2708
J. Phys. Chem. 1980, 84, 2708-2715
Anion Solvation Properties of Protic Solvents. 2. Salt Distribution Study Y. Marcus,’ E. Prom, and J. Hormadaly Department of Impnic and Anelytlcal Cbmlsby, The Hebrew Univws#y of 3eruselem, Jerwekm, Israel ( R w M : June 11, 1978; In Fhal Form: May 14, 1980)
Standard Gibbs free energies of transfer of chloride anions from water to organic solvents AGob(C1-,H@+S), based on the tetraphenylarsoniumtetraphenylborate extrathermodynamicassumption, have been seleded from the data in the literature, and correlated with the solvent index ET. The expression AGob(Cl-,HzO-S)/(RT In 10) = (29.5 f 1.4)- (0.116 f 0.007)(ET/kJmol-’) is found to express the data sufficiently well, so that AGOe could be calculated for a large group of protic solvents for which ET data were recently obtained. Also, the distribution of potassium chloride between dilute solution of crown ethers in these solvents and aqueous solutions was measured, and the standard Gibbs free energies of distribution, AGO&.,, were obtained. These are related to the former quantities by AGot’(C1-,HzO-S)/kJ mol-’ = ACow/kJ mol-’ + (116/cs) + (29 f 3) where cg is the dielectric constant of the solvent. This semiempirical expression is rationalized in terms of the interactions leading to the distribution equilibrium. Distribution measurements as described here are proposed as a general method for obtaining individual standard Gibbs energies of transfer of anions from water to immiscible solvents.
Introduction
In a recent study’ it was shown how the polar and hydrogen bonding properties of protic solvents can be expressed by means of spectroscopic indexes such as ET,2, or AN. These quantities characterize the solvents as electron-pair acceptors (or hydrogen bond donors) and thus measure mainly the anion solvation property of the solvents. It is the purpose of this paper to substantiate the relation2 between ET (or any quantity that is well correlated with it) and the anion solvating properties. These are measurable’ by the standard Gibbs free energy of transfer of anion X- from water to the solvent S, AGoh,(X-,H20-S), provided a suitable extrathermodynamic assumption, such as the Ph4AsBPh4assumption, is accepted. This assumption states that the standard Gibbs free energy of transfer of tetraphenylarsonium tetraphenylborate from water to any solvent at any temperature is twice those of its constituent ions, which are equal. This assumption has been recently thoroughly discussed3and seems to be the most useful one, and closest to the true state of the matter. The existing data on AGotr,(C1-,H20-S) have been examined,‘ and the most consistent set selected for comparison with the ET values. Most of the available AGo”(C1-,H20-S) values pertain to polar aprotic solvents, almost all of them miscible with water. For water immiscible solvents, however, a direct value of this quantity would become available, if it were possible to transfer a chloride salt in such a manner that the standard Gibbs free energy of transfer of the cation is completely independent of the solvent. Then the distribution equilibrium constant should give a quantity which differs from AGoc(C1-,H20-S) by a constant. An approach to such a possibility is found in the studies of Villermaux and Delpuech6and of Marcus and Asher? who used cryptates and crown ethers, respectively, to solvate and “hide” the cation. In the latter study it was argued that the distribution of potassium chloride between its aqueous solution and a solution of a suitable crown ether in an immiscible solvent is primarily sensitive to the anion-solvating properties of the solvent. In the present study this idea is examined further, and transfer Gibbs free energies are derived for a large number of solvents (mainly protic), such as substituted phenols, from distribution data. Corresponding ET values are also obtained by calculation for those solvents in which it could not be measured directly.’
