Jacob Jorne and Charles W . Tobias
2576
Thermodynamics of Ion Solvation of the Alkali Metal Chlorides in Aluminum Chloride-Propylene Carbonate Solution Jacob JornV' and Charles W. Tobias hr.ganic Materials Research Dlv$ion. L a w e m Berkeley Laboratory and Oepartment of ChemicalEngineerb?g, University of CaKforni.4, Serkeky, California 94720 (Receked May 30, 1974)
PuaUcationcosts assisted by the Unkers& of CaKfornia
The free energies of solvation of the alkali metal chlorides in unit molality AlCl:l--propylene carbonate solution were obtained from emf measurements. The individual free energies of solvation were estimated using the method of Latimer, Pitzer, and Slansky. Free energies of transfer, AG ,O(M ), estimated by comparing the results to similar data for aqueous solution, are -0.6, -4.2, -4.7, -3.1, and -5.0 kcal/mol for Li+, Na+, K-' , Rb+, and Cs +, respectively. The negative sign indicates that the cations are on a lower energy level and strongly solvated by the local negative charge of the solvent dipole. The estimated free energy o f transfer of 61- is +10.:3 kcavmol, and the molal association constant of C1- with AI(PC)(;:'+ in PC is 1.9 X IO5. The standard entropies of transfer of the alkali metals are discussed in terms of internal structure and order in the solution. +
Introduction
In a previoiis.paper,' the standard electrode potentials of solution in propylthe alkrili metals in unit molality AICI:% ene carhonatc? (PC) were evaluated using emf measurements a t 25 anti 36' of the general cell %f(s) i M C l (solu~ioni n AlCI, (1 H I ) in PC) i.TlCl(s)I TI(Hg), where M represents I i , Na, K, Rb, and Cs. With the exception of I X I , the alkali metal chlorides are practically insolu l h in I'C, however, in the presence of AICI:' a complex is formed between the chloride and AICl:] IfCt AlC1, -r M' -1- AlC1,This reaction arid the stability of the alkali metals in alkali metal chloride-.AICl:j solutions in PC enables the electrodeposition of tlw alkali metal a t ambient temperature and the evaluation o!' the standard electrode potentials and activity coefficients.' In the presomt paper, the standard electrode potentials of the alkali metals and their temperature dependence are weif to estimate the free energies and entropies of solvation of individual ions in AlCI:S(1 m)-PC solution. The evaluation of single-ion solvation energies and the establishment of ii universal scale of standard potentials are fund;iment.al problems in solution chemistry. The solvation fret? energies, enthalpies, and entropies are of great importance hecauw they reveal the nature of the ion -solvent interactions. Review of Related Work The following brief review covers thermodynamic measurements in I'C and related aprotic solvents; the direct work in I'C is presented a t the end of this section in greater detail. Most of the studies were performed in the following common aprotic solvents: acetonitrile (AN), formamide (FA), N - met.hylformamide (NMF), dimethyl sulfoxide (I).MSO), dimethylformamide (DMF), and propylene carhonate (PC). Emf and ticat of solution measurements were performed in NMF,:'J DMSO," lf; FA,I7 2o and AN." 23 The measured standard potentials were used to evaluate stan-
dard ionic free energies and entropies of solvation. Enthalpies of solvation were obtained mostly by direct calorimetric measurements in FA,24,2" NMF 4,:1.%,%27 DMF .1,5.'LS DMSO,2429 and PC.24J(l.:3I In a series of papers, Friedman and coworkers estimated the enthalpies of transfer of ions from water to I'C.:30J2 The individual ionic enthalpies of transfer were estimated using the method Latimer, Pitzer, and Slansky.:':' Ion asstKiations in PC were checked by conductance measurements.:io Regularities and specific effects in enthalpies of transfer of ions from water to PC, DMSO, FA, and NMF were discussed by Friedman.34 The trend of the halide ions is the same in each case, while a varying trend of the alkali metal ions reflects differences in solvent basicity. The basicity of the solvent is suggested to be in the order I'C < FA < DMSO < NMF. The assumption that 1'C is a nearly ideal solvent for ions is discussed in light, of the disagreement with the Born equation, although the agreement is better for PC than for water. A summary of the solvation enthalpies of various ions in water, PC, and DMSO is presented by Krishnan and Friedman.:i5 Solvation enthalpies of nonelectrolytes, mostly alcohols and hydrocarbons, were measured in water, PC, and DMSO.:U;Enthalpies of transfer of various 1:l electrolytes from PC to methanol and DMF are presented el~ewhere.:'~ Solvation enthalpies of hydrocarbons and normal alcohols in several highly polar solvents, including PC, are reported by Krishnan and Friedman.:3H The thermodynamics of LiCl and 1,iBr,:j9 NaI,"O I,iI and KIJ1 were measured by Salomon using the emf method. The potentials of the cell type MIMX in I'Cl'I'lX(sjl'I'I(Hg) were measured, where M represents l i , Ne. and K, and X represents C1-, Hr-, and I-. In the case of the potassium system, potassium amalgam replaced the metallic potassium. The data were corrected for the free energy of formation of the TI amalgam,42 and the standard potentials were obtained by extrapolation to infinite dilution following the Guggenheim equation.j:' The thermodynamic quantities AGO, AHo, and ASo for the cell reactions were calculated from the standard potentials and their temperature dependence. The thermodynamics of single ion solvation in I'C and
