7 -17 c s + -28.1' -17.7 -34.6 F' 19.9 Ag+ -106 -3 5 c1- 28.2 3.5 14.2 -0.4 17.9 35.6 27 NH4+ -36.4' Br- 10.9 -1.5 -4.3 0.6 17.2 13 Ba2+ -40.2k -85.5' I- -7.3 -6.8 -11.0 -15.0 -0.7 2

H + -43.9s Pr4N+ 16 .d 9y

Zn2+ -23.9k -41.3 -62.7e -53.2' N3- 2 . v -1.0' Cd2+ -27.5k -63.3' SCN- -4.7 -10.9' -10.0' Hg2+ -160' C104- -18.8 -11.8 -11.0 -23.4 -15.3 -11 Me4N+ -2.1' -1 3 BF4- -20.8' Et4N+ -3.7 5.5' -4.0',d -7.3' -9.2C'd CF,SOc -3.9' 1.5" -3.4"

solvent solvent MeNola" MeCN DMSO T M S HMPT 1.2-DCIE MeN0204 MeCN DMSO TMS HMPT 1,2-DCIE

H + 3.0' -11.25 73 Pr4N+ 11.5 10.68 16.V 174 1.6 Li+ 25.8 -13.0' -27.1 12q -57.4 Bu4N+ 21.5 19.1C,d 25.Q 26s 5.3 9.0 Na+ 11.5 -13.3 -29.2 -16 -50.6 -25.1 Ph4As+ -6.9 -11.1 -10.6 -11 -25.8 -22.8 K+ -13.5 -22.9 -35.4 -26 -46.6 -28.0 Pic- -4.0 -12.4' -12.3s Rb+ -17.7 -24.6 -38.1' -28 -43.8 -27.6 BPh4- -6.9 -11.1 -10.6 -11 -25.8 -22.8 c s + -16.6 -26.1' -33.0 -26 -45.0 -27.2 F 3 w Ag+ NH4+ Ba2+ -8.5' -78.5' -1 22.0'J 1- -7.8 -7.6 -11.5 -8 -5.8 -15.5 Zn2+ 20.1' -62.2e -74.8"" N3- 8.8 -2.5' 15 15 Cd2+ 8.2' -70.Se -93 I5'J SCN- -4.99 -4.9' -4.6 Hg2+ -76 c104- -19.2 -16.08 -18.2 -184 -20.7 -24.3 Me4N+ -13.5 -15.3 -16.4 -164 -34.1 -15.9 BF4- -12.9' -14.5'

-52.7 -53.3 -14 c1- 21.2 19.3 20.0 27 38.2 16.3 -35.3s -64.2'' Br- 7.1 8.0 4.6 13 17.7 0.8

Et4N+ -1.8 1.8C.d 3.3' -6.1 -10.0 CF3SO3- 0.8' 2.15 -0.5e.x

"The data are the selected values from ref 4, unless otherwise noted, valid for 298 K, except for ammonia (240 K) and tetramethylene sulfone (303 K). bThe abbreviations for the solvents are defined in Table I, except for NEA = N-ethylacetamide, 'Castagnolo, M.; Sacco, A.; deGiglio, A. J. Chem. Soc., Faraday Trans. I 1984, 80, 2669. dKondo, Y.; Shiotami, H.; Kusabayashi, S. J . Chem. SOC., Faraday Trans. I 1984, 80, 2145. 'Hedwig, G. R.; Owensby, D. A,; Parker, A. J. J. Am. Chem. SOC. 1975, 97, 3888. fDanil deNamor, A. F.; Ghousseini, L.; Schulz, R. A. J . Chem. SOC., Faraday Trans. I 1984, 80, 1323. ZMiyaji, K.; Morinaga, K. Bull. Chem. SOC. Jpn. 1983, 56, 1861. *Ahrland, S.; Ishiguro, S.; Portanova, R. Ausf . J . Chem. 1983, 36, 1805. 'Tomkins, R. P. T.; Feakins, D.; Waghorne, W. E. J . Chem. Thermodynam. 1977, 9, 707. 'Cox, B. G.; Waghorne, W. E. Chem. SOC. Rec. 1980, 9, 381. kHedwig, G. R.; Parker, A. J. J. Am. Chem. SOC. 1974, 96, 6589. 'Cox, B. G.; Hedwig, G. R.; Parker, A. J.; Watts, D. W. Ausf . J . Chem. 1974, 27, 477. "Abraham, M. H.; Ah-Sing, E.; Danil deNamor, A. F.; Hill, T.; Nasezadeh, A,; Schulz, R. A. J. Chem. Soc., Faraday Trans. 1 1978, 74, 359. "Abraham, M. H.; Danil deNamor, A. F.; Schulz, R. A. J. Chem. SOC., Faraday Trans. 1 1980, 76, 869. "N-Ethylacetamide, from A,,B"(MeOH+NEA) of Fuchs, R.; Bear, J . L.; Rodewald, R. F. J . Am. Chem. SOC. 1969, 91, 5797; and A,,Ho(W+- MeOH) from this table. PArnett, E. M.; Moriarty, T. C. J . Am. Chem. SOC. 1971, 93, 4908. qChoi, Y.-S.; Criss, C. M. J . Chem. Eng. Data 1977, 22, 297; with the value for 1- taken as -8 kJ mol-'. 'Robinette, A. F.; Amis, E. S. Ado. Chem. Ser. 1979, 177, 355. Johnsson, M.; Persson, I. Inorg. Chim. Acfa 1987, 127, 25, 43. 'Ahrland, S. Pure Appl. Chem. 1982, 54, 1451. "Vandyshev, V. N.; Korolev, V. P.; Krestov, G. A. Zh. Obshch. Khim. 1985, 55, 2409. rMecik, M.; Chudziak, A. J. Solution Chem. 1985, 14, 653. "Hedwig, G. R.; Parker, A. J. J . Am. Chem. SOC. 1974, 96, 6589. "Castagnolo, M.; Petrella, M.; Inglese, A,; Sacco, A.; DellaMonica, M. J . Chem. Soc., Faraday Trans. I 1983, 79, 221 1; used A,,Ho- (CF,SO<,W-HMPT) to adjust values for Ba2+, Zn2+, and Cd2+. YGomaa, E. A. Thermochim. Acta 1984,80, 355; with values for MeOH from this table. ZVorob'ev, A. F.; Kostyuk, B. G. ; Mazaletskii, A. B. Vesfn. Mosk. Unic., Ser. 2, Khim. 1977, 18, 287. ""Danil de Namor, A. F.; Ghousseini, L. J . Chem. SOC., Faraday Trans. 1 1986, 82, 3275.

free energies and enthalpies, is the TATB one.1° This assumption states that for the reference electrolyte tetraphenylarsonium tetraphenylborate (TATB) the contributions of the cation and the

anion to the quantity in question are the same. A large set of standard molar Gibbs free energies of transfer, A,,Go(X,W+S), of ions (X) from water (W) to nonaqueous solvents (S), updated3 from the set previously employed,' has been assembled on this basis in Table I. A similar set of standard molar enthalpies of (10) Marcus, Y . Pure Appl. Chem. 1986, 58, 1721.