Gibbs Free Energies of Transfer of Chloride Anions Single ion Gibbs free energies of transfer are based mainly on solubility and on emf data.’ The former require extrathermodynamic assumptions concerning transfer activity coefficients; the latter require such assumptions concerning liquid junction potentials. Attempts have also been made to calculate these quantities from electrostatic theories of so1vation.S The Ph&BPh4 assumption seem to have several advantages over the others, and there are good arguments for letting it supercede them.s*gConceptually, it is simple: such large ions as the tetraphenylarsonium cation and the tetraphenylborate anion have their charges so well shielded from the solvent by the bulky phenyl groups that the solvent cannot distinguish between the signs of the charges. The ions are also of approximately the same large size, so that their electrostatic fields are weak and similar. The electrostriction of the solvent that they cause (relative to an uncharged analogue, such as tetraphenylgermanium) is small, and again approximately the same for cation and anion. Therefore it is very reasonable to assume that the standard Gibbs free energy of transfer of the salt tetraphenylareonium tetraphenylborate divides equally between its constituent ions. There is ale0 no reason to believe that this division should be different at one temperature from what it is at another, so that ala0 the entropy and enthalpy of this salt divide equally between its ions. Experimentally, the standard Gibbs free energy of transfer of an anion X- is obtained from the combined resulta of four solubility experiments,’O namely of the salts Ph4AsBPh4and Ph,AsX in water, and of the same salts in the solvent S. The ion-ion interactions, hence the exom Gibbs free energies relative to the standard states in water and in, S respectively, are negligible or can be evaluated separately, provided the solubilities are sufficiently low. Then the standard Gibbs free energy of transfer is
ACo*(X-,H2WS) = RT[2 In s(Ph4AsX,H20)- 2 In s(Ph4AsX,S) + In s(Ph4AsBPh4,S)- In s(Ph4AsBPh4,H20)1(1) where s is the solubility. The numerical value of AGO” depends on the concentration scale in which s is expressed, and in the following the molar scale (M mol dm-9 will be used,l’ unless otherwise noted.
o o z z - ~ ~ ~ ~ 1 a o 1 z o a 4 - z,0010 i ~ a ~ o0 i 1980 Amerlcan Chemlcal Society
The Journal of phvslcal Chemistty, Vol. 84, No. 21, 1980 2700
Anion Solvation Properties of Protlc Solvents
TABLE I : Standard Gibbs Free Energies of Transfer of Chloride Ions at 298.15 AGob(C1-,H,O+S)/kJ mol-' solvent (symbol) (EI/kJ mol-')
a
water (H,O) (264.0) trifluoroethanol (TFE) (260.0) formamide (FA) (237.0) methanol (MeOH) (232.0) N-methylformamide (NMF) (218.0) ethanol (EtOH) (217.0) 1-propanol (Pr6H) (212) dimethyl sulfoxide (Me,SOSO) (188.5) acetonitrile (AN) (192.3) propylene carbonate (PC) (195.0) propionitrile (PN) (183.0) nitromethane (NM) (193.5) dimethylformamide (DMF) (192.0) dimethylacetamide (DMA) (183.0) tetramethylenesulfone (TMS) ( 184.0)k N-methylpyrrolidone (NMP) (176.5) acetone (Me,CO) (176.5) hexamethylphosphoric triamide (HMPT) (171.0)
b
c
d
K, Molar (mol am-') e
f
g
Scale,
i
h
0 -6i 6 12i 2 13.2g 1 3 i 2 21 (43.4) 16.5 20.14 16i 2 25.54 26 (45.7) 33.3 36.4 40 38.5 38.5 (49.1) 36.4 38.9' 37i 2 (60.2) 40.5 36.4 42 42.3 36.8k" (54.2) 36.4 40.43 39i 3 45.8 36.0 42 42.3 37.7 (49.7) 36.4p (50.2)m 40i 4 40 39.7p 46.8 31.8 49.8m 41i 8 42.2 33.1 (23.4) 32 51.4 46.3 41.7 46 46.0 46.d (57.1) 42.p (55.2)m 45i 3 48i 3 (63.4) 46.7 58.8 50.9 46.9 49 52i 2 52.6 63.p 47.4 63.1 (37.1) 42 52.7 53.1 5 59.9 60.5 54.2 45.2 49 55.2 56i 3 (73.1) 50.9 60.5 51.4 57 58.6 59i 6 67.9 53.5 64.5 52.2 53.7 69 0.0 0.0 0.0 0 0.0 0.0 0.00 -11.3 -10 14.3 11.9 9.6 13 13.8 13.8 14.3 16.6 11.4 14 12.6 12.6' 21 20.5 15.5O 16.6 16.6 21
0.0 0.0 7.4 18.3 (32.5) 11.4
0.0