Thermodynamic:$of ion Solvation
2577
water is summarized hy S a l o m ~ nThe . ~ ~free ~ energies and Since the chloride ions are being complexed by the AI3+ ions to form AlC14- ions, one can assume that the free enerenthalpies of solvation of individual ions were evaluated gy of solvation of chloride ion in A1C13 (I m 1-PC solution is from the corresponding values of the salts, and by extrapoconstant and independent of the nature of the alkali metal lalion (to infinite ionic radius) of the plot of the differences cation. Therefore, we assume that the free energy of solvaof cation and anion conventional energies us. l / r . Accordtion of the alkali metal chloride in AlC13 (1 m )-PC solution ing to Salomon, this method of splitting the solvation enerbehaves according to gies into individual ionic contributions is preferable to the traditional method of Latimer, Pitzer and S l a n ~ k ywhich ,~~ introduces a single adju4xble parameter in the Born equation. where ri is the Pauling crystal ionic radius of the alkali Cogley, Butler, and G i ~ n w a l dstudied ~ ~ the selective solmetal and 6, is the Latimer, Pitzer, and Slansky's paramevation of ions by water in PC. The equilibrium constants ter33 for cations in PC. Figure 1 presents the plot of for the association of water with individual ions were ob4 G o,,~,(MCl) us. l/(ri &). A linear plot was obtained for tained under a relatively mild set of extrathermodynamic the alkali metal cations for 6, = 0.50. The intercept at infiassumptions from protic magnetic resonance (chemical nite crystal radii gives the free energy of solvation of GI- as shift) measurements. The affinity of water at low concen4G0,,~,(C1-) = -90.0 k c a h o l . IJsing this result the free trations in PC for alkali metal cations correlated well with energies of solvation of the individual alkali metal cations the free energy of transfer of these ions from PC to bulk can be estimated. Table I1 summarizes the estimated free water. energies of solvation of single ions at 25' in BE13 (1m 14% A general equation for the estimation of ionic entropies Also included, for comparison, are the free enerin various solvents, including PC, is presented by C r i ~ s . ~ solution. ~~ gies of solvation in pure PC and in water estimated by It is concluded that the solvent structure, rather than baSalom~n.~~~ sicity, plays the predominant role in determining the value It can be seen from Table I1 that the free energies of 801of the ionic entropies. vation sf the individual cations, obtained in the present Parker4Ggives ar. extensive review on the protic-dipolar work in AlC13 (1 m ) solution in PC, show similar trend to aprotk soivent effects on rates of organic bimolecular reacthose estimated by S a l ~ m o n in ~ ~pure * PC. 'The presence of tions. The observations that dipolar aprotic solvents are A1C13 in the solvent changes the free energies of solvation excellent media for many organic reactions are explained by approximately 1-5 kcal/mol. Li+, Na+, and K' are more by positive free energies of transfer of anions. The review strongly solvated in the presence of AlC19. contains extensive and very useful information on the solsolvation of Rb+ and Cs+ remain almost the same, probavation of ions in aprotic solvents and on solvent activity bly because of their large size, and in agreement with the coefficients (medium effects). On the general subject of solpopular assumption that the large alkali metal cations have vation of individual ions in nonaqueous solvents, the reader no specific interaction with solvents, and therefore their is referred to a review of 1'0povych.~~ energies of solvation are independent of the solvent. The Free ~ n e ~of ~~ i ~~ s~of Single ~ a Ions ~ in iAlC13 ~ (1n free energies of solvation of all the alkali metals are lower in AIC13 (1 m)-PC than in water, which indicates that the cations are more strongly solvated in AlCE?--PC than in Using the standard cell potentials which were obtained water. for the alkali metals in A1C13 (1 m)-PC solution,2 it is now The free energy of solvation of the chloride ion in AlCC13 possible to calculate ths: tree energy of solvation for the salt (1 m)-PC solution is lower than in pure PC. The chloride MC1 (where M is Li, Na, K, Rb, or Cs) in AlC13 (1 m)-PC. ions are believed to be complexed by the AI3+ ions accordThe free energy of sohation of single alkali metal ions will ing to the following exchange reaction5* then be estimated according to Latimer, Pitzer, and Slansky's TJsing AG O p m f for the cell reaction K 461Al(PC)63' A1C14- -t 6PC (5) Rri, t T1C1, 9 . 