Energetics of,Ion Transfer from Water to Solvents The Journal of Physical Chemistry , Vol. 92, No. 12, 1988 3617

TABLE 111: Properties P ( i ) of the Solvents at 298 K no. solvento T * ~ ab pb I O / @ 6 2 / ~ ~ ~ ~ c V/IOO

I W 2 MeOH 3 EtOH 4 I-PrOH

6 TFE 7 EG 8 Me2C0 9 PC

I O FA 11 NMF 12 NEA 13 DMF 14 DMA 15 DEA 16 NMPy 17 NH3d 18 Py

20 MeCN 21 MeN02

23 DMSO 24 TMSc 25 HMPT

5 1-BuOH

19 2-CNPy'

22 PhNO2

26 1,l-DCIE 27 1,2-DCIE

1.09 1.17 0.60 0.93 0.54 0.83 0.52 0.78 0.47 0.79 0.73 1.51 0.92 0.83 0.71 0.08 0.83 0.00 0.97 0.71

(0.9)' (0.0)' (0.9)' (0.0)' 0.88 0.00 0.88 0.00

(0.86)' 0.00 0.92 0.00

(0.34)" (O.O)'*k 0.87 0.00

(1.2)m 0.00 0.75 0.19 0.85 0.22 1.01 0.00 1.00 0.00 0.98 0.00 0.87 0.00

(0.48)'" (0.10)' 0.81 0.00

0.47j 0.66 0.75

(0.80) ' 0.88 0.00 0.52 0.48 0.40

(0.48)' (0.8)'

0.69 0.76 0.78 0.77

(0.43)'*k 0.64

(0.29)' 0.40' 0.06 0 . 3 9 0.76 0.39 1.06

0.00

(0.8)'

(0.10)'

0.125 0.31 0.41 0.49 0.57 0.38 0.265 0.48 0.155 0.090 0.055 0.075' 0.27 0.265 0.311 0.3 1 0.42 0.82 0.1059 0.275 0.27 0.285 0.215 0.23 0.34 1 .oo 0.97

2.29 0.18 0.88 0.41 0.68 0.59 0.60 0.75 0.55 0.92 0.57 0.72 1.05 0.56 0.41 0.74 0.74 0.85 1.55 0.40 1.08" 0.59 0.64" 0.93' 0.62 0.77 0.49 0.93 0.41" 1.27 0.54 0.96 0.93 0.22 0.47 0.81 0 . 7 6 0.979 0.60 0.53 0.68 0.54 0.49 1.03 0.61 0.71 0.75 0.95 0.46 1.76 0.34 0.85 0.40 0.79

a For the names of the solvents shown here as abbreviations see Ta- bles I and 11. bFrom ref 2. 'From ref l l ; h2/1O0O in J m ~ - ~ , V/100 in (cm' mol-l)/lOO. dAt 240 K. 'At 303 K. 'From Boeck, J.; Gritzner, G. Z . Phys. Chem. (Neue Folge) 1982, 230, 181. $From Lemire, R. J.; Sears, P. G. J . Solution Chem. 1981, I O , 511. Casteel, J. F.; Sears, P. G. J . Chem. Eng. Data 1975, 20, 10. "From listing of group contributions to molar energy of vaporization and volume: Barton, A. F. M. Handbook of Solubility Parameters and other Cohesion Parame- ters; CRC: Boca Raton, FL, 1983; pp 64ff, 142ff. 'Estimates by R. W. Taft, on the basis of analogous solvents with similar groups; the zero value of a of secondary amides is due to their self-association. 'Revised value, from Miles, S. G.; Beak, P. J . Org. Chem. 1985, 50, 1216, for water and unpublished results of R. W. Taft, 1986, for water and the other solvents so marked. kFor the "monomeric" individual solvent molecule rather than for the bulk solvent. 'Vaughn, J. W.; Sears, P. G. J . Phys. Chem. 1958, 62, 183. mEstimated from the relationship T* = 0 . 2 3 ~ ( f i is the dipole moment in Debye units, for ammonia T* pertains to the monomer rather than the bulk solvent) from Kamlet, M. J.; Abboud, J.-L. M.; Taft, R. W. Prog. Phys. Org. Chem. 1981, 13, 485.

transfer, AtrHo(X,W+S), has also been prepared4 and updated in Table 11.

Although subject to continuous updating and checking for consistency (the additivity rule for cation and anion values, giving the measured quantity for the electrolyte, must be obeyed), the data set is necessarily incomplete. For At,,Go(X,W-+S) it pertains to 25 solvents and 34 ions, and for A,,HO(X,W-.S) it does so to 18 solvents and 30 ions, but only 55% and 61%, respectively, of the data matrices are filled. The quality of the data also varies considerably from item to item; the overall mean standard error is 6 kJ mol-', probably less than that for the items given with a digit behind the decimal p ~ i n t . ~ , ~

The properties PO.) of water (W) and of the nonaqueous solvents (S) to which the above-mentioned quantities pertain are listed in Table 111. The solvatochromic indices K*, a, and /3 are from a recent comprehensive listing by two of us and co-workers.2 The relative permittivity, e, and the thermodynamic quantities 62 and Vare from a compilation in a book by another one of US.^' For some of the solvents estimates of the required quantities had to be used, as indicated in the table, since no firmly established measured values are available. Solvents containing sulfur donor atoms are excluded from the present consideration and are dis- cussed in a separate paper.12

TABLE IV: Prowrties Ai of the Ions ion z O.I/P ab 1 0 0 ~ ~ Ro/lOc

H+ Li+ Na+ K+ Rb+ cs+ NH4+ Ag+ TI+ Ba2+ cu2+ Zn2+ Cd2+ Pb2+ Hg2+

F c1- Br- I- 1,- N,- CN- SCN- NO3- CIO, B F4- CH3COF CF3SO3-

1 1 1 1 1 1 1 1 1 2 2 2 2 2 2

1 1 1 1 1

-1 -1

-1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1

Small Cations 3.04m 0.00 1.45d -1.02 0.98 -0.60 0.72 -0.58 0.67 -0.53 0.59 -0.54 0.68 -0.60 0.87 0.70h 0.67 0.20 0.74 -0.66 1.37 0.38 1.33 0.35 1.05 0.58 0.85 0.41 0.98 1.27

