J . Chem. SOC., Faraday Trans. I , 1982, 78, 1431-1449 Washburn Numbers Part 4.-The Erdey-Gruz Experiment. Relative Solvent Transport Numbers for Ion Constituents in Mixtures of Water with Raffinose, Glycine, Ally1 Alcohol, Dimethylsulphoxide and Dioxan BY DAVID FEAKINS,* ROBERT D. O’NEILL,~ W. EARLE WAGHORNE AND ANTHONY J. I. WARD Department of Chemistry, University College, Belfield, Dublin 4, RepublIc of Ireland Received 14th April, 1981 Erdey-Gruz’s diffusion experiment has been used to obtain the sum of the transport numbers of water by ions, relative to a second solvent component, En& = (n+)&+(n-)&. The theory of the experiment is described in detail; the corrections for the effect of salt on solvent activity, lacking in Erdey-Gniz’s work, have been made. The experimental method involved a diaphragm cell and analysis of changes in mixed-solvent concentration by interferometry.The En& are combined with Washburn numbers, w&, some of which are new values obtained from cells with ion-selective electrodes. With w& = (n+)& t+ - (n-)& r-, the ionic n& are obtained unambiguously for systems containing low concentrations of glycine, ally1 alcohol, dimethylsulphoxide (DMSO) and dioxan. These data were also calculated for a 0.75% (w/w) raffinose+water mixture using transport and diffusion data from the literature. The ng values for the raffinose + water system, which probably approach closely the dynamic solvation number, N , of the ion in pure water, are Li+( 16), Na+( lo), K+(6), Cl-(4) and H+( 1).In the remaining systems these figures are reduced by the competition of the organic molecule for solvation of the ion. In the glycine + water system the ions transport glycine preferentially. Consider a binary mixture of water with a second component, which can be another liquid such as dioxan, or a solid such as raffinose. Suppose that an electrolyte is dissolved in the resulting mixed solvent. If an electric current is passed, an ion will move in the field direction and, because of preferential solvation, will normally move one component of the solvent with respect to the other. For highly aqueous mixtures we normally discuss the movement of water with respect to the non-aqueous component of the solvent.’ When 1 mole of ions of type i crosses a hypothetical plane perpendicular to the direction of motion it carries (ni)w moles of water relative to the second component.In this paper we show how (n& can be determined. The Washburn number, ww, of a binary electrolyte in a binary aqueous mixture2 is the number of moles of water transported to the cathode in an electrolysis relative to the second solvent component per Faradayl and is given by ww = (n+)w t, - ( K ) ~ t-. (1) The t are the ionic transport numbers. Washburn numbers are available for a number ofmixtures ofhigh water content;’? 39 they depend on the electrolyte and on the concentration and nature of the non-aqueous component. t Present address: University Laboratory of Physiology, Parks Road, Oxford OX1 3PT 1 Faraday’s constant, F, i.e. 9.648 456 x lo4 C mol-I.14311432 WASHBURN NUMBERS Notional separations of ww into (n+)w and (n-)w have been attempted on extra-experimental rea~oning.~? However, we showed recently5* that a method suggested by Erdey-Gruz et al.’ for the determination of ‘solvation numbers’ can be adapted to determine (n+)w and ( K ) ~ unambiguously. In this method the sum of these numbers is measured in a diffusion experiment, giving eqn (2): Solution of eqn (1) and (2) leads to (n+)w and (n-)w. In Erdey-Gruz’s diffusion experiments, a binary aqueous mixed solvent of a given composition was separated from a solution of the electrolyte made with a binary mixture of the same composition. This can be represented as The M are the concentrations of non-electrolyte (S) and electrolyte per kg of water.Diffusion occurred and the reference solution was then analysed for solvent composition and electrolyte concentration. The details of Erdey-Gruz’s experiments are confused; for example a number of electrolyte concentrations are incorrectly quoted. In our first report5 we combined our own measurements of ww with some of Erdey-Gruz’s diffusion results; however, when we began our own diffusion experiments we realised that he had left out an important correction. This omission does not detract from the significance of his work and, indeed, prompts the following discussion of the principle involved. (a) In the diffusion experiment the electrolyte moves from the solution into the mixed solvent, carrying En, moles of water per mole of electrolyte with respect to the second solvent component, by virtue of the microscopic forces between the ions and the solvent molecules. (b) At the same time the activities of the two solvent components change when the salt is added.An additional flow of solvent will then arise from the resulting gradient in chemical potential in the cell. There is thus a macroscopic coupling of the flows of electrolyte and solvent. This effect is of the same order of magnitude as the microscopic coupling; it cannot be eliminated by extrapolation to infinite dilution because proportionate changes in the two flows occur. Following Ortmannss we use eqn (3): Studies of the free energy of transfer of the electrolyte, AG,, from water to mixed solvents tell us how the chemical potential of the electrolyte (3) varies as the proportion of non-aqueous component ( 2 ) is increased with respect to water (1).In most cases of interest, the glycine + water system being an exception, AG,, and hence the right-hand side of eqn (3), is