Cecil M. Crlss Universily of Miami Coral Gables. Florida 33124 Mark Salomon Power Sources Technical Area US. Army Electronics Technology and Devices Laboratoty (ECOM) Fort Monmouth. New Jersey 07703
I
I
Thermodynamics of Ionic Solvation And its Significance in Various Systems
In spite of the enormous amount of effort that has been devoted to the study of aqueous electrolytic solutions, there is still no really satisfactory theory describing their behavior. It has frequently been said that our understanding of aqueous solutions may be enhanced a t a faster rate by looking a t a variety of nonaqueous solvent systems. In general, such systems do not have all of the complicating facets of aqueous solutions, and by making judicious choices of solvents it is possible to eliminate certain features such as hydrogenhondine. ~ h e r . h o d p a m i chas s heen one of the more powerful tools empluqed for investiaatinnsolvation of ions in aaueoussolutions, and in the past 15 Gars, significant progr&s has been made in the emplovment of this tool for the studv of nonaqueous systemi M U C ~of the recent interest has been stimulated by a desire to ( I J compare the known thermodynamic values of electrolytes in water with those of other sol"ents in the hope of elucidating the structure of both aqueous and nonaqueous solutions and (2) to apply these concepts to solvent effects on the rates and mechanisms of chemical reactions. The relatively large number of data for nonaqueous solutions that have been reported in the literature now makes it possible to see some trends in kinetic and thermodynamic values in various solvents. As these trends are placed on firmer theoretical ground i t will be possihle to develop reliable methods for estimating properties of electrolytes in solvents for which little or no data are available. In view of the large body of literature now existing for thermodynamic properties of electrolytes in various solvent systems, and its conspicuous absence in all but the advanced or specialized textbook, it appears timely tomake an examination of what types of data are now available, how these data are being used in current chemical concepts, what success they have met for interpreting structural effects, and what trends can he discerned. The purpose, then, of this paper is to examine the present state of the art of the properties of ionic solutions, particularly as related to nonaqueous solvents. The Medium Effect
One of the more useful concepts employed for studying the effect of solvent on ion solvation is the "medium effect." This concept was introduced some 50 years ago by Bjerrum ( I ) and its present ~ h a s was e h e a n hv the works of Pleskov (2) and In the last several years, much interest has been ~trehluw(.i~. aenerated in this area of chemistrv as seen hv the number of zetailed reviews now available (4f The defiiition of the medium effect for a simple monovalent ion, M+, can he described by the processes given in the figure. In this figure, the cation in water (w) is removed to the gas phase and then returned to
-A%Iv /"'(g$olv - FX
+ .x
in wafer)
in solvenf
A*,
s)
Born-Haber type cycle far the transfer of Mt horn water to solvent s
solution in another solvent, s. The "real" free energy change for the process is, from the figure
+ z F x . - AG.,I,(M+)~- ZFX,
A a t = AG8,~,(Mt).
(1)
A a t = AGdM+) izF(x..-
(2) xd (3) Aat = AadM+). - Aa,.dMf), In the figure and eqns. ( 1 3 ) , A a t and AG, are, respectively, the "real" free energy and "chemical" free energy of transfer; x is the surface potential, z is the ionic charge, and F, is the work of transferring a unit charge across the dipolar liquidlair interface. If the ion in both solvents is a t the same concentration, then the total medium effect can be written as
Andion) = Aa$'(ion)
+ RT ln(y+,$y*,,)
(4)
where = AGP(ion) + zF(x, - xw) AaLO(ion) (5) It should be noted that values of u. u, are often 4.1V so l ~ is of the same that the term F(x, - x-) s 2 k c a l / ~ o which order of magnitude as AGtO (ion) values. According to Owen's definitions (5), Amt is the total medium effect, A a P is the primary medium effect, and the logarithmic term in eqn. (4) is the secondary medium effect. This latter quantity is usually of the order of 0.1-0.01 kcalhole and is therefore often neglected compared to A d . The mean activity coefficients, y+, are referred to the hypothetical state for unit concentration in the eiven solvent. While AG+O (ion) values are not e x ~ e r i mentally determinable, AatO (ion) values are, in principal, measurable: these latter measurements are however not free from criticism (cf. discussion in ref. ( 4 e ) ) . In order to arrive at a set of AG,O (ion) values. one often starts with the determination of thermodynamic'propertiesofa seriesof salts, say MX. From our definition in euns. (1-51 and notine that z r...r . zx- = 0, it follows that
-
+
-
(6) Aat"(MX) = AGto(MX) There are two basic extrathermodynamic assumptions com-
Volume 53, Number 12, December 1976 / 763
monly used to split the AGtO(MX) values into individual ionic components (4). The first assumes that the chemical potential of a large, relatively nonpolarizable ion is independent upon the nature of the solvent. There are several variations of this assumption and the most successful appear to he (4c, d ) AGt0(Ph4Asf)= AGtO(PhrB-) (7) AGP(TAB+)= AGP(Ph4B-) (8) where Ph4Ast is the tetraphenylarsonium cation, Ph4B- is the tetraphenylboride anion, and TAB+ is the triisoamylasn-butvlammoninm cation. A second u o ~ u l a assumution r sumes that AGtn (ion) can be obtained from plot$of AGtO (MX) for a series of salts havine either the anion or cation in rr,mmon against l/r, and extrapolating to infinite ionic radius h r . 'l'his is of course thr Born model for ion-solvent interactions and modifications to account for dielectric saturation and ion-auadrupole, di~ole-diuole,and dipole-auadmpole intrracti,ms haw been proposed ( 4 ) .Hothaisumptionssuffer I n m serious rritirisms hut the fact remains that for all but a few cases, A c t " (ion) values appear to be in remarkable agreement. One major exception involves the sign of A c t 0 (H+)for the transfer of hvdroeen ions from water tomethanol. and (8)invariably give positive Values ohtained from eqis. (j) values for this auantitv. (4c.. d .) while the Born-tvue -. extrauolations yield negative values (4e). The importance of AG,O (ion) values lies in its application to various kinetic and solvent structure problems. A far more sensitive quantity relating to structural effects is the enthalpy of transfer, AHtO(ion). Details revealed in AHtO (ion) values are often lost in the simnler AG+O(ion) values because in the latter quantitit: TMS02> H20,PC >AN > SDMF (12) THT, SDMF >> DMSO, SO2 > AN > HzO> TMSOZ> PC, DMS (13)
and
Structural Propeeies We consider first the entropy of a system which gives quantitative information roncerning the amount of disorder within the emrem. lonir entrnpies give us information on the degree of order within a solution. However, hecause of the way in which the standard state is defined (hypothetical one mold standard state) the values one obtains for standard ionic entropies have a very special meaning. Any entropy change in the svstem (both solvent and ion) upon introduction of the ion is blamed entirely upon the ion. This means that if a noncomplex ion has a more negative entropy in one solvent than another, then the effect of the ion is to cause a greater net amount of ordering- in the first solvent. Similarly, for two simple ions for which that part of the inherent entropy arising from the difference in atomic weight (312 R InM) has been removed, the one with the more negative entropy has a greater net ordering effect on the solvent. Thus standard ionic entropies can serve as useful probes for determining the ordering or disordering effect that ions have upon the structure of a solvent. For a hypothetical ion having an entropy of zero in water, the "a" parameter in eqn. (10) for a given solvent is identical to the entropy of that ion in the solvent, and generally the "a" parameter gives the relative position of the entronirs ions~in the various solvents. The solvents for - - - of , all ~ the ~ ~ which "a" parameters have been evaluated (7b), listed for increasing values of "a," are AC < NHn < AN < DMF a EtOH < MeOH < DMSO = PC < NMF < F < Hz0 < D20. This indicates that most ordering occurs in acetone and the least ordering (or the greatest disordering) occurs in D20. A close examination of the physical properties of the above series of solvents, along with various spectral data suggests that the solvents a t the right tend to he more highly ordered initially than those a t the left. For example, water is well-known to be three-dimensionally polymerized. X-Ray evidence for the d i d state of formnmid; indirates that this solvent forms a two-dimensionid polymer suggesting that the liquid state is partly two-dimensionally polymerized. Similarly it has been sugeested that NMF forms a chain polymer in the liquid state. .. 'I'hr arguments are not as rlenr cut for other sulvents; the alcohols have wrak H-bonds and the apmtic solvents have nu hydrogen l)ondinp, hut they have extremely high d~polemo. ments wh~chcan lend to order. Convincing arguments have been made suggesting that the strong dipole solvents have more order within them than the weakly H-bonded alcohols and ammonia. One can look at this trend in terms of two processes occurring, first disruption of the inherent structure of the DUIe solvent leading to an increase in entropy and second, an orientation of solvi.nt molecules mound thLion leading toa decrease in entropy. Since the highly urderedsolvent~arr most capable of being disordered, it f i r electrolytes in these solvents that the entropies are most positive. Criss and Salomon (4e) have generaGzed this observation by the rule that e n t r o ~ i e sof ions are most positive in those solvents whi:h haue ihe highest degree of internal order in the pure state. AG," (ion) and AHtO(ion) studies have resulted in additional types of structural interpretations. One can, under certain conditions, relate these quantities to specific coordination sites, molecular bonding properties, and kinetic effects
~~.
(see below). In discussing the effect of ionic solvation on structure, it has become apparent that electronic structures, in addition to ion size, play an important role (11,12). As an example we consider the ability of a given solvent to solvate the ions K+, Ag+, and C1-, respectively,
~
H20,SOz > DMS > PC, DMSO, AN, DMF, TMSO? (14) The order for K+ and Ag+ correlates well with the "hard-soft" acid-base classification of Pearson (13,14) and has been discussed in terms of this concept (11,12). Anrotic solvents are notoriouslv noor solvators for small anions as indicated by their large positive values for AGto(X-) (4.11. 12). Water is a good solvator for small anions such as ~ 1 beca"se of the agility of C1- to enter into hydrogenhondine. In a ~ r o t i solvents c where H-bonding is nonexistent. anion solvation generally occurs via weak elec~rostaticandlor mutual ~olarizabilitvforces ( 4 ~ )In . recent works (12) it has been f o k d that in addition to water, SO2 and alkyl sulfites can stronalv coordinate C1- ions and this was attributed to a-honding bctween lnw lying 3d orhitals on sulfur and the Rp orbitals of CI-. The sulfur atom in DMSO ran heconsidered (15) to he either sp3 or s p U hybridized corresponding, respectively, to the resonating structures CH.,
In the presence of a halide ion, X-, structure (I) becomes dominant and because the 3d orbitals on sulfur are no longer available, DMSO is a poor solvator for X-: e.g. AGtO(CI-) for the transfer from water to DMSO is +10 kcal/mole. In the alkyl sulfites, e.g. DMS, the important structures appear to be (111) and (IV) in which
the hybridization of the sulfur is either sp% or sp%fd2.Thus the extra stabilization of C1- in DMS via structures (111) and/or (IV) were attributed to the existence of low lying 3d orhitals on the sulfur (12c): support for this view comes from molecular orbital calculations where this type of d-p a bonding was found to stabilize the analogous (Cl-SO& comnlex (12b). ~ t ' h a slong been known (16) that a t the liquid-air interface, there exists a net preferential orientation of solvent dipoles resulting in a potential difference across this interface. This potential difference, called the X-potential, is taken as positive if the dipoles are oriented with their negative ends towards the eas phase. The x-potential is not directly measurable and for somi time there kxisted uncertainty as to the sign and ~ . evidence favoring a positive value for magnitude of X H ~ The xHz0is the negative temperature coefficient of d x ~ , o l d T(17) and a theoretical calculation by Stillinger and Ben-Naim (18). An empirical determination of x can be obtained from real free energy measurements for a series of ions and extrapolating to infinite radius; i.e.
This method has been used to determine the surface potential of acetonitrile (19) (XAN= -0.10 V). Using this value for XAN in eqn. (2) and appropriate free energy data, it was found (20) that x ~ , oa 0.10 V. These results indicate that in water, the surface dipoles are preferentially oriented with the oxygen Volume 53. Number 12, December 1976 / 765
directed towards the gas phase and in AN, the preferential orientation corresponds to the hydrocarbon part directed towards thegas phase. The surface potentials of the alcohols (4e, 20) and DMF (21) appear to be negative and positive for DMSO (20). Kinetic Effects
The medium effect shows UD . verv. dramaticallv in the rates of rhemical reartions. Two widely studied reactions are the n~rcleophilicsutwtitution( S y l )reactions
The SN1path was found to be operative in the solvents (in order of decreasing rates) DMSO > HzO> CH3N02> CsHsOH > n-CaH7OH (22) For the SN2mechanism, the solvent order was found to be
and the Menshutkiu reactions 6+
6-
-
R:,N + R'Y = [R3N.- ..R'Y]i R3NR'+ + Y(16) The ratio of specific rates for these reactions in some reference solvent (k0,,r) to that in solvents (kO.) is given by -kO"' - expl6AGt/RTJ = eap{[AGt" (t) -
AGtn (r)]lRTI (17)