Large Ions 0.357 0.297 0.264 0.242 0.235 0.304' 0.238

0.015m 0.14d 0.44 1.10 1.39 2.06 1.36 0.64 1.41 1.05 0.16 0.18 0.36 0.69 0.44

Anions 0.75 -0.66 0.55 -0.09 0.51 0.17 0.45 0.50 0.32' 0.87 I 0.51 0.66 0.52 0.41 0.447 0.85 0.53 0.03 0.42 -0.30 0.43 -0.30 0.62 -0.22 0.459

9.2 16.0 22.8 29.5 32.2 14.9e 31.4

-0.01 0.01 0.07 0.27 0.41 0.67 0.47 0.49 0.97 0.50 0.13 0.12 0.32 0.95 0.61

2.3' 3.Y 6.11 7 . 9

11.5' 3.2k

10.9'

0.99 0.22 2.48 0.82 3.15 1.16 1.46 1.75

I2.97f 3.1 1 1.12" 2.92 0.79 4.05 1.65 2.83 1.02 5.79 1.28 5.20 1.78 1.36 4.469 1.8'

"he Pauling crystal radius (coordination number 6) for monoatomic ions and the thermochemical radius for polyatomic ones from ref 13 and the van der Waals radius for tetraalkyl or -aryl ions from ref 14 are used for r/nm and for I000 = (400~/3) ( r /nm) ' . bFrom ref 9. <Molar refractivities for the mean sodium D line at infinite dilution in water, RD/(cm3 mol-I), based on RD(Na+) = 0.65 cm3 mol-', from ref 15. dThe radius for Li' was taken as 0.069 nm: Marcus, Y. J . Solu- tion Chem. 1983, 12, 271, and ref 13. 'The van der Waals radius of the picrate anion was taken as 0.329 nm, based on the intrinsic (van der Waals) volumes from Leahy, D. E; Carr, P. W.; Pearlman, R. S.; Taft, R. W.; Kamlet, M. J. Chromafographia 1986, 21, 473, and group additivity of the volume. /The radius of 13- was taken as 3'1' times that of I-. gThe radius of trifluoromethanesulfonate was taken as the sum of the van der Waals radius of the fluoride atom and its distance from the center of the ion according to its geometry: Marcus, Y . ; Loewenschuss, A. J . Phys. Chem. Ref. Data 1987, 16, 61. "The softness parameter of Ag+ is larger than the value obtained from its estimated enthalpy of hydration: see footnote b to Table I in ref 9. ' From ref I . 'From ref 15. kAssumed to be the same as for picric acid, estimated from its molar magnetic susceptibility (Francois, J. Bull. SOC. Chim. Fr. 1962, 506) and the relation of that to the polarizability according to T. Nakamura (quoted in ref 11). 'Assumed the same as for trifluoromethanesulfonic acid, calculated from the data in the 1986 Aldrich Catalog. "From fitting of AhydH" = -80.5 - 33.7/(r/nm) with R,,, = 0.9996 for the alkali metal ions to the data from ref 11. "From ref 1.

The properties Pi of the ions (X) to which the thermodynamic functions of transfer pertain are listed in Table IV. The radii of the ions, employed in the quantities O . l / r and lOOu, are the Pauling crystal radii for coordination number 6 for the monoatomic ions and thermochemical radii for polyatomic ones, taken from a recent review,I3 where references to the sources are given. For

( 1 1) Marcus, Y. Ion Soluation; Wiley: Chichester, 1985. (12) Marcus, Y. J . Phys. Chem. 1987, 91, 4422.

(13) Marcus, Y.; Loewenschuss, A. Annu. Rep. C, 1984, R . SOC. Chem. (London) 1985, 81.

3618 The Journal of Physical Chemistry, Vol. 92, No. 12, 1988 Marcus et al.

TABLE V Mutual Dependence of the Properties of the Solvents and of the Ions (Correlation Coefficients for Pairwise Linear Relationships)

Prooerties of the Solvents ~~

property( 1) property(2) a p 10/e 62/1000 1//100

7r* 0.220 0.062 0.529 0.300 0.196 a 0.075 0.084 0.468 0.437 P 0.241 0.019 0.328 10/t 0.507 0.135 s2 / 1000 0.620

Properties of the Ions

property( 1)

-0.216 0.291 0.565

property (2) U 1 ooc Small Cations

O.l/r 0.129 -0.400 U -0.363 1 ooc

Large Hydrophobic Ions O.l/r -0.974 1000

Anions 0.1 / r -0.621 -0.819 -0.762 U 0.490 0.608 1 ooc 0.691

-0.903 0.967

the tetraalkyl or -aryl ions the van der Waals radiiI4 are employed. The softness parameters, u, of the ions are from a recent report by one of u s 9 In the previous work,] an attempt was made to estimate the softness parameter values of tetraalkyl or -phenyl ions from their molar refractivities and electrical fields. This may not be completely justified, and it was preferred in the present paper to treat these ions separately, omitting the dependence on their softness in exchange for including a direct dependence on their polarizability, via their R D values. These were taken as the infinite dilution aqueous solution values,15 whereas for the other ions the RD data are mainly from Heydweiller,'6 as in the previous work.'

Results For a meaningful statistical analysis of the dependencies of

A,,G'(X,W-S) or AtrH'(X,W+S) on the properties P(j) of the nonaqueous solvents and the properties Pi of the ions, these properties must be reasonably independent of each other. The mutual correlations of the properties, as linear expressions of the form

(3) property(1) = a + b(property(2))

were tested, and the results are presented in Table V. Appreciable dependencies (correlation coefficients > O S ) of solvent properties were found only between 10/t and both T* and 62/1000 and between the latter and V/lOO. Caution will have to be exercised in cases where dependencies of A,,Go(X,W-S) or AtrHo(X, W+S) on these solvent properties are found. It was more difficult to find mutually independent properties of the ions. The (small) negative correlation of the volumes of the ions with the reciprocals of their radii is understandable, becoming more important for the anions and the large, hydrophobic ions. For the latter, also, lOOv is strongly correlated with RD, and only one of these properties should be employed at a time.