experimentally positive. From the left-hand side we see that the activity of the non-aqueous component then increases when the electrolyte is added. In these circumstances it is a flow of the non-aqueous solvent component that accompanies that of the electrolyte in the experiment described above. In most cases the effect is larger than the true coupled diffusion; and it led Erdey-Gruz to the erroneous conclusion that the ions were preferentially solvated by the non-aqueous component.D. FEAKINS, R. D. O'NEILL, w. E. WAGHORNE AND A. J. I. WARD 1433 The distinction between the two types of coupling was clearly recognised in the treatment of diffusion in the water + glycine + potassium chloride system by Woolf et a1.,9 and we rely on their treatment here.Recently M'Halla et have carefully analysed the irreversible thermodynamics involved and have obtained En, in a number of systems using a different kind of diffusion measurement. The experiments give (rz+)w to 1 ; this is more than adequate for a preliminary interpretation of the resultski the present state of knowledge; and to know the individual numbers at all is an advance. Here we assemble (n+), for a number of systems containing relatively low concentrations of non-aqueous component. Ally1 alcohol (prop-2-en- 1-01) was chosen for comparison with Erdey-Gruz's work; he chose it originally because it can be chemically analysed.For this and glycine+water systems we present the full thermodynamic, transport and diffusion data. Measurements of w& are already available for dimethylsulphoxide (DMSO) system^;^ details of e.m.f. measurements on dioxan + water systems will be given in later papers. Data from the literature have been used to give values for the key raffinose.+ water systems."$ The overall experimental strategy is summarised in fig. 1. WASHBURN e.m.f. method (Feakins 1961) transport cell solvent activity (W or S) v.p. etc. 'W c w .. t I ww - ERDEY - GRUZ Z:nW FIG. 1 .-Overall experimental strategy. 47 FAR 11434 WASHBURN NUMBERS PRINCIPLE OF THE DIFFUSION MEASUREMENTS It is helpful to use different concentration scales for different parts of the argument; the gain from the change of variable offsets any lack of consistency.At the beginning of an experiment the contents of the diffusion cell can be represented as in cell (I) above. The diffusion is referred to the solvent frame.9 At this stage we take as our solvent pure water and not the mixed solvent; and we define the molalities M, and M3 with respect to 1 kg of water, as distinct from m2 and m3 defined with respect to 1 kg of mixed solvent. The fluxes of non-aqueous component, J 2 , and electrolyte, J3, in this ' water' frame are given in terms of the phenomenological coefficients (L,j)l by eqn (4) and (5) or, writing Xi = (dpi/ax) and dropping the subscript 1 - J2 - L22x2+L23x3 J3 L32 x2 + L33 x3 ' It is convenient to work in terms of the Erdey-Gruz number of the non-aqueous component, Cn,, given by = L23/L33* (7) It is easily shown for the individual n and hence for Cn that Y Yl Cn, = -?En, where y denotes mole fraction in the mixed solvent in place of x used otherwise above.J2/J, is the total number of moles of non-aqueous component which accompany one mole of the electrolyte as it diffuses, and was incorrectly identified by Erdey-Gruz7 as Ens. As seen above, J2/J3 would in his experiments have contained a contribution from the macroscopic coupling, since (ap2/ax) was non-zero. There are two ways of proceeding. (a) In all but one of the experiments described here we used Erdey-Gruz's original condition and determined the flux of solvent arising from the gradient (ap2/ax) separately.(b) It is also possible to arrange that (ap2/ax) is zero, and we report one result obtained with this condition, which we are now exploring more fully in this laboratory. (a) Rearranging eqn ( 6 ) we have NowD. FEAKINS, R. D. O'NEILL, W. E. WAGHORNE AND A. J. I. WARD 1435 and L23 = L32, as required by the Onsager relations. Thus The term (X,/X3)CnS is normally very small compared with 1, thus The average ratio of the fluxes (J2/13) in cell (I) was measured, following Erdey-Gruz, by analysing side B at intervals, typically 1, 2 and 3 days. If (J2lJ3) is extrapolated to zero time its value should then correspond to infinite dilution of the electrolyte, whatever the initial value of M,; this procedure should also give the initial ratio of fluxes at t = 0, (J2/J3).Note that the second term of eqn (12) does not contain the gradients of chemical potential in the cell, although the first term does. The denominator of the first term is easily obtained as the flux of electrolyte. J,, is the flux of component 2 arising from the difference in its chemical potential between sides A and B due to the presence of the electrolyte. This difference can be calculated using eqn (3) and obtained in a two-component system by changing the concentration of the second solvent component to give the cell The flux of component 2 at zero time in this cell will be expected to be close to J,, in cell (I), but only as M, --+ 0, and therefore ( M ~ ) A -+ ( M , ) ~ , will the simulation be exact. In principle, therefore, extrapolations both to zero time and to zero M, are required to obtain a meaningful Ens, which would then be the value at M, = 0.In practice, our present experiments were not sensitive enough to detect systematic variations in the at finite times and electrolyte concentrations. The results presented are therefore averages. Within the presen! error limits they are indistinguishable from the values at infinite dilution and' have been so treated. Cnw calculated from the Cn, values of eqn (13) are thus treated as CnO, for comparison with wO,, the Washburn numbers at infinite dilution. (b) If (ap2/ax) = 0, then eqn (8) becomes J2/J3 = L23/L33 = Cn,. This condition can be arranged artificially at the beginning of the experiment by having diffusion take place from a three-component mixture into a two-component mixture, the concentration of component 2 having been changed in the three-component mixture to make (p2)* = (P,)~ in cell (I).The problem of simulating the flux of component 2 separately in two-component systems is eliminated and with it, probably to a good approximation, the necessity for extrapolation to M, = 0 (see above). 47-21436 W A S H B U R N NUMBERS A non-zero value of (ap,/ax) evolves during the experiment. Its effect was eliminated by extrapolation of the apparent Zns to t = 0. This should give Zng to good approximation, since the diffusion is taking place into a solution in which M, = 0. PRINCIPLES OF THE ANALYSIS We shall consider method (a) in detail. It should perhaps be remarked that a complete analysis of the measurements to give all four practical or phenomenological diffusion coefficients is neither, for the present purpose, necessary nor would the present experimental method have been chosen if it had been necessary.The measurements are made in an apparatus-fixed frame with which the volume-fixed frame coincides13 if changes in partial molal volume with concentration are ignored, as they will be here. Our method of analysis allows a rather direct conversion from the volume-fixed to the solvent-fixed frame. Consider cell (11). Before diffusion a volume V of the contents of side B contains, say, N , moles of water and N , moles of S , and, of course where the are the partial molal volumes. In calibrating the interferometer, reference solutions were made by weighing out small amounts of component 2, AN2 moles,* and making up a solution using the original mixed solvent to the volume V.Then k ( N , 6 + N , K)+ AN, V, = V. (15) Using this calibration we can determine the AN, value appropriate to any diffusion solution by interpolation. In the original mixed solvent, N , moles of component 2 are associated with N , of component 1 in volume V ; now N,+(AN,/k) are associated with N l . In the solvent frame, then, with But AN2 &/ is small compared with unity, and then (AN,), = AN,( 1 +q). The argument can be readily extended to the analysis of the three-component system, cell (I). Here let An3 be the number of moles of electrolyte that have diffused into a total volume V ; it is determined by conductiometric titration.The quantity An, corresponding to AN, can be determined as above, but now the calibration involves solutions of equal molarity in the electrolyte. Now and ( An,K An3E) +- (An,), = An, 1 +- V V +An,..). V * The AN2 of eqn (1 5) is defined on a 'mixed-solvent volume' scale and is not the more familiar (AN2)" measured on the volume-fixed frame for which = (AN,), 1 +--= ( :;)D . FEAKINS. R. D. O’NEILL, W . E. WAGHORNE A N D A. J. I. W A R D 1437 Thus (I2/J3) = (An2)1/ = An2/An3‘ The value of (AN2), obtained from cell (11) with the molar ratio adjusted on side A to give the same initial difference as in cell (I) does not accurately simulate the average flux of component 2 in cell (I). In cell (I) the chemical potential of component 2 changes with time not only because of its own movement from A to B but also because of the flux of electrolyte.A simple correction can be made to (AN2), assuming the linearity of Ap2 in M, (see below). If (AN:)1 is this corrected value, then in the solvent frame we have (’22/’3> = (AN:)l/(An3)l - AN,* (1 + AN,* E/ V ) - An3(1+An2V,/V+An,E/V)’ To a good approximation we can take (J22/J3) = AN,*/An, especially as t -+ 0. The apparent Zns is thus given by eqn (16) : with An2 - AN,* AM Zn, = AN,* = AN2 XL An3 A% where AM, is the initial, and Am3 the mean difference in electrolyte concentration between sides A and B. CALCULATIONS OF ACTIVITY Ortmanns8 has shown how the variation in activity of the solvent components of binary systems with electrolyte activity can be calculated using eqn (3).A simpler analysis than his, which was based on the molar scale, is possible if the ‘water’ scale is used for the concentrations of components 2 and 3. Transforming eqn (3) to this scale we have, at constant p , T, and n, (95) =(%) . aM3 Mt aM2 M3 The right-hand side of eqn (18) can be obtained from measurements on the kind of electrochemical cells with glass electrodes described later in the paper; also available are amalgam ce1ls.l The information is usually obtained as the free energy of transfer of the electrolyte, AGt, from water to a mixed solvent of a particular composition, i.e. M2, and i3 AG, Two approximations were made. (i) AG, was often not available at the high M, used, but where it was, it was negligibly different, for the present purpose, from AG;, the value in the standard state; thus AG: values were normally used.(ii) It was also sufficiently accurate to take a mean value of the gradient of AG: with M,. AG; must be transformed from the usual scales to the ‘water’ scale. With the right-hand side1438 WASHBURN NUMBERS of eqn (1 9) taken independent of M, we can write dAG, &2 = (&3 for the change in chemical potential of component 2 on addition of a salt to make a concentration M, in the binary mixture. In the experiment with the binary system, M, is changed on side A to give the difference Ap,. Now dp, = RTd In a, = RT(d In M, + d In y,). Activity data (for sources