J. Chem. SOC., Faraday Trans. I, 1986, 82, 2577-2588 Ionic Solvation in Water-Cosolvent Mixtures? Part 12.-Free Energies of Transfer of Single Ions from Water into Water-Propan- 1-01 Mixtures Ibrahim M. Sidahmed and Cecil F. Wells* Department of Chemistry, University of Birmingharh, Edgbaston, P.O. Box 363, Birmingham B15 2TT The spectrophotometric solvent-sorting method for determining the free energy of transfer of the solvated proton, AG;(H+), between water and mixtures of water-cosolvent has been applied to mixtures of water with propan- l-ol. The assumptions underlying the method are examined critically and the consequences of varying the standard states of the species involved in the solvent sorting in the mixture are explored. The resulting values for AG,"(H+) are used to determine AG,"O(-) from AG;(HX) and these values for AG,"(X-) are used to determine AG:(M+) for other cations from AG,"(MX).The variation of AG,"(i) for individual ions in water-propan-1 -01 are compared with the variation of AG,"(i) in mixtures of water with other cosolvents. Values for AG,"(Ag+) and AG"(CNS-) are determined for other water-cosolvent mixtures. The spectrophotometric solvent sorting methodl7 for determining the free energy of transfer of the solvated proton from water into a water-cosolvent mixture has been applied to mixtures containing methan01,~ ethan01,~ propan-2-o13 or t-butyl alcohol5 as cosolvent as well as to mixtures containing non-alcoholic cosolvents.2t We now report its application to water-propan- l-ol mixtures. As with the other cosolvents, following the determination of the free energy of transfer of the proton, AG:(H+), values for AG,"(X-) are determined from values for AG,"(HX) and values for the free energies of transfer of cations M+ are determined from values for AG,"(MX).The positive structural contribution' to the change in the temperature of the maximum density of water by the addition of propan-1-01 suggests that propan-1-01 at low concentrations increases the amount of structure in water.8 This view is supported by the minimum found in the relative partial molar volume of propan-1-01 in water, v2 - V i , at a mole fraction of propan-1-01 x , z 0.05,9 the minimum in the excess volume of mixing Vg at x , x 0.05,1° the minimum in the excess enthalpy of mixing AHE at x, z 0.05,11 the minimum in the partial component of the compressibility for propan- l-ol at x , x 0.05,12 the maximum in the viscosity 'I at x, z 0.11 l3 and the maximum in the ultrasonic absorption at x , x 0.14.l4 In these properties, propan-1-01 in its mixtures with water behaves in a manner similar to the other alcohols mixed with 11, l5 Experimental A.R.propan-1-01 was used with the other materials as described earlier.lP6 The concentration of unprotonated 4-nitroaniline was determined spectrophotometrically at 383 nm as t This paper by Dr Wells should be read with the paper by Blandamer et al., J. Chem. SOC., Faraday Trans. 1, 1986, 82, 1471. It serves to clarify the distinctive approaches of these two workers. 25772578 Free Energies of Transfer of Ions Results and Discussion Determination of AG,"(H+) (a) Derivation of Relationships It has been suggested16 that the standard states employed in the derivation of the relationships used to calculate AG,"(H+) by the solvent-sorting procedure should be investigated. Before proceeding to a determination of AG,"(H+) for water-propan- 1-01 mixtures we therefore examine critically the method used in relation to other suggestions.The free energy of transfer of the proton between water and a water-cosolvent mixture consisting of n(H,O) moles of H,O and n(R0H) moles of