Since, however, the data base is incomplete, some of the correlations had to be carried out with fewer than all of the independent variable. These were then more mutually dependent than the results for the entire set in Table V suggest. In some cases,

(14) Krumgalz, B. S . J . Chem. SOC., Faraday Trans. 1 1982, 78, 437. (15) Soffer, N.; Bloemendal, M.; Marcus, Y . J . Chem. Eng. Dura 1988,

(16) Heydweiller, A. Phys. Z . 1925, 26, 526. 32, 43.

also, the range of values covered by the independent parameters was not as wide as that of the entire set, shown in Tables I11 and IV. The form of eq 1 requires the correlated data to pass through the origin, Le., there is no independent term. (If the solvent into which the ion is transferred is chosen to be water, then S = W, and all the - P(JW values are zero, as is At,Go.) If the TATB assumption is not accepted, then for every solvent there is an additive term of the same size for all the ions (but of opposite signs for the cations and anions). In the correlations this will appear as an independent term but devoid of physical meaning. The correlations therefore do not depend on whether this assumption is strictly valid or not.

The results of the fits according to eq 1 of A,G'(X,W-S) of each ion separately to the differences of selected properties P(j) of solvents and of water for the three classes of ions small cations, large hydrophobic ions, and anions are shown in Table VI. Corresponding fits of the A,JP(X,W-S) data are shown in Table VII. In some cases, marked in the tables, one or two solvents were excluded from the fits, since they made for excessively large standard deviations of the fits, sd (in kJ mol-'), and lowered the multiple correlation coefficient, Ram. For these cases, the absolute values, A, of the deviations of the A,,G'(X,W-S) or At,Ho- (X,W-S) from Tables I and I1 from the values calculated with the A,(j) values in Tables VI and VI1 are shown in terms of the sd of the fits in footnotes to the latter tables. Otherwise the values of A were generally <sd or at most up to 2 sd in a few cases. Values of the coefficients A,(j) that are smaller than their own standard deviations are enclosed in parentheses. Generally, the values of A,(j) are 10 or more times their own standard deviations, hence highly significant.

The fits shown in these tables are for selected properties (three for the small cations and the anions, two for the large hydrophobic ions) out of the entire set of properties listed in Table HI. The selection was based on the F(m,n) statistic, where m is the number of independent variables and n the number of data for each ion, with the additional constraint that the same set of independent variables was to be used for each class of ions. Trial and error led to the best set of independent variables, Le., the one giving not only the largest F(m,n) but also the smallest standard deviations, sd, and the largest correlation coefficients, R,,,, of the fits for the individual ions.

The standard Gibbs free energies and enthalpies of transfer of the small cations, both univalent and divalent, except for the H+ ion, could be expressed with statistically adequate justification by the use of only three independent variables, T * , a, and p:

A,,G"(X,W-S) = A, ( r )Ax* + Ai(a)Aa + A,(P)AP (4)

No terms in lo/€, 62/1000, or V/100 were required. One solvent, NH3, consistently yielded very large deviations, A, especially for the silver and divalent cations. This problem is due to the softness of this particular solvent and is addressed in a separate paper."

For AtrGo of the hydrogen ion the set of independent variables given by eq 4 was inadequate. When a* was replaced by V/100, the correlation was improved appreciably to the statistical coefficients shown in Table VI, but when the set of independent variables a, 0, and V/lOO was applied to the other small cations, the statistics of the fit worsened considerably compared with the results in Table VI. For A,Ho the sd of the fits were similar to those of P,,G' and to those of the data employed, f6 kJ mol-', except for the cases of H+, Ag', and Ba2+.

The At$' of the large hydrophobic ions were found to require only T * and 62/1000 as the independent variables. No terms in a, 0, lo /€ , or V/100 were required. The negative deviation of 5-12 kJ mol-] of the experimental AtrGO of the picrate anion for transfer into alcohols and formamide from the expected values is explained by the neglect of a term in a, required for anions capable of accepting hydrogen bonds (see below). The solvent dependence of A,JP of the tetraalkylammonium cations required V/ 100 instead of a'/ 1000 for the fit but again without terms in a, P, and lo /€ , In all the cases, however, the correlations failed for AtrH0 for transfer into the alcohols, the predicted values being 5-25 kJ mol-' more negative than the experimental values. There


TABLE VI; Fits of A&"(X,WdS) to the Properties of the Solvents

The Journal of Physical Chemistry, Vol. 92, No. 12, 1988 3619

Small Cations

ion n range A(*) A ( a ) 4 / 3 1 R C O , , sd H+Q Li+ Na+ K+ Rb+ c s +

TI+ NH4+ Ba2+ cu2+ Zn2+ Cd2+ Hg2+ Pb2+

Ag+

12 13 206 22 20 19' 1 7d 15 6 4

12' 6

1 6 9

11

-28 to 50 -35 to 48 -17 to 32 -16 to 39 -13 to 29 -13 to 28 -44 to 50 -26 to 16 -28 to 27 -26 to 58 -43 to 73 -86 to 42 -58 to 42 -44 to 64 -36 to 64

[73.2] -64.2 -50.0 -41.7 -48.9 -47.9 -51.6 -34.4 -13.1

-134.3 -176.5 -147.3 -115.6 -167.2 -1 13.7

41.5 3.8 5.6 6.0 8.4

10.6 11.3 5.8

31.0 6.5

16.2 17.4 34.0 -2.1

-0.8

Large Hydrophobic Ions

-52.4 -90.5 -36.4 -37.5 -21.5 -20.6 -70.5 -42.4

32.7 -225.8 -220.6 -160.9 -96.0 -93.3

-202.9

0.907 0.942 0.896 0.936 0.897 0.915 0.954 0.965 0.999 0.979 0.939 0.985 0.941 0.918 0.955

8.1 5.7 5.3 4.0 4.4 3.8 5.4 2.5 0.6 7.0

11.1 6.8 8.8

13.5 8.5

ion n range A(.rr) A(6) R C O , , sd Me,N+ 141 -5 to 18 -27.9 3.6 0.869 2.7 Et4N+ 1 I * -10 to 11 -35.8 10.4 0.9 16 2.2 Pr4N+ 10 -22 to 0 -38.9 16.7 0.965 2.1 Bu4N+ 9 -32 to 0 -51.7 27.0 0.966 3.6 Ph4As+ 20' -40 to 0 -25.2 24.6 0.971 4.1 Pic- 12 -7 to 0 (-2.3) 3.9 0.871 1.6 BPh, 20' -40 to 0 -25.5 24.6 0.971 4.1