a R. Alexander, E. C. F. KO,A. J. Parker, and T. J. Broxton, J. A m . Chem. SOC., 90,5049 (1968);Ph,AsBPh, assumption, R. Alexander, A. J. Parker, J. H. Sharp, and W. E. Waghorne, ibid., 94,1148 assigned uncertainty: i 1.7 kJ mol-'. (1972);Ph,AsBPh, assumption ("group 1" entries from Table VIII, p 1153,for Ag+,except for H,O 3 CH,CN transfer, for which value in "Note added in proof", p 1155, was used, combined with sum of entries of Ag' and Cl- in Table II, p 1149). Same work as b, but Ej assumption (Table II on p 1149). A. J. Parker, U. Mayer, R. Schmid, and V. Gutmann, J. Org. Chem., 43,1843 (1978);Ph,AsBPh, assumption, figures given in integral numbers of kJ mol-', from which uncertainty of i 1 kJ mol-' is deduced. The values are stated by the authors to update those in a, b, and c . e B. G. Cox, Annu. Rep. Chem. SOC.,70, 249 (1973);Ph,AsBPh, assumption. f B. G. Cox, G. R. Hedwig, A. J. Parker, and D. W. Watts, Austr. J. Chem., 27, 477 (1974);Ph,BPh, assumption. g D. Badoz-Lambling and J. C. Bardin, Electrochim. Acta, 19, 725 (1974); ferrocene assumption (ref 12). M. Salomon and B. K. Stevenson, J. Ph s. Chem., 77,3002 (1972);M.Salomon, ibid., 79, 2000 (1975);Ej assumption, reliability estima+dq at i8 kJ mol-' , ?Selected values (ref 4). Values in parentheses in columns A-h were excluded from the averaging. 0.Po vych, A. Gibovsky, and D. H. Berne, Anal. Chem., 44, 811 (1972); At 303 K (30 C). I I. M. Kolthoff and M. K. Chantooni, J. Phys. converted from molal scale; uncertainty i 1.9 kJ mol-'. Chem., 76, 2024 (1972),obtained the same values as reported in column f , except for Me,SO; assigned uncertainty i 0.9 kJ J. Courtot-Coupez, M. Ledemezet, A. Laouenan, and C. Madec, J. Electroanal. Chem., 29,21 (1971). B. G. mol-'. Cox, A. J. Parker, and W. E. Waghorne, J. Phys. Chem., 78,1731 (1974). O A. J. Parker, Pure Appl. Chem., 25, 345 (1971). M. H. Abraham and A. F. Danil de Namor, Based on the AGotr(AgCl,',H,O+S) = AGotr(AgBr,-,Ii,O+S) assumption. J. Chem. SOC.Faraday Tmns. 1 , 74, 2101 (1978);Ph,AsBPh, assumption. J
Q
Table I shows the data found in the literature for X- = C1- and the values selected as best representing AGOtr(Cl-,H20-S) for the solvents l i ~ t e d The . ~ entries include values based on assumptions other than the Ph4AsBPh4 one: the Ej assumption (i.e., that the liquid junction potential between Ag/O.Ol mol dm-3 AgC104 (in H20 or in S) half cells linked by 0.1 mol dm-3 tetraethylammonium picrate in one of the solvents is negligible) and the ferrocene assumption (i.e., the standard potential of the Pt/Fe(C6H6)2+,Fe(C6H6),half cell is the same in the solvents12). The former has been shown7 to give results consistent with those of the Ph4AsBPh4assumption, while the latter shows some discrepancies. The selected values reflect the preference of the Ph4AsBPh4assumption, and the discarding of values which are inconsistent with the correlation with ET, discussed further below. Although the entries in Table I are given to one decimal place, most of the authors agree that their accuracy is no better than ca. 1 2 kJ mol-', which corresponds to f0.4 units in AGOtr(C1-,H20-S)/(RT In 10) = log rtr(X-,H20-S). Some of the selected values are possibly known somewhat better, since estimates by different authors agree to better than this limit, but others have wider limits of uncertainty. Krygowski and FawcettI3 have shown that, in general, the following relationship holds:
Q = 80 + (YET + ,BDN
(2) where Q is a property of the system, E T expresses the generalized acid (acceptor) properties and DN the generalized base (donor14)properties of the solvent, and 80, a, and j3 are solvent-independent coefficients. For the particular case where Q is the Gibbs free energy of transfer
of chloride, which is a good representative anion,16theyla obtained the expressiod8 AGow(C1-,H20-S)/(RT In 10) = 31.5 - (0.122 f 0.014)(E~/kJmol-') (3) with a correlation coefficient of -0.960, equivalent to a standard deviation of f2.9. This is based on a list of ten solvents, taking the AGok(C1-,CH30H-S) values from Parker." These have been augmented later (columns b-f in Table I), and with the present knowledge summarized by the "selected" values in Table 1,18for eighteen solventa, somewhat modified relationships result. If a linear dependence is assumed (Figure l) AGoW1-,H20-.S)/(RT In 10) = (29.5 f 1.4) (0.116 f 0.007)(E~/kJmol-') (4) with a standard deviation of h0.8 and a correlation coefficient of -0.976. A nonlinear relationship was suggested between AGoh(C1-,H20-.S) and the acceptor number AN of Mayer et al. (Figure 4 of ref 19), which in turn is linearly related to E T (although a linear relationship was presented by this group in a later publication, Figure 2 in ref 15). In fact, the quadratic equation AGoe(Cl-,H2+S)/(RT In 10) = (51.8 f 1.3) (0.326 f 0.007)(E~/kJmol-') + (4.83 f 0.31) X 1O4(&/kJ = (0.071 f 0.017)(264 &/kJ mol-') (4.83 f0.31) X 10-'(264 - &/kJ mol-')2 (5) gives an only slightly lower standard deviation, f0.7. In the second version of (51,264 kJ mol-' is the E T of water
2710
The Journal of Physkal Chemistry, Vol. 84, No. 21, 1980 I
HMPT
,
I
Marcus et ai.
solvation. In these reactions, as also in reactions 8,10, and 13 the bar over a symbol designates the species as a solute in the organic phase in a hypothetical state of being only partly solvated, as little or as much as it is in fact solvated when a pair of the ion-paired complex KCw+Cl-(org). Reactions 7-14 can be summed to give the overall reaction 6, hence the Gibbs free energy can be summed similarly. On rearrangement, the following equation results: AGotr(Cl-)= AGodisb - (AG"B,,(K+) + AGoionpa& + (AGohydr(K+)- AGocompJ - (AG0,(Cw) + AGod(C1-) AG"d(KCwC1) (16)
-20' 170
190
210
250
230
E T / k J l n o l 270
Flgure 1. Correlation of standard molar Gibbs free energies of transfer of chloride anions (Ph,AsBPh, assumption) from water to solvents S, AG0"(CI-,H20-*S), with the transition energies E, of the betaine 302 in these solvents: empty circles, entries from Table I; black circles wlth error bars, selected values; continww m e , leastquare quadratic eq 5; dashed curve, least-squares linear eq 4.
(Figure 1). The question whether or not a linear free energy relationship exists between AGotr(C1-,H2&S) and E T (or AN) does not seem to the present authors to be very important for the purposes of correlation, but the simpler expression (eq 4) will be used for extrapolation. Transfer of Chloride from Water to Immiscible Solvents The transfer of chloride anions from water to an organic solvent S is always accompanied by the transfer of an equivalent number of cations. Consider now the case where these cations are potassium ions, and in the organic solvent is dissolved a complexing agent, Cw, that binds the potassium ions strongly and is insoluble in water. For a solvent with not too high a dielectric constant (say cS < 20), ion pairs will be the predominant species in the organic solvent, and if this is reasonably immiscible with water, the following distribution equilibrium will be set up: K+(aq) + Cl-(aq) Cw(org) e KCw+Cl-(org)
+
(6)
Here the descriptives (as) and (org) designate both the phase in which a given species is found and the state of its equilibrium interactions with the solvent, Le., complete solvation. AGOdisb is the standard molar Gibbs free energy change for this equilibrlium reaction, where all the solutes are in their standard states of the hypothetical 1 M (mol dm-3) solution with no solute-solute interactions. This overall transfer reaction can be carried out in stages, as follows: Was)
-
K+(g)
-AGohy&')
(7)
- cw
AGoBornW+)
(8)
-
K+(g) K+ Cw(org) +
-
- - K+ + CW
Cl-(aq)
KCW+
Cl-(org)
c1KCw+ + E Cl-(org)
KCw+Cl-
-
AGo,(Cw)
KCw+Cl-(org)
AGocOmp1
(10)
AGob(C1-)
(11)
AGod(Cl-)
KCw+Cl-
(9)
AGOion pair
AGOd(KCwC1)
(12) (13) (14)
In reactions 9,12, and 14, the standard Gibbs free energy is subscripted by pd designating a reaction of partial de-