the cosolvent is given by the difference in the standard chemical potentials : AG,"(H+) = pz(Hzolv) [ TPn(H,O) + n(ROH)] -pE(H&J (TPH,O). (1) By definition the standard state for p~(H&lv)[TPn(H20) +n(ROH)] must be in the mixture and that for pE(Hiq) (TPH20) must be in pure water, as is normal in considering the difference in the free energies of species between two 1iquids.l' As we are ultimately going to determine the concentration of species of the solvated proton spectrophoto- metrically on the molar scale, we adopt the molar scale (subscript c) here.Ify is the activity coefficient in the mixture, the standard state for p~(H~olv) [ TPn(H20) + n(ROH)] is y(H+) = 1 .O and [H+] = 1 .O with y -+ 1 .O as [H+] -+ zero; and ify' is the activity coefficient in pure water, the standard state for pz(H,+,)(TPH,O) is y'(H+) = 1.0 and [H+] = 1.0 with y' -+ 1.0 as [H+] -+ zero. AG:(H+) is divided into two parts for this determination. First, the solvated proton in water, H+(H,O)b, is transferred from water into the mixture using the Born expression for dielectric continua.In general in this treatment x is not specified except that it is assumed that b >, 5, the minimum being one sphere of H,O molecules surrounding H,O+ (only for the purposes of the Born calculation is b specified as 5 to provide a radius for the sphere transferred of 3rHz0, where rHzO is the radius of the water molecule). Ne2 AG(Born) = p~(H,+,)[TPn(H,O)+n(ROH)] --pz(H&)(TPH20) = ~ (D,1- D,1) (2) 6rHz" where Hiq = H+(H,O),, N is Avogadro's number, e is the electronic charge, D is dielectric constant and subscripts s and w indicate the mixture and pure water, respectively. The standard state for &(Hiq) [TPn(H,O) + n(ROH)] is defined in the mixture" and the standard state for p;(Hzq)(TPH20) is in pure water.As our investigations are restricted to mixtures which are largely aqueous in composition, with the mole fraction of ROH never exceeding x, M 0.2-0.3, it is assumed that other contributions to this transfer resulting from the departure of H2q from pure water and its reception into the water-rich mixture cancel out. As the contribution of AG(Born) to the total AG:(H+) is small, we consider that errors arising from deviations from these reasonable assumptions can be neglected. As shown elsewhere,, although the free energy of solvation of an ion i of charge ze and radius r derived from Born charging effects, AG(i)g0lv = (z2e2/2r)(Dg1 - l), is not on any concentration scale, the free energy of transfer of i between water w and the solvent s arising from Born effects, AG(Born) = AG(i)g0lV - AG(i)?lV, is on the molar scale., Therefore, eqn (2) is defined on the molar scale.Following this transfer in eqn (2), the solvent molecules around the proton relax to provide the stable situation in the mixture. This contribution to AG:(H+) is given by AG2 = P:(H:olv) [7-w320) +n(ROH)I -Pz(H,f,) ETWH20) + 4ROH)I (3) where the standard states for both chemical potentials must now both be defined in theI. M. Sidahmed and C. F. Wells 2579 mixture.17 This rearrangement of solvent molecules around the proton in the mixture is represented by the equilibrium : K where (ROH;),,, is a proton solvated by both H20 and ROH. It is assumed that x, is low enough in the water-rich conditions to restrict the composition of (ROHZ),,, to a ratio ROH/H+ = 1.0.As process (4) takes place entirely within the mixture, the standard states for all the species involved must be defined in the mixture1' and the standard free energy change for equilibrium (4) is given by AG"(5) = d(ROHi)mix + d(H2O)mix -&W2q)rnix -pz(ROH)rnix- ( 5 ) For the initial transfer of one mole of Hiq in eqn (2) between the two media, the free energy for the rearrangement of solvent molecules in the mixture is given by AG, = [ROHi] AG"(5) ( 6 ) (7) and the total free energy of transfer is given by AG,"(H+) = AG(Born) + AG2. AG"(8) = /4(ROH~)mix + P;(H~O)H~O -/G(Hiq)rnix -pZ(ROH),oH It has been suggested16 that eqn ( 5 ) should be (8) with the standard states for pi(H20) and pZ(R0H) being the so-called absolute rational states of pure water and pure ROH, respectively (subscript x).Although these two standard states are convenient for many processes involving the actual mixing of pure H,O and pure ROH, and especially so for the determination of the excess thermodynamic quantities of mixing, they have no absolute status.l8 In particular, they contravene the rule that the standard states for processes occurring entirely in a homogeneous liquid medium must be defined in that medium.l' Indeed, eqn (8) represents the standard free energy change for the fictitious equilibrium : (H:q)mix + (KoH)R.OH (RoHZ)rnix + (H20)H20 (9) which cannot occur in two miscible components H20 and ROH, and therefore, eqn (4) and ( 5 ) represent the equilibrium in the mixture.Following the normal procedure1' for determining the difference in free energies of species between two liquids, the standard states of all the species involved in the rearrangement (4) in the mixture n(H,O) + n(R0H) must be defined in the same mixture. For the solute species H$q and ROHZ on the molar scale this is y = 1.0 and [i] = 1.0 with y + 1 .O as [i] + zero. For the bulk components, H,O and ROH, in any particular mixture n(H,O) + n(ROH), their respective standard states, po(H,O) [ TPn(H,O) + n(ROH)] and p"(R0H) [TPn(H,O) + n(ROH)], are defined for each bulk component in that particular mixture, n(H,O) + n(ROH), without any solute species, e.g. HLq or ROH:, present. On the molar scale, the activity coefficient of each bulk component for that particular mixture, y" = 1.0 when the molar concentration of all solute species is zero.It should be noted that it is not assumed that p"(ROH)[TPn(H,O)+n(ROH)] = p"(H,O) [TPn(H,O) + n(ROH)] and neither, as has been suggested,16 does this assume that the chemical potentials of pure H,O and pure ROH are equal. Of course, in the normal way17 the standard states adopted for H,O and ROH in each particular mixture are related to standard states defined as activity = 1.0 for H20 in pure water and activity = 1.0 for ROH in pure ROH, even though these states canot be used for equilibrium (4) in n(H,O) +n(ROH) after transfer from H20. Iff(H,O) andf(R0H) are the activity coefficients on the mole-fraction scale of H,O and ROH in the complete2580 Free Energies of Transfer of Ions mixture of bulk and solute components related to the standard states of each respective pure bulk component defined as unity, f(H20) =fd(H20) y”(H20) Y”’(H20) and f(R0H) =fd(ROH)y”(ROH)y”’(ROH) where fd(H20) and f,(ROH) are degenerate activity coefficients17 on the mole fraction scale (subscript x) defined by p:(H,O)[TPn(H,O)+n(ROH)] = p34,O)(TPH2O)+RT lnfd(H,O) and p:(ROH)[TPn(H,O)+n(ROH)] = pg(ROH)(TPROH)+RT In fd(R0H) and y”’(H20) and y’”(R0H) in each case are factors converting y” from the molar to the mole fraction scale.From eqn (4) and (9, for any mixture n(H,O)+n(ROH) where for ROH; and H& the standard states are y = 1.0 and [i] = 1.0 with y -, 1.0 as [i] -+ zero and y” for H,O and ROH are as defined above arising from the presence of solutes in the mixture n(H,O) + n(R0H).This equation can be rewritten as AG, = - [ROH,] RT In Kc wR & 4 = Y(ROH;) Y”(H,O)l[Y(H:q) Y”(ROH)I. (12) where theconcentrationquotient Kc = [ROHz]/([H:,] [ROH]), wR = [H,O] in themixture and (1 3) For the transfer of one mole of protons between water and the mixture, i.e. [ROH$]+[H:,] = 1.0, all the quantities in eqn (12) can be determined. When a trace concentration of 4-nitroaniline B is added to aqueous acidic solutions, equilibrium (14) is set up in water K : B,, + H:q e BH;q + H20 and K; is given by where the standard state in water for BH+, B and H,+, is y’ = 1 .O and [i] = 1 .O withy’ -+ 1 .O as [i] -+ zero and y’(H,O) assumes pure water as the standard state. However, when B is added to acidic solutions in the mixture n(H,O) + n(ROH), equilibria (1 6) and (1 7) are set up in conjunction with equilibrium (4) Kl Bmix + W:q)mix * BHLix + H2Ornix (16) to which eqn (1 8) and (19) apply where the standard states in the mixture for B, BH+, H& and ROH; are y = 1.0 and [i] = 1 .O with y -+ 1 .O as [i] -+ zero and y”(H20) and y”(R0H) are as defined above for aI .M . Sidahmed and C. F. Wells 258 1 mixture containing dissolved species. If c and cR are the concentrations of B determined spectrophotometrically in acidic solutions in water and in the mixture, respectively, for a constant added total concentration of [B] = co for a constant temperature, eqn (20) can be deduced1-6 (20) where 4 = y(B) y(RoH;)/[y(BH+) y”(R0H)I and 4 = y(B) y(H,f,)/[y(BH+) y”(H,O)I, ccR K24 COCR wR cO ----- (cR - ‘> - Kl 4 (cO - cR) [ROHIT + K1 provided eqn (21) holds,? where F ; = y’(B)y’(H4q)/y’(BH+)y’(H20), w = [H,O] in pure water and [ROH], is the total molar concentration of ROH added to the mixture.It has been shown for a wide range of cosolvents in water-rich conditions that linear plots of cc,/(c, - c) against cR/(co - cR) are obtained experimentally for constant [ROH], and constant temperature at an ionic strength of 1 .OO, confirming the validity of assumption (21).lp6 From eqn (20), the slopes of these linear plots are given by where F, and K, are as defined for eqn (12) and (13). Moreover, for these linear plots, the ratio slope/intercept = K24, enabling the calculation of [ROH;] using yielding a range of values with the varying [HCl] used for each [ROH],.Experimentally, it has been found for a range of cosolvents in water-rich conditions that the latter K, values for varying [HCl] at constant [ROH], calculated using eqn (24) agree well amongst themselves for each [ROH], and also agree very well with the specific value for K , c1 calculated from the slope of the plot of CCR/(CR - c) against c,/(c, - c,) at the same [ROH],. We must conclude, therefore, that in general F, = 1.0. As Blandamer et al. desire,lG the y-values comprising F, can be related to the pure liquids H 2 0 and ROH using the degenerate activity coefficients. fd(H20) and f,(ROH) defined in eqn (10) and (1 1) on the mole-fraction scale can be used together with y”’(H20) and y”’(R0H) to relate y”(H20) and y”(R0H) to their respective pure liquids and similarly y values for solute species can be related to pure water y’ values via y’ = ydy, where yd is also a degenerate activity coefficient17 defined on the molar scale by ,uz( i) [ TPn( H20) + n( ROH)] = &( i) ( TPH ,O) + R T In yd( i).Rearranging eqn (13) for F, to relate y(i) and y”(H20) to pure water and y”(R0H) to To find [ROH;] in eqn (12), eqn (26) and (27) are used:1-6 [ROH;] = 0.5{A-(A2-4[ROH]r)~}. (26) (27) A = ([ROH], + 1 +&I) t Not w/wR = 1.0 as stated by Y. Marcus in Zon Solzlation (Wiley, Chichester, 1985), pp. 161 and 204.2582 As experimentally F, = 1.0 and wR is given by Free Energies of Transfer of Ions where d, is the density of the mixture and M,,, and M , are the respective molecular weights of ROH and H,O, all the quantities in eqn (12) are now known.(b) Evaluation of AG:(H+) for Water-Propan-1 -01 Mixtures Values of cR were determined spectrophotometrically at 383 nm19 and 25 "C for added concentrations of HC1 in the range 0.1-0.8 mol dm-3 for 5, 10, 15, 20, 25, 30, 35 and 40 vol % of propan-1-01 with co = 1.45 x lop4 mol dmp3 and with ionic strength made up to 1.00 mol dm-3 by adding NaCl, as before.1-63 l 9 Slight turbidity was found in solutions containing 5, 10 and 1 5 vol % propan- 1-01 and this was corrected for by using a suitable blank. Values of c for the same range of HCl concentrations in water with the ionic strength maintained at 1 mol dmp3 using NaCl were also determined spectrophotometrically. Owing to a separation into two layers for the mixture containing 40 vol % propan- 1-01 and I mol dmp3 NaCl with no added HCl, the extinction coefficient E of 4-nitroaniline could not be determined by the usual procedure19 for this mixture: E for 40 vol % propan-1-01 was therefore found by extrapolation of the values of E at the lower concentrations of propan-1-01.Good linear plots were obtained for ccR/(cR-c) against cR/(c,-cR) in 10, 15, 20, 25, 30, 35 and 40 vol "/o propan-1-01 with the intercept = wc,/K;I;;, confirming the validity of assumption (21) also for water- propan-1-01 mixtures. However, the scatter on the points for 5 vol % propan-1-01 was too great to draw such a plot for that concentration. The accuracy of the extrapolated value for E in 40 vol % propan-1-01 was tested by repeating the calculation of values for cR with slight variations of E either side of the extrapolated value.Only the plot of CCR/(CR-C) against cR/(co-cIt) using the values of cR derived from the extrapolated value of E gave a straight line; plots using slightly higher or lower values for E curved away below or above, respectively, from the latter plot. Values of K,C1 determined from the slopes of these linear plots using eqn (22) and corrected for the small contraction of volume on mixing water with propan-l-o11-6 are shown in table 1 . This table also contains values of K, calculated for each added acid concentration using eqn (23) and (24). The values of K,F, calculated from the ratio slope/intercept of the linear plots are also included in table 1 . For any particular mixture n(H,O) + n(R0H) good agreement is obtained between these latter values for Kc and for the value for K, C1 determined from the slope except, as found with all other cosolvents used,1-67 l9 at the higher concentrations of propan-1-01 where [ROH:] becomes high enough for ([Hiq] - [ROH;]) z zero in eqn (24), causing scatter in the values for K,.We conclude, therefore, that F, = 1 .O for water-propan-1 -01 mixtures in water-rich conditions, as found for all other water-cosolvent mixtures Values for AG, were calculated on the molar scale using eqn (12) with F, = 1 .O. Values for [ROH;] were calculated using eqn (26) and (27) with the values of K, in table 1 obtained from the slopes of the plots of CCR/(CR - c) against c,/(c, - cR). Values for wR were obtained using eqn (28) with the values of d, at 25 "C interpolated from the data of Chu and Thornpson2O and of Mikhail and Kimel,13 which are in good mutual agreement.The values of AG2 for water-propan-1-01 are plotted against solvent composition in fig. 1. Values for AG(Born) were calculated on the molar scale using eqn (2) with the dielectric constant interpolated from the data of Akerlof.21 As eqn (7) gives values of AG(H+) on the molar scale, these were corrected to the mole-fraction scale using the equation: AG,"(H+) = AG(Born) + AG, + RT In (d, M,/d, M,) (29)I. M. Sidahmed and C . F. Wells 2583 Table 1. Values of K , (dm3 mol-I) calculated from K , F, and of K, K1 (dm3 mol-l) derived from the slopes at ionic strength = 1.00 mol dm-3 and at 25 "C in water-propan-1-01 mixtures total added acidity 8.21 12.44 16.75 21.16 25.65 30.24 34.92 /mol dmP3 (0.0261) (0.0408) (0.0569) (0.0745) (0.0937) (0.1 15) (0.139) concentration of propan- 1-01 [wt % (mole fraction)] 0.096 0.37 0.60 1.15 1.6 1.8 1.9 2.1 0.153 0.35 0.57 1.07 1.6 1.7 1.8 1.9 0.192 0.35 0.58 1.04 1.5 1.4 1.7 1.7 0.383 0.34 0.57 1.07 1.5 1.3 1.9 1.6 0.766 0.34 0.56 0.87 2.0 2.1 3.2 3.6 K , C 1 0.337k0.004 0.56f0.01 0.97+0.01 1.30+0.01 1.47kO.01 1.54k0.03 1.66k0.02 (from slope) K2 4 45.7 27.8 15.9 11.8 10.5 9.9 9.5 2 0 0.02 0.04 0.06 0.08 0.10 0.12 0.lL X2 Fig.1. Variation of AG, for eqn (12) for water-propan-1-01 mixtures at 25 "C with mole fraction of propan- 1-01. where M, = lOO/[(wt % ROH/MR0,) + (wt % H20/M,)] and d, is the density of water at 25 "C. The resultant values for the free energy of transfer of H+ on the mole fraction scale are contained in table 2.Free Energies of Transfer of Anions Values for AG:(X-) can be calculated from values for AG:(HX) using the values of AG:(H+) in table 2 in the equation AG:(X-) = AG:(HX) - AG;(H+). H2(g) Pt I HC1, H 2 0 + propan-1 -01 I AgCl, Ag. (30) (31) Several sets of workers have determined E" values for the cell Claussen and French,22 Roy et and Elsemongy and F o ~ d a ~ ~ have determined E"2584 Free Energies of Transfer of Ions Table 2. Values for the free energy of transfer of individual ions from water into water-propan-1-01 mixtures at 25 "C concentration of propan- l-ol mole wt % fraction H+ Rb+ Agt c1 3.86 5.00 7.43 10.00 10.00 10.00 10.00 10.00 10.70 13.80 15.00 16.70 20.00 20.00 20.00 20.00 20.00 20.00 21.90 25.00 26.50 30.00 30.00 30.60 34.30 35.00 37.60 40.00 40.00 40.00 40.00 40.00 0.01 19 0.0155 0.0235 0.0322 0.0322 0.0322 0.0322 0.0322 0.0347 0.0458 0.0503 0.0567 0.0697 0.0697 0.0697 0.0697 0.0697 0.0697 0.0776 0.0909 0.0976 0.1 14 0.114 0.1 17 0.135 0.139 0.153 0.167 0.167 0.167 0.167 0.167 - 0.77 - 1.03 - 1.67 -2.65 - - - - - 3.02 -4.59 - 5.27 - 6.23 - 7.4 - - - - - - 7.8 - 8.2 - 8.3 -8.5 - - 8.6 - 8.7 - 8.7 - 8.8 - 8.8 - - - - OH- __ CNS- - 1.22" 3.09" 3-62" 3.13" 3.09d 3.09" _.- - 5.8" 8.2b 8.8" 8.1" 8.1d 8.0" 8. lf 9.1" 9.7b 9.4" - - - - - 9.8" 10.6" 11 .8" 10.2" 10.5" 10.5f - - - - E" data for HCl taken from: aref. (26), "ref. (24), "ref. (23), ref. (22), "ref. (25) and f ref. (27). on the mole-fraction scale for cell (31) for a range of solvent compositions and the free energy of transfer of HC1 on the mole-fraction scale is given directly by the equation: AG:(HCl) = 96.5(Ek -Ei)/kJ mol-l.(32) Gentile et al.25 have used cell (31) to provide values of E$ on the molality scale and values for AG,"(HCl), calculated from eqn (32) have to be corrected to the mole-fraction scale (kJ mol-l) using the equation: AG,"(HCl) = AG,"(HCl), + 1 1.41 log (Mw/Ms). glass electrode I HC1, H,O + propan- l-ol I AgC1, Ag (33) Smits et a1.26 have determined values for AG,"(HCl), on the molar scale using the cell: (34)I . M. Sidahmed and C . F. Wells 2585 and these values have been corrected to the mole-fraction scale (kJ mol-I) using the equation : AGi(HC1) = AGF(HCl), + 1 1.41 log ( M , dJM, d,). (35) Schwabe and Miiller2' have determined E L for the cell: H2(g), Pt I HCI, H 2 0 + propan- 1-01 I Hg,C12, Hg (36) and the values for AG,"(HCl), calculated from eqn (32) have been converted to the mole- fraction scale using eqn (33).All these values for AGi(HC1) have been combined with the values for AG,"(H+) in table 2 to produce values for AG,"(Cl-) on the mole-fraction scale using eqn (30). These latter values are collected in table 2. Good agreement is obtained between the values for AG,"(Cl-) from the various sources for the same solvent composition, except for some deviation of those derived from the E" measurements of Roy et a1.23 Dash and Padhi28 have determined E" on the mole-fraction scale for the cell: Ag, AgCNS AgCl, Ag (37) from which, after correction for the liquid junction potential,2s values for AG,"(HCNS) can be calculated using an equation analogous to eqn (32).Values for AG,"(CNS-) have been calculated using these values with the values of AGE)(H+) in table 2 in eqn (30). The values for AG,"(CNS-) are given in table 2. Values for Kip = [H+] [OH-]y2, have been determined for the ionization of water in water-propan-1-01 mixtures.29 These values for (Kip), on the molar scale were first converted to the molality scale (Kip)m using the equation: and the resulting values on the molality scale were used in eqn (39)Ip6 to determine the sum of the free energies of transfer of H+ and OH- on the molality scale. m, and m, are the molalities of water in pure water and in the mixture, respectively, and agzO is the activity of water in the mixture on the molality scale.Values for ahzO on the mole-fraction scale were calculated from the activity coefficient of water in the water-propan-1-01 mixtures relative to pure water determined by Butler et aL30 and these were converted to the molality scale using the equation:31 a",,,(molality) = 55.509a",,,(mole fraction). (40) Values for AG~(H+),+AG,"(OH-), on the molality scale were then converted to the mole-fraction scale using eqn (33) and values for AGi(OH-) were then calculated using eqn (30) and the values for AG:(H+) in table 2. The resultant values for AG,"(OH-) are shown in table 2. Free Energies of Transfer for Metal Cations Smits et al.32 have determined the free energy of transfer for RbCl on the molar scale from E" measurements on the cell: glass electrode I RbC1, H 2 0 + propan-1 -01 I AgCl, Ag using an ion-selective glass electrode.These values have been converted to the mole- fraction scale using an equation analogous to eqn (35) and values for AG,"(Rb+) have been calculated using the equation : AG,"(Rb+) = AG,"(RbCl) - AG,"(Cl-) (41)2586 Free Energies of Transfer of Ions ' Ag+ - l o t Fig. 2. Variation of the free energy of transfer of individual ions between water and water- propan-1-01 mixtures with the mole fraction of propan-1-01 at 25 "C. with the mean values for AG,"(Cl-) in table 2, excluding those derived from the E" measurements of Roy et al.,23 and are given in table 2. Values for the solubility product, Kip, for AgCl in H,O-propan-1-01 have been collated by Dash et al.33 and KYp in water has been determined by Gledhill and Malan.34 Values for the free energy of transfer for AgCl on the molar scale were calculated using the equation : (42) and these have been converted to the mole-fraction scale using an equation analogous to eqn (35).When combined with values for AG,"(Cl-) in an equation analogous to eqn (41), the values for AG,"(Ag+) which result are contained in table 2. AG:(AgCl), = RT In (cp/KZp) Comparison of Values for AG:(i) Fig. 2 shows that the distribution of values of AG,O(i) for varying i is similar to those found with most other cosolventsf-6 where the equilibrium OH- + RQH e RO- + H 2 0 (43) lies to the left. For these latter conditions AG:(OH-) > G,"(CI-), as found for ethan01,~ ethanonitrile6 and urea.6 When equilibrium (43) lies farther to the right, AG:(Cl-) > AGt(OH-), e.g.for with the latter becoming negative for ethane- 1,2-diol and 37 For low mole fractions of cosolvent, AGP for an alkali-metal ion like RbS is negative for propan-2-01,~? 