Anions ion n range A(.rr) A ( a ) A( V / 100) Rm,, sd

F- 7 0 to 71 -24.0 -88.7 -74.9 0.999 1.7 CI- 2 1' 0 to 58 -15.5 -30.3 11.9 0.98 1 4.5 Br- 2 2.' 0 to 46 -14.4 -20.4 11.6 0.980 3.5 I- 2 1' 0 to 31 -17.8 -8.9 9.1 0.974 2.5 CN- 8 0 to 40 (-6 0 ) -41.1 -15.0 0.983 3.7 SCN- 14 0 to 22 -8.5 -9.9 3.8 0.9 14 3.5 N < 14 0 to 49 -8.7 -24.1 11.7 0.975 4.3 13- 9 -41 to 0 (4.2) 24.4 (7.2) 0.896 6.3 NO,- 6 0 to 24 (-7.4) (-2.9) 21.4 0.891 5.4 ClO,- 1 5k -7 to 22 -29.1 (-2.6) -4.9 0.776 5.1 MeC02- 6 0 to 66 -17.0 -44.8 (1 2.9) 0.987 5.5

"The set of independent variables ?r*, a, and /3 cannot express the set of At,Go(X,W--S) values adequately, and the numbers given here pertain to the set V/lOO, a , and /3 instead. b2-CNPy excluded, A = 4.8 sd. 'PhN02 excluded, A = 6.6 sd. dMeCN excluded, A = 6.4 sd. ' N M F and Py excluded, A = 3.1 sd and 44.7 sd, respectively. !FA excluded, A = 3.7 sd. gPC and 1,2-DCIE excluded, A = 4.7 sd and 4.6 sd, respectively. * P C excluded, A = 3.2 sd. 'DMSO, TMS, and HMPT excluded, A = 3.7 sd, 4.3 sd, and 4.0 sd, respectively. 'TFE excluded, A = 7.2 sd, 7.5 sd, and 8.9 sd, for Cl-, Br-, and I-, respectively. k F A and NMPy excluded, A = 3.1 sd and 3.2 sd, respectively.

is no ready explanation for this. The AtrGO of the anions could be fitted to the expression

AtrGo = A,(a)Aa* + A,(a)Aa + A,(V)V'/100 (5)

without requiring terms in @, lo/€, or 62/1000. The sd of the fits were within the f 6 kJ mol-] of the experimental data employed. An expression similar to eq 5 expressed the AtrHo data for anions.

The dependencies of the coefficients A,G) on the properties P, of the ions could be described by the general expression 2, with the results shown in Table VIII. It is seen that only two or a t most three properties of the ions suffice to express the A,G) within the uncertainties of the latter. The properties required for the A,G) coefficients of the AtrGo are generally also those that are required for the coefficients of the AtrHo. The charge comes in only in combination with the reciprocal of the radius, either as the self-energy, z* / r , or as the field strength, z / r , of the ion.

For the small cations, the A(n) coefficients of the AtrGo depend about equally on the self-energy of the ions and on their softness parameter. The coefficients for Ag+ and NH4+ were excluded from this correlation, since they deviated by 4.9 and 2.8 sd, respectively. The A ( a ) coefficients were hardly dependent on the field strength of the ions, depending mainly on their volumes. The coefficients for NH4+, Zn2+, and Cd2+ were excluded, deviating by 9.2, 6.0, and 6.1 sd, respectively. The A(@) coefficients had a weak dependence on the softness of the ions, depending about equally strongly on their field strength and polarizability. The

coefficients for NH4+ and Ba2+ were excluded, deviating by 5.4 and 6.4 sd, respectively.

The A(a) coefficients of the AtrHo of the small cations depend about equally strongly on the self-energy and the polarizability or the volume of the cations. The coefficients for H+ and Ag+ were excluded, deviating by 19.1 and 4.9 sd, respectively. For the fits of the A ( a ) coefficients, those of H+ and Ba2+ were excluded, deviating by 2.3 sd each. the A(@) coefficients required three ion properties for their proper description. The coefficients of NH4+ and Zn2+ were excluded, deviating by 4.5 and 6.8 sd, respectively.

In the A,G) coefficients for the transfer of the large hydrophobic ions it was preferred to distinguish between R, and c' as the variables in A,(*) and A,(6) (or A,(V)) , respectively, in spite of the good mutual correlation between them (Table V). This was since in A(a) it is the polarization by the solvent that plays the role, whereas in A(6) it is the work by the volume-occupying ion against the cohesive energy of the solvent that does so. It should be noted that these correlations with the properties of the ions relate only to the tetraalkylammonium ions and not to the tetraphenylarsonium and -borate ones or to the picrate anion.

The range of the field strength of the anions is rather narrow: O.lz/r varies only from -0.75 for F- to -0.32 for 13-, so that it does not seem to be a good independent variable. Still, it was required strongly by the correlations of all the A,G) coefficients for both the A,,G0 and AtrHo of the anions. For both A(*) and


TABLE VII: Fits of A,,Ho(X,W-S) to the Properties of the Solvents

Small Cations ion n range A ( r ) A(a ) A @ ) R,,, sd

H+ 6" -44 to 73 -49.7 -30.5 -135.6 0.933 12.2 Li+ Na+ K+ Rb+ cs+

NH4+ Ba2+ ZnZ+ Cd2+

Ag+

12b -57 to 12 4.2 (2.5) -71.0 0.898 17 -50 to 0 16.4 17.6 -22.8 0.900 14' -46 t o 0 1 1 . 1 21.3 -14.4 0.952 1 I -43 to 0 6.6 24.2 -18.4 0.979 13 -45 to 0 (2.1) 26.1 -14.9 0.986 6d -53 to 0 26.3 21.0 -55.7 0.850 7 -64 to 0 (-3.5) 19.3 -63.7 0.994 7 -122 to 0 23.2 68.6 -37.9 0.961 7' -75 to 0 59.1 29.5 -38.8 0.976 5' -93 to 0 35.7 38.4 -67.5 0.998

Large Hydrophobic Ions

7.1 7.0 4.7 3.4 2.6 2.7 2.4 4.1 7.3 2.8

Me4N+ Et4N+ Pr4N+ Bu4N+ Ph4As+ Pic- BPh4-

ion

I O -34 to 1 -8.7 -23.5 0.943 3.4 1 I f -9 to I O -19.9 -8.7 0.775 2.9 79 0 to 17 -24.0 (-0.3) 0.660 5.6

13h 0 to 26 -34.0 5.0 0.725 6.9 14 -26 to 2 -11.3 -19.0 0.926 2.9 4 -12 to 0 (-3.7) -23.3 0.923 2.9

14 -26 to 2 -11.3 -19.0 0.926 2.9

Anions n range A ( T ) A ( a ) A(V/100) R,,,, sd

c1- 15' 0 to 38 3.6 -8.4 18.8 0.973 2.7 Br- 14' -16 to I8 9.5 (2.1) 17.1 0.823 4.1 1- 1.5' - 2 9 t o 7 8.5 13.3 11.6 0.809 4.2 SCN- 6 -10 to 0 4.0 4.8 (0.5) 0.910 1.6 N3- 6k -3 to 15 (-6.5) 5.1 11.0 0.767 3.7 C104- 15 -24 to 0 (-3.9) 11.4 -4.7 0.915 3.8 CF3S03- 6 -4 to 5 -12.3 5.5 1.6 0.904 1 . 1

"MeCN excluded, A = 4.4 sd. *NH3 excluded, A = 5.9 sd. 'NMPy excluded, A = 3.4 sd. dNH, and Py excluded, A = 5.0 sd and 5.2 sd, respectively. 'MeCN excluded, A = 9.1 sd for Zn2+ and 19.1 sd for Cd2+. fI,2-DCIE excluded, A = 3.5 sd. ZTMS excluded, 4 = 2.6 sd.

FA excluded, A = 10.7 sd. "EA excluded, A = 10.7 sd for CI- and 3.1 sd for Br-. 'FA excluded, A = 2.7 sd. k T M S excluded. A = 3.2 sd.

A ( a ) of the AtrGo the values for Clod- were excluded, deviating by 5.8 and 4.4 sd, respectively, and for A ( a ) also NO3- had to be excluded, deviating by 3.9 sd. For A( V) three ions had to be excluded: F, CN-, and 13-, with deviations of 28.0, 7.4, and 8.7 sd, respectively. For the enthalpies there were only seven anions altogether, but only in the case of A(*) had one to be excluded: CF3S03-, deviating by 3.8 sd.

Discussion The strong electric field of an ion causes its solvation energetics

to be dominated by a large electrostatic term, and the solvent molecules around it to be immobilized to a great extent. According to Abraham and Liszi" the first solvent layer around the ion is characterized by values of the relative permittivity and of its temperature coefficient that are common to all solvents, including water: 2.0 and -0.0016 K-I, respectively. Therefore on the transfer of an ion from water to a nonaqueous solvent the major fraction of the electrostatic term in the Gibbs free energy and the enthalpy of solvation, the amount that pertains to this first layer, will cancel out. Only a small remainder fraction of the electrostatic term, the amount that pertains to layers of the solvent beyond the first, manifests itself in the Gibbs free energy and enthalpy of transfer.

This small remaining contribution to the Gibbs free energy of transfer is positive, involving two terms. One is a term in the difference in the thicknesses of the first solvation shell in the solvent and in water, divided by the product of these thicknesses. The

(17) Abraham, M. H.; Liszi, J. J . Chem. SOC., Faraday Trans. 1 1978, 74,

(18) Marcus, Y . J . Chem. Soc., Faraday Trans. 1 1986, 82, 233. (19) Marcus, Y . J . Solution Chem. 1986, 15, 291.

1604, 2858 .

other term is in the difference in the reciprocals of the relative permittivities, l / c s - l/cw (the first term of which is modified by the ratio of the radii of the ion with its first solvation shell). Although the reciprocal of the relative permittivity was offered to the statistical analysis as a variable, it was not sufficiently significant to be absolutely demanded. (It was generally taken as a fourth choice, both in the present analysis and in the one reported previously on a smaller set of ions and solvents.') Thus these second-order effects have to be taken care of by the other quantities appearing in eq 1 and 2. The difference in the thicknesses of the first solvation shells can be expressed by a difference in the molar volumes of the nonaqueous solvent and water, leading to a term in AV. The relative permittivities are linearly correlated (to a limited extent; see Table V) with the R* values, and hence their difference leads to a term in AT*. A similar analysis shows an origin of such terms also in the enthalpies of transfer.

The set of solvent properties employed in the present study is admittedly somewhat arbitrary. It is based on the results of the previous study' on the one hand and on the desire to explore the use of the solvatochromic solvent properties T* , a, and @, which are so successful in linear solvation energy correlations involving nonionic solutes, and in correlations involving ions, on the other. Two limited previous attempts of doing so come to mind: one is Kolling's correlation of the Gibbs free energies of transfer of the two ions of tetraphenylarsonium tetraphenylborate from water to 13 nonaqueous solvents.20 The other is the attempt by two of us and co-workers*' to correlate the Gibbs free energies of transfer of the combined ions of tetramethyl- and tetraethylammonium chloride, bromide, and iodide from methanol to 13, mostly different, nonaqueous solvents.

Table IX presents a comparison of the fits achieved by the latter attempt (columns 2) with those obtained in the present study (columns 4, with the needed parameters from Table VI) for two representative combinations of cation and anion: tetramethylammonium chloride and tetraethylammonium iodide. It should be noted that the data that were fitted were not exactly the same. One (columns 1) originated in a particular set of experimental data after the contribution to I,,Go of the ion pair was taken into account, and the other (columns 3) was taken from averages of data3 pertaining to each of the participating ions individually. It should also be noted that the worst disagreement between the value estimated and the "experimental" value occurs for the two solvents that have very low relative permittivities: diethyl ether (Et,O) and ethyl acetate (EtOAc). For these the "experimental" value to be fitted is a relatively small remainder after the subtraction of the much larger contribution to AlrGO of the ion pair, so that the former could be beset by a large error. For all the other solvents both series of fits are adequate, with similar deviations that are generally within the limits of &6 kJ mol-' reported for both series of fits.

Some alternative fits of the data in Tables I and I1 with the solvent properties have been attempted. For instance, the use of only two parameters (T* and p) for the small cations worsened the fits considerably: the correlation coefficients were in the range 0.6-0.8, and the standard deviations of the fits were generally >10 kJ mol-', compared with the values of Table VI. The use of the monomeric values, a, and p, of the hydrogen-bond-donating and -accepting abilities of self-associated solvents (water and the alcohols), instead of the bulk values reported in Table 111, worsened the fits similarly. It is concluded that given the set of solvent properties listed in Table 111 from which to choose the most significant contributions, the variables included in Tables VI and VI1 cannot be improved upon from statistical considerations only. The same applies to the variables shown in Table VI11 that pertain to the ion properties.

The results of the linear solvation energy relationships presented in Tables VI-VI11 may now be rationalized in terms of the differences between the interactions of the ion and its first solvation

(20) Kolling, 0. W . Anal. Chem. 1980, 52, 987. (21) Taft, R. W.; Abraham, M. H.; Doherty. R. M.; Kamlet. M. J. J . Am.

Chem. SOC. 1985, 107, 3105.


TABLE VIII: Fits of the A , ( j ) Coefficients to Properties of the Ions

The Journal of Physical Chemistry, Voi. 92, No. 12, 1988 3621

A,G) n range 0.1z2/r O.lz/r d lO0u RD/10 R C O , , sd A,,Go of Small Cations

A ( T ) 1 1 -177 to 0 -32.6 30.3 0.988 9.1 A ( a ) I O -2 to 11 (-0.3) 5.3 0.792 2.6 4 / 3 1 1 1 -220 to 0 -37.2 (-1.6) -37.8 0.964 20.4

A,,Go of Large Hydrophobic Ions A(*) 4 -52 to 0 -52.9 -4.6 0.945 5.0 A ( @ 4 0 to 27 -21.3 1.04 0.993 1.4

At,Go of Anions

A ( & ) 9 -88 to 0 74.7 30.2 0.879 12.3 4 v) 8 -5 to 22 -38.3 -2.8 0.886 3.6

AtrHo of Small Cations A(*) 9 0 to 60 10.0 -6.1 0.969 4.2

A(P) 9 -136 to 0 -41.6 -8.0 16.4 0.965 10.7

AtrHo of Large Hydrophobic Ions A(* ) 4 -34 to 0 -6.0 -3.8 0.987 2.3 A(YI 4 -24 to 5 -81.5 -0.87 0.986 1.9

AlrHo of Anions A ( T ) 6 -12 to I O -6.5 15.5 0.900 2.8 A(&) 7 -8 to 13 25.0 4.3 0.867 2.9 A(YI 7 -5 to 19 -55.1 -4.7 0.905 3.4

A ( r ) I O -24 to 4 30.2 2.9 0.912 3.5

A ( Q ) 9 0 to 39 9 6 (2.5) 34.9 0.952 4.5

TABLE IX: Comparison of the Fits Obtained Here with a Previous Fit of Ah,Go(R4N++X-,H2*S)/(kJ mol-')"

(CH3)+,N+ + C1- (C2HS)4N+ + I- solvent 1 2 3 4 1 2 3 4

H20 0 - 2 0 0 0 0 0 0 MeOH 16 19 19 19 4 8 8 9 EtOH 28 27 31 26 13 12 19 13 I-PrOH 33 30 37 30 16 14 24 15 2-PrOH 37 37 40 21 19 24

MeCN 39 44 45 36 5 15 10 6 MeN02 33 28 33 31 2 2 9 1 DMSO 26 25 38 35 2 -5 1 3 DMF 34 39 43 41 3 7 12 5

MeCOEt 62 58 53 21 23 19 EtOAc 53 45 27

1-BuOH 37 35 41 34 19 18 29 19

Me2C0 53 50 60 46 16 17 9

Et20 131 131 74 83 85 43

uColumn 1: data from ref 21, transformed from A,,Go(R4N++X',- MeOH-.S)/(kcal mol-') values. Column 2: fi t in ref 21 to AtrGoO + sr* + act + hs2 with AtrGoO = 167 and 115, s = -190 and -164, a = -100 and -68, and h = 0.285 and 0.264 for the two salts, respectively. Column 3: data from this paper, Table I. Column 4: fit to [A- (a,R4Nt) + A(a,X-)]As* + A(6)A62/1000 + A ( a ) A a + A(V)AV/ 100, with the coefficients from Table VI.

shell with its aqueous environment on the one hand and of such an entity with its environment in the nonaqueous solvent, on the other. The preference of the ion for the one or the other environment is governed by the sign of the standard Gibbs free energy of transfer: it will prefer to be in the aqueous solution if AtrGo is positive and in the nonaqueous solution if it is negative.

The standard entropy of transfer into all solvents is almost invariably negative and large,4 exceptions being the largest hydrophobic ions, for which A,Jo is positive. The ion immobilizes the solvent in its first solvation shell with similar entropic effects in water and in the nonaqueous ~ o l v e n t . ~ ~ ~ ' ~ - ' ~ However, water that is released on the transfer of the ion from the aqueous to the nonaqueous solution returns to the structured bulk water, with a loss of entropy, which is not the case with the nonaqueous solvent that is released in the reverse transfer. It is understandable, therefore, that positive AtrGo values will result for AtrHo values that are insufficiently negative. A discussion of both the standard molar Gibbs free energy and the standard molar enthalpy of transfer is thus instructive.

For small cations the sign of At$ depends on the relative sizes of the sum of the first two terms in eq 4 and the third term. The

first term makes a positive contribution, since both its factors are negative. All the solvents have a negative AT*, and the negative sign of A(T) is governed by the coefficient of z2/r, this factor being large for high-field ions. This term thus describes the electrostatic ion-dipole interaction, and on its account the ions would prefer the aqueous environment. The second term makes a small negative contribution to AtrGo, but it is more difficult to understand. All the solvents have a negative Aa, though the alcohols, formamide, and a few others with a methyl group near the positive atom of a dipole (acetone, acetonitrile, nitromethane) have values of Aa less negative than the others. The second term could be an expression of the expulsion of the bulkier cations from the structured water (the term increases with v), the effect being less if the solvent also is structured (smaller Aa for the alcohols). It ought to be pointed out that a similar effect was noted also in the previous report on this problem,' where a term in ET, the electron-pair-acceptance parameter of Dimroth and Reichardt' had to be used in the description of the At,Co of the cations. The third term in eq 4 can be either positive or negative, depending on the sign of A@ Its first factor is always negative, due to both the z2/ r and RD terms, with only a small modifying contribution from the term in u. Thus both a high self-energy and a high polarizability of the cation aid in its accepting an electron pair from a solvent of high basicity, which has a large p and hence a large positive A(3 value. Only if the third term predominates and is negative will the cation prefer the nonaqueous solvent over water.

The AtrHo of small cations depends on the same variables as A&', but contrary to the latter, the first term in AtrHo is generally negative. This arises from the negative AT* combined with a positive A ( P ) , the sign of which is due to the balance between the positive z 2 / r term and the negative RD term. The coefficients in A ( @ ) of At,Ho are similar to those of A(P) of A&', except that the field strength replaces the self-energy (moderating the ad- vantage of the divalent cations) and except for the sign of the minor term in RD. In sum, A @ ) is least negative for large univalent cations and becomes more negative the stronger their electric field. The resulting A,,Ho is generally negative, except for the transfer of high-field ions into solvents of low basicity, where no com- pensation for the large negative enthalpy of hydration can be provided by the solvent. The more frequent cases of positive AvGo, combined with usually negative A,Ho, are thus ascribed mainly to the large negative entropy of transfer, commented on above.

For the large hydrophobic ions At,,Go is made up of two opposing terms. The first is positive, due to the negative signs of both the P* and A(T) factors. The positive effect of this term on A,Go can be ascribed to dipole-induced dipole interactions. The small


size of the water molecule permits it to approach closer and hence makes its dipole more effective in inducing dipoles in the large ions. The induced dipoles are larger, the larger the polarizabilities of the ions, measured by RD, causing the ions to favor water on this account. The second term in A,,Go, that in 62, is negative, however, and generally larger than the first. This is readily understood in terms of the work required for the creation of the cavity in water, which is larger than that in any of the solvents (negative 8') and increases with the ion size, working in favor of transfer of the larger ions from water into the nonaqueous solvents. The balancing of the two terms causes &,Go to change from positive to negative or from negative to more negative as the ion size increases, less highly structured solvents being favored over more highly structured ones. Tetramethylammonium ions may favor water over solvents with very low T* values (i.e., having low dipole moments), but tetrabutylammonium or the tetraphenyl ions will always favor transfer into the less structured solvents.

The expression for the AtrHo of the large hydrophobic ions is similar to that for the A&', the first term making a positive contribution and the second a negative one, the dipole-induced dipole interactions being responsible for the positive contribution to both thermodynamic functions. However, the second, negative, term in AtrHo is generally not as negative as the corresponding one in AtrGo. This reduction in the negativity or even the becoming positive of this term in A,,Ho as the ion size increases reflects the lessening in the interaction energy as the distance between the centers of the ion and the solvent increases with both ion and solvent size. The balance between the two terms is thus in favor of a negative At,Ho for the smaller of the hydrophobic ions and of a positive Ar,Ho for the larger ones.

The preference or otherwise of anions for water over nonaqueous solvents is described by eq 5 , where all three terms turn out to be positive, so that water is practically in all cases the preferred environment. In the first term the factor AT* is negative and so is A(T), the term in z / r predominating and z being negative. This is the term that describes the electrostatic interactions, which is strongest for the solvent with the largest T* (Le., water) and for the smallest ion (having the largest z / r ) . In the second term the factor Aa is almost always negative (except for trifluoroethanol, which has a larger a value than water) as is A(&), producing a positive contribution. This comes from the hydrogen bonding of those solvents capable of it to the anion, which is by far the strongest for water, and the effect of this term is smaller for the alcohols than for most other solvents. This term is generally the dominant one (and therefore AIrGo of the halide anions into trifluoroethanol is, in fact, negative, the anions preferring the more strongly hydrogen-bonding solvent). The third term in eq 5 is also positive, both its factors being so. A( V) increases as the ion becomes smaller, and AVincreases as the solvent becomes bulkier,

signifying that there is space for fewer and fewet solvent molecules around the anion. This contribution to the reluctance of the anions to enter a nonaqueous solvent is thus a steric effect. Altogether, therefore, anions prefer to stay in an aqueous environment. Since the field strength is the leading term in all the A,G) factors, this effect increases the larger this field is.

For AtrHo of the anions not all the terms in the expression analogous to eq 5 are positive: on the contrary, the first two are negative. Only for chloride (there are no data for fluoride) does the second term permit a positive AtrHo to be achieved, signifying an energetic preference for the strongly hydrogen-bonding water. For the larger anions this is not the case. The third term does provide the expected positive contribution, both A( V) and AV being positive. This can be interpreted as the energetic effect of the repulsion of the large anions from the highly structured water. The larger the solvent molecule, the greater is the contribution of this term.

The balancing between the contributions from the A ( a ) A r * + A(a)Aa terms on the one hand and from A(V)AVon the other causes A,,Ho to be in some cases positive and in others negative and generally rather small. For the halide anions it becomes less positive or more negative (transfer from water into the solvent is energetically favored) as their size increases, as is expected from overall electrostatic considerations. There is some paucity of data concerning the AtrHo of anions, and the conclusions are not as firm as for their AtrGo. This quantity is seen to be governed more by the negative entropy change, which produces a positive Gibbs free energy of transfer, even if AtrHo is mildly negative.

Acknowledgment. Dr. F . Anvia is thanked for carrying out many of the computer calculations. Y.M. thanks Dr. M. H. Abraham for fruitful discussions. This work was supported in part by the US.-Israel Binational Science Fund, Grant No.

Registry No. TFE, 75-89-8; EG, 107-21-1; PC, 108-32-7; FA, 75-

84-00292.

12-7; NMF, 123-39-7; DMF, 68-12-2; DMA, 127-19-5; DEA, 685-91-6: NMPy, 872-50-4; Py, 110-86-1; 1-CNPy, 100-70-9; DMSO, 67-68-5; TMS, 126-33-0; HMPT, 1608-26-0; 1,l-DCIE, 75-34-3; 1,2-DCIE, 107-06-2; Pic-, 14798-26-6; H+, 12408-02-5; Li', 17341-24-1; Na+, 17341-25-2; K+, 24203-36-9; Rb', 22537-38-8; Cs', 18459-37-5; Ag', 14701-21-4; TI', 22537-56-0; NH4+, 14798-03-9; Ba2+, 22541-12-4; Cu2+, 15158-1 1-9; Zn2+, 23713-49-7; Cd2+, 22537-48-0; Hg2+, 14302- 87-5; Pb2+, 14280-50-3; Xle,N+, 51-92-3; Et,", 66-40-0; Pr4N+,

F-, 16984-48-8; Cl-, 16887-00-6; Br-, 24959-67-9; I-, 20461-54-5; 13-, 14900-04-0; N3-, 14343-69-2; CN-, 57-12-5; SCN-, 302-04-5; NO3-,

CF,S03-, 37181-39-8; MeOH, 67-56-1; EtOH, 64-17-5; 1-PrOH, 71- 23-8; 1-BuOH, 71-36-3; MeCN, 75-05-8; MeNO,, 75-52-5; PhNO,. 98-95-3; Me2C0, 67-64-1.

13010-31-6; Bu~N', 10549-76-5; PhdAs', 15912-80-8; BPhd-, 4358-26-3;

14797-55-8; Clod-, 14797-73-0; TcOd-, 14333-20-1; CH,CO<, 71-50-1;

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