On the left-hand side of this equation is the desired quantity, the standard molar Gibbs free energy of transfer of chloride ions from water to the organic solvent. On the right-hand side, the first term, AGodistr,is experimentally available from the distribution measurements. The second term, (AGo~,(K+) + AGOi, &), depends on the solvent solely through the dielectric constant es and will be designated by AGo(eS). The third term, (AGohyh(K+)AGompJ, is independent of the solvent altogether and will be designated by AGO,. The last term, (AGO (Cw) AGo,(C1-) + AGo,(KCwC1)), depends on the socent, but it is maintained that this dependence is usually mild, and this term will be designated as AGO,, which is nearly a constant. Hence, (16) can be rewritten as
+
+ = AGodisb - AGo(€s) + AGO',
AGotr(C1-) = AGOdistr - AGo(es) AGO, - AGO,
(16a)
(16b) The last version considers the sum of G O , and G O , as indeed solvent independent. Thus, the solvent sensitivity of AGotr(C1-)is expressible in terms of an experimentally available quantitiy, AGO&, with a correction term AGO(Q), which can be calculated from electrostatics. This electrostatic term is the sum of AGoBo,(K+) and of AGOionpair. The former is a modification of the classical Born expression, taking into account the dielectric saturation near the ions, by adding a quantity A to the crystalline radius of the ion:
GoBorn(K+) = - ( 1 / 2 ) ( N ~ e ~ / 4 n e ~ )-( l l/es)(l/rK+ + A) = -(138.9)(1/2)(1 l/es)((l/rKt A)/nm) kJ mol-' (17)
+
Latimer and his co-workers20showed that the modified Born equation is capable of reproducing the hydration Gibbs free energies of ions. Koepp and his co-workers2' showed that the same equation is valid for methanol, acetonitrile, formic acid, formamide, and quinoline, with nearly the same value of A for solvation as for hydration. It may thus be assumed that A is a parameter which is solvent independent and that the value assigned to it will quantitatively affect the magnitude of this term. For the second term, Bjerrum's expression for the ion-pairing equilibrium constant will be used, with conversion from the molar to the rational concentration scale, and with the approximationz2 (&(b) N b-l exp b. Here Q(b) is the Bjerrum integral, where b = (e2/47re&T)(l/(r~++ rcl-))(l/~) Hence . AGOion pair = -RT In [4000NAvS-'(rKt + r ~ l - ) + ~l RT In b - RTb = RT In [(e2/16000nrd(T)(r~+ +
Vs/cm3 mol-')/es)l -
+
(NAe2/47reo)(rK+ rc1-)-l(l/qJ = constant 138.9(l/es)/(rK+ rCl-)/nm) kJ mol-' (18)
+
Here Vs is the molar volume of the solvent, expressed in
Anion Solvation Propertlea of Protic Solvents
cm3 mol-l, and the first term in the second line of eq 18 is considered as approximately constant, Le., solvent independent, since the dependence on (VS/Q)is logarithmic only, and is not expected to be of importance. The sum of the two solvent-dependent terms, eq 17 and 18 thus gives -AG"(e,) = -(AGoBoa,(K+)+ AGOion pnir) = -constant 138.9[l/,((a+/nm) + 4 - ~ / ( ( P K + + r ~ ~ - ) / n m ) I ( l . / d (19) If the crystal radius values are used, Le., rK+ = 0,133nrn and rcl- = 0.181 nm, eq 16 becomes
AG'"(CI-,H~O-$)/kJ (442 - 69.5/(0.133
I
mol-' = AGgdist,/ZrJ 9 - constant J- AG", ( 2 0 ~ )
f @)/es
= AGadisk/kJ mor1 9 (116/4 1- AGO",
(2Ob)
If the quantity A is assigned the value zero, i.e., dielectric saturation is neglected, the solvent-dependentelectrostatic term becomes -80/ts, If it is assigned the value 0.140, corresponding to the radius of an oxygen atom, the term becomea +188/es. Since the value 0.080 has been shown to be appropriate for aqueous solutions:a and A has been assumed to be solvent independent, the use of A = 0.080 seems most appTopriate. If the two constants are combined, expression 20b results. This representation of bGotr(C1-,E120-$) in t e r m of AG'* and es will be examined in the light of experimental data in the sections that fallow. The assumptions made in the derivation of ('16b) will be discussed in detail in the Discussion.
Flgure 2. Correlation of the standard mokr Glbbs free energies of distribution of potassium shlortde between dilute soiutrons of ttw crown ethers DCC (circles) and DES (squares) In organic solvents, AB',, and tho traneitiin energies E~ of ths betaine 30*in these sol~ents(eq 22). Data for DBC moved up 10 W mol-' to avoid canfusbn between the two sets of dab.
according to eq 15, AGO&,,, were obtained as averages from all the data for a given solvent and crown ether as
-RT In Ig,l -RT In [DO + B ) 2 / y + i ~ a 2 ~ a ~ ~ ~+( ~B')~-, (C'KCID)I 1
Ai\Godiats
(21) (see eq 14 in ref 6), eo being the initial concentration and ya the activity coefficient in the final, aqueous, solution of concentration c°Kcl/ (1-k D). &o shown in Table 11are Experimental Section the dielectric constants es of the solvents and the anion As the complexing agent Cw, two cyclic polyethers were solvation indexes ET, obtained spectroscopical1y.l The used: dicyclohexo-18-crown-6 (eicosahydrodibenzovalues of for the two series with the crown ethers 2,5,8,15,18,21-hexaoxacyclooxadecin,DCC) and dibenzoBCC and DBC are plotted egainst ET in Figure 2. There 18-crown-6 (octahydrodibenzo-2,5,8,15,18,21-hexaoxa- exist clear negative correlations, obeying the expressions cyclooxadecin, DBC). They were obtained from Mdrich, ~ o b t by ~ ~east-$~uares ~ n ~ ~ calcul~tions) Fluka, and Nippon Soda companies and were remystaUized from acetone before use. The DCC consisted of a mixture ~ G ~DCC)/kJ ~ molv1 ~ =~ t ~ ~ ~ of isomers which was not separated. The potassium -(0.231 A O.O19)(ET9/kJmol-') 9 (41.7 f 3.9) (22a) chloride was of analytical reagent grade, and triple distilled water wa5 used. ThLe organic solvents were dried with LfGadjltr(withDBC)/kJ rno1-I = molecular sieves andl distilled, and the constant boiling m(0.229 & O.O12)(ET/kJ n~lol-')+ (44.5 f 2.6) (22b) middle fraction was used. The solvents were preequilibrated with water before the crown ether was dissolved in The former gives AG'& with a standard deviation of f2.6 them. kJ mol-l, the latter with one of 11.7 kJ mol-l. Since the Aqueous solutions of potassium chloride, generally 0.100 slope i s virtually the s m e , its mean, -0.230,will be wed, or 1.00 mol dm-$,were equilibrated with organic solutions but the intercept for DBC extractiom is 2.8 kJ rno1-l more of the crown ether, generally 0.100 mol dm3, by shaking positive than for DCC extractions (the difference being them together in a glass flask in a constant temperature within the experimental uncertainty). Values of ET can bath, generally at 25.0 f 0.2 'C, for a few hours. Equifrom these correlations for those solvents, librium is knowna to be reached in much shorter times. where it could not be measured directly' or had not been After standing in the bath for phase disengagement, alireported in the literaturea2 These values ape shown in quote of the two phases were removed by pipets, and the Table III, along with values d ET obtained indireclty, via potassium concentration determined by flame photometry the %' or AN indexes.' The agreement between the values a t 766 nm. calculated from both the DCC and the DBC distribution In some cases, Le., for solvents which are not liquid at is within the combined uncertainties. The predicted ET 25 "C, a higher temperature was used. The water-satuvalues (with a mean deviation of k5 kJ mol-l) are naturdy rated solution of the crown ether in some such aohents, not as accurate as the directly measured values can be however, supercooled readily, and could be handled at 25 (with w mean deviation of k0.5 kJ mol-l). The agreement "C. for the alkyl-substituted phenol, where comparative data exist, is n ~ too t good, but the other indirect methods1 Results sometimes show discrepancies in ET of similar magnitude Representative distribution ratios I) = c x c ~ ~ o r ~ ) ~ c x ~ for , ~ athese ~ ) and some other solvents. for the solvents examined in this study (mainly substituted The main purpose of this paper is not the estimation phenols), as well as fior solvents studied previously> are of ET indexes, but rather the estimation of AGOtrshown in Table 11. The Gibbs free energy for distribution (CI-,H20+S) values for the many solvents for which ET
t
~
2712
Marcus et al.
The Journal of Physical Chemistry, Vol. 84, No. 21, 1980
TABLE 11: Standard Gibbs Free Energies for Distribution Reaction 6 of Potassium Chloride between Aqueous Solutions and Organic Solutions of the Crown Ethers DCC and DBC at 298 K DCC ET,
no. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 a
solvent
'S
dibutylamine" benzonitrile" aniline" N-methylaniline 2-chloroaniline dichloromethane" chlorofrom" tributyl phosphate" nitro benzene" diisopropyl ether" anisole" butyl acetate" ethyl acetate" benzyl acetate" acetophenone" cyclohexanone" benzaldehydea 2-ethylhexanoic acid" hexanoic acid" pentanoic acid" 2-bromobutyric acid 2-ethylhexanol" 1-decanola l-octanol" l-hexanol" benzyl alcohol" 2,2,2-trichloroethanol 2-chlorophenol" 4-chlorophenol 4-fluorophenol 2-cresol 3-cresol" 4-cresol 4-ethylphenol 2,4-xylenol 3,4-xylenol 2-isopropylphenol 2-sec-butylphenol 2-tert-butylphenol 4-butylphenol 4-sec-butylphenol 2-methyl-5-isopropylphenol 2-tert-butyl- 5-methylphenol 2,6-di-tert-butylphenol 4-nonylphenol methyl salicylate 2-hy droxyethyl salicylate
3.0' 25.2 6.9' 6.0 13.4 9.1 4.8' 8.0' 34.8 4.0 4.3 5.1b 6. Ob 5.1 17.4 18.3'
From ref 6.
' At 293 K.
' At 303 K.
kJ mol-'
- 142
175.5 185.5 180.0 190.5 172.0 163.5 165.5 175.5 142.0 155.5 159.5 173.0 170.5 222.0
17.8& 2.6 2.7'
232.0 231.5 271.5 193.5 201.0 203.0 206.5 214.0 237.0 232.0
9.9 8.1 10.3' 13.3 13.1' 6.3 10.oe 6.8 12.2 13.0
21 9.5 223.5 254.5 256.0 21 2.5
6.3 12.2 4.7
8.1
9.4' At 313 K.
e
209.5 207.5 205.0 24 9 230.0 21 6.0 206.5 172.0 224.5 190.0 243.5 At 323 K.
and/or A G O d B t r data have been, or can be, obtained. If eq 4 and 22 are combined, AGO@is directly related to AGO&& AGotr(C1-,H20-S)/kJ mol-l = (48.5 & 4.0) + (2.85 f 0.15)(AGo&trwith DCC/kJ mol-') (23a) = (40.5 f 4.0) + (2.85 f 0.15)(AGodistrwith DBC/kJ mol-') (23b) With the limits of error given, the prediction of AGO@from has a standard deviation of f 4 kJ mol-l, as against the mean value of f 2 kJ mol-' for the directly determined values (Table I). Equation 23 thus presents an empirical way to predict Gibbs free energies for the transfer of chloride anions from aqueous solutions to water-immiscible solvents, by measuring the distribution equilibrium of potassium chloride between its dilute aqueous solution and diluted solutions of the crown ethers DCC or DBC in these solvents. For calculated values of AGotr(C1-,HzO-S), Table IV, see the paragraph at end of text regarding supplementary material.
DBC AGOdii;
log D
kJ mol-
14.8 0.0 -10.8 -3.9 -9.6 3.6 3.1 4.7 1.2 14.6 10.4 10.6 6.7 5.5 - 0.1 -1.9 - 2.8 0.8 - 8.4 -11.1
-1.53 -1.31 -1.24 -1.18 -0.46 - 0.10 -0.13 0.22
- 0.4 - 2.6 -3.3 - 3.9 - 11.4 - 14.8 - 14.5 - 18.3
-0.37 - 0.25 -0.58
-12.2 -13.3 - 10.4
-0.53 0.05
-10.7 - 6.6
- 0.53