3 9 acetone,,> 3 y dioxaq29 t-butyl DMSO,,? ethanonitrile6 and urea6 as cosolvents, but positive and ca. zero for methanol with AGt(Rb+),,? and negative values are found here for propan-1-01. For x, < 0.2, AG:(Ag+) is more negative than AG,"(Rb+) for methanol,,* 3 9 propan-2-01,~. t-butyl alcohol,2+ dioxan,2$ dimethyl sulphoxide,2T dioxan,27 acetone,2* 3 9I. M . Siduhmed and C. F. Wells 2587 I ,CNS:2- PrOH 5 4 I - 0 E ".._ 1 / 0.05 0.20 - x2 glycerol Fig. 3. Variation of the free energy of transfer of CNS- and Ag' ions between water and water+osolvent at 25 "C with mole fraction of cosolvent.t-butyl alcohol,23 DMSO29 and ethanonitrile,'j as found in fig. 2 for propan- 1-01, but the latter cosolvent is unusual in having AG,"(Ag+) more negative than AG:(H+), only observed previously for ethanonitrile,6 with AG,"(Ag+) = AG,"(H+) for DMS0.2> For other cosolvents, dioxan,2v 3 3 ti DMS0,2~ ethanol4 and urea,6 AG,"(CNS-) < AG,"(Cl-), as found here for propan-1-01. As E" values for cell (37)28 and Ksp values for AgC133 are now available for some other cosolvents for which AG,"(i) have been determined, it is appropriate here to determine AG,"(CNS-) and AGF(Ag+) for the mixtures of these cosolvents with water to see how they compare with the above discussion. AG,"(HCNS) has been calculated using eqn (32) from Eo values on the mole-fraction scale28 for methanol, propan-2-01 and glycerol as cosolvents and values for AG,"(CNS-) have been calculated using the appropriate values for AG,"(H+)2~3 in eqn (30).These values are plotted against solvent composition in fig. 3. When compared with the values for AG,"(C1-),2 AG:(CNS-) < AG,"(Cl-) for all these cosolvents, as found with the other cosolvents;2 moreover, AG,"(CNS-) with glycerol is negative, like AGZ'I-) for this cosolvent,2 with positive values for AGF(C1-).2 Using the values for Ksp for AgCl with cosolvents ethanol and propan-2-01 on the molar scale,33 values for AG:(AgC1), on the molar scale have been calculated using eqn (42) and, after correction to the mole-fraction scale using an equation analogous to eqn (35) and subtracting the appropriate values for AG,"(CI-) for these cosolvent~,~-~ values for AG;(Ag+) on the mole-fraction scale are obtained.These values plotted in fig. 3 show that AG:(Ag+) is more negative than AG,"(Rb+) with the same cosolvent,2$6 as found above for the other cosolvents. Moreover, when compared with the appropriate AG,"(H+)2$ and unlike many of the other cosolvents, AG,"(Ag+) z AG:(H+) for ethanol and propan-2-01, resembling DMSO in this respect. This analysis shows, therefore, using the values for AG,"(Ag+) calculated here for the cosolvents propan- 1-01, propan-2-01 and ethanol, that the earlier finding with other cosolvents of - AG,"(H+) > - AG,"(Ag+) is not necessarily the normal situation.References 1 C. F. Wells, Adu. Chem. Ser., 1979, 177, 53. 2 C. F. Wells, Aust. J . Chern., 1983, 36, 1739.2588 Free Energies of Transfer of Ions 3 C. F. Wells, J . Chem. SOC., Faraday Trans. 1. 1973, 69, 984; 1974, 70, 694; 1978, 74, 636. 4 C. F. Wells, 1. Chem. SOC., Faraday Trans. 1, 1984, 80, 2445. 5 C. F. Wells, J . Chem. SOC., Faraday Trans. 1, 1976, 72, 601. 6 C. F. Wells, J. Chem. SOC., Faraday Trans. 1, 1975, 71, 1868; 1978, 74, 1569; 1981, 77, 1515; Thermochim. Acta, 1982,53, 67; G. S. Groves and C. F. Wells, J. Chem. Soc., Faraday Trans. 1, 1985, 81, 1985, 3091; G. S. Groves, 1. M. Sidahmed and C. F. Wells, unpublished work. 7 G. Wada and S. Umeda, Bull. Chem. SOC. Jpn, 1962, 35, 646. 8 H. S. Frank and M. W. Evans, J . Chem. 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