k", where AGS (I) and Z AGtO( r ) are, respectively, the chemical free energies of transfer of the activated complex and of the reactants. It should be noted that only chemical free energies and not real free energies appear in eqn. (17) since the z F x terms cancel between the initial and activated states. Considering reaction (15) for RX = methyl halide and Y- = halide, it is found that snecific rate ratios (em. (17)) are of the order ~~-~ (4c) , 10-"-10-6 when the reference solvent is eithkr water or MeOH and s is a dipolar aprotic solvent such as DMF or AC. Parker ( 4 c ) has shown that these large rate enhancements are due mainly to the lower stability of the reactant anion in the dipolar aprotic solvent. The Menshutkin reactions display both upon the a decrease and an increase in kO.,tlk,O ~.~ . depending . nature of s. Using MeOH as the reference solvent &d R3N = (CH&N and R'Y = p-nitrobenzyl chloride, i t is found that k," is enhanced in most dipolar aprotic solvents and is diminished in nonpolar aprotic solvents (e.g. benzene, ether, hexane). Abraham (22) has shown that these effects are mainly due to an increase or decrease in the solvation of the activated complex, RsN-R'Y, and that the terns I: AGtO( r ) in eqn. (17) is of minor importance. The nature of coordination of the activated comple< be it electrostatic, mutual polarizability, or a-bonding is not particularly clear for the Menshutkin reactions. An interesting reaction studied by Pearson and coworkers (23) is ~~
CCll > CsHs > t-CIHSOH> AC > DMF > A N (23) There are two apparent anomalies evident in eqns. (22) and (23). Oneis concerned with the fact that since C1-is a strong nucleophile, one might expect reaction (18) to always prnceed via the SN2 mechanism. It is obvious that electrostatic and mutual polarization forces are not sufficient to account for either the effect of solvent on mechanism or the order of decreasing rate because (1) nitromethane, which does not form stable compounds with Pt(I1) and which is a poor solvator for anions, might logically be expected to favor the SN2 mecbanism; and (2) the position of DMSO in eqn. (22) is somewhat of a surprise. The position of CHsN02 in eqn. (22) has heen explained (23) by postulating an increase in stabilization due to s-bonding between the filled d-orbitals of P t and the empty p-orbital of N. The position of DMSO in eqn. (22) is also attributable to n-bonding since the soft basic S-center is capable of forming strong r-bonds with the soft acids (cf. structure (11) above). Literature Cited 111 Bierrum. N..end Lars8on.E.Z. Physik. Chem.. 127,358 119271. (21 Plpskov. V. A., Usp. Khim., 16.254 (19471. 131 Strehlow.H.,Z. Elektrach~m..56,827 11952). Id1 (a! Kina. E .I. "Acid-Rare Eguilihria,"Pergam~m, New York. lW$;(blSLrehlov, H.. m "The Chemistry of Non-AqueousSoluenLs." (Editor Lapov~ki.J.J.1,Academic Press. Nou York, 1966: lcl Psrker,A. J.. Chrm.Reu.. 69,111969): Id) Popovych, 0.. Crit RPV.A n d Chem 1.73 11970): le1 Cris,C. M.,and Salomun, M.,in 1"Phyrical Chemistry u i 0 m n i Solvent ~ Systems,"(Edilar. Cnuingfon, A. K.. and Dickinwn, T.), Plenum Pless, London, 1913. (5) Owen,B.B..J.Amer ChemSoc.. 54.1758119121. (61 Gurney. R. W.."lonic Processes in Solutivn: Dover, New Ymk, 1962. 171 la1 Crisr,C.M..Held.RP..and I.uksha.E.,J. Phva Chem.. 72.297011968): lhl Crirs. C.M., J.Phyr. Chem., 78, LOW 119741. 1 s F r a n k F.. and Reid, D. S., J. Phys. Chem.. 73.3152 119691.
.
2682 119741. (12) Is1 Salomon. M., and Stevenson, R. K.. J. P h y Chem.. ~ 77,1002 119781: lhl S d l ~ m o n M.. J. Phyr. Chem.. 79. 429 11975): lc) Salumon. M.. J . P h v r Chem.. 79. 2000
,.",",. ,,O"C,
and for which two mechanisms are operative depending upon the solvent. The first is the solvent path ( S N ~ )
The second mechanism is a nucleophilic displacement (SN2) which proceeds according to
(13) Pearson. R.G.,J. Amer Chem Soc. 85,3533~1965). (11) Ahrland,S., Chatf, J.,and Davies. N.R., Quart. HPU. Chem. S o < . 12. 265 119581. 1151 Moffit, W. E., Proc. R o y Sor.. ILondon). AZOO,409 119501. (161 la1 Lange, &and Mish&nka, K. P., Z Phyx. Chm.. A149.1 11930): lb) Kloin, 0.. and Lange, E.Z. Elrclrorhem., 43.670(19371. 117) la1 Randles,J.E.B.,andSchiffrin,D..l..J Electroanalyl. Chrm.. Ill.4801196S);Ihl Schiffrin. D. J.. Trans. Famdoy Soe.. 66.2464 119701. 118) Sfillinger, F. H..snd Ben-Naim.A., J Chem Phyz.. 47,4431 119671. l. 10. :I60 1191 Case. R., Hu-h, N S.,Parsons, R.. and Peover, M. E. J. E ~ ~ r t m u l yrhrm.. 119651. (201 Sdomon. M.. J.Ebetrochem. Sor.. 118.1603 119711. 1211 Ganzhina, I. M.. Damaskin. R. R.. and Kaganovich. R. I.. El~klrnkhimiyo.8. 93 119721. 122) Abraham, M. H.. Chem Cornmun 1807 119691. (28) la) Poamon.R.G.,G?ay.H.B..andBamlo.F.. J. Amsr. Chem Siir.. 82,787 11960): lhl Posrson.R. 6..J . CHEM.EDUC.,38.164 119611.
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