8 mol of PC 1 mol of AICI, --+ MCZ (solution ir 1 111 AlCl,-PC, such that my,,, = The free energy of transfer of 61- from pure PC to AlCh (1 m )-PC solution is estimated from the diffelpence between 3 ) + TI, (1) its free energies of' solvation in AlCls (1 m ) -PC and pure plus the formation and lattice energies, it is possible to calPC (see Table 11) as -1.8 kcal/mol, hence the e q ~ i ~ i b r i u m culate the free salvation o f MCl for all the alkali metals constant for the exchange reaction can be estimated from ~ G o , o i , ( M C I ) = AGOd + ACof['T1C!,] K 4[AGo90iv(C1-)Ai~lg-pC- ACosOlv(C1-)pcI =- - RT hGof[MC1,] Jr AGolat[MC1,] (2) (6) where K = exp [(4X 1800)/(1.98 X 298)] = 1.9 X IO5. This is the molal association constant of C1- with Al(PC)s3+ in PC SOAGo,,~[MC1,] = AGof(M,) AGof(C1,) lution. It should be mentioned here that a large association AGof(MC1,) iI - A (3) constant of C1- with A1(PC)e3+was predicted by nmr studFree energies of formation, AGO*,were taken from Wagies.54 Indeed, this should be the reason for the high solubilJANAF,49and Latimer.j0 Ionization potentials, I , ity of the alkali metal chlorides in AlC13-PC solution, while were obtained from Jessori and Muetterties,51 and the electhey are nearly insoluble in pure PC. The association constant can be used to estimate C1- concentrations 1y1 AlC19tron affinity, A, of the chloride ion was obtained from Berry and Reimann.5z '$able I presents the results. The last PC systems. The error in the estimated value of K may be quite large, since it was obtained from the difference becolumn gives the crystal ionic radii of the corresponding altween two values which were obtained by extrapolation. K kali metal! according to Pa~ling.53
+
J-
*
The Journal of Physical Chemistry. Vol. 78, No. 25. 1974
Jacob Jorne and Charles W. Tobias
2578
TABLE 1: Free Energies of Solvation of the Alkali Metal Chlorides in AICls (1 m)-PC Solutionu Salt
2 045 1 885 2 116 2 116 2 122
KCl RbCl CSCl 1
AGOomf
AG”r(TIC1,)
AG”f(MC1,)
AG”l,t(MCl)
-47,170 - 43,475 -48,800 - 48,800 - 48,940
- 44,460 -44,460 - 44,460 -44,460 - 44,460
-91,700 -91,890 - 97,760 -98,480 - 96,600
-188,500 -170,600 - 154,100 - 149,000 - 144,900
E” ___ _____
LiCl NaCl
AGos0~.(R/IC1~ - 188,430
)*P
0 607 0 958 1 331 1 484 1 656
- 166,640 - 149,600 - 143,780 - 14 L , 700
Free energies are given in calories per mole, E” in volts, and rp in Hngsttoms.
TABLE BI: Free Energies of Solvation of Individual I o n s a t 25” in AICI, (1 m)-PC in Pure P C and in Water
the vacuum-solvent interface. Free energies of transfer, in the present work, are referred to as the “chemical” free en____ ergy. Table I11 summarizes the estimated free energies of SG 05”1, of individual ions from water to AlCl:, (1 m )-PC Ion (M)AlcIl-w ~ G o s o ~ v j M ) ~Ar G b o s a ~ v ( M ) ~ L ~transfer b solution and to pure PC. The negative values for the alkali -97.8 -98.4 -95 . 0 Li + metal cations indicate that these ions are more bound in -71.9 -72.4 Na --- 76 .6 PC than in water. The positive free energy of transfer of -56.6 -54.9 K i--- 59 , 6 chloride ion means that C1- is loose in PC and poorly sol-50.7 .--513 .8 -54.5 Rb -52.7 -46.7 --51. .7 CS vated, in agreement with the general observation that an-88.2 -100.3 -90.0 c1ions are poorly solvated in aprotic solvents.4G Refn Present. woik. Solvent: AlCl:, (1 m)-PC solution. Standard Entropies of Transfer of the Alkali Metal erence 44a. Free energies of solvation in kilocalories per Chlorides AlC13 (1 m)-PC Solution mole on a. molal hasis. _I
+
+
180
/’
I
1
The standard molal entropies for the general cell reaction M,
+
TlC1,
-
+
0
MC1[A1C13(1 i n ) - P C I
+
‘Tl,
(7)
were calculated from the temperature dependence of the standard cell potentials.2 These values are tabulated in Table IV, along with the values for the corresponding cell reactions in water. The aqueous standard entropies were calculated from Latimer’s tables.5O The difference between the standard entropies corresponds to the following transfer process: MC1 (solution in HzO such that, n y ~ c =l 1) 9.8 mol of PC 1 mol of AlC13 MC1 [solution in AlC19 (1 m )-PC such that m y MC1 = 11 55.55 mol of HzO. The calculated standard molal entropies of transfer are presented in the third column of Table IV, However, if one wants to express the entropy of transfer on a volume basis, a small correction is necessary for the difference in the specific vol umes of the two solvents55 01.2
0.4
0.6 l/(r+
0.8
1.0
12
s,), [kl]
Free energies of solvation of the alkali metal chlorides vs. l/(r 4- 6) in AIC13 (1 m)-PC solution at 25’.
Figure 1.
is a measure of the expected strong tendency of the free chloride ions to substitute the PC molecules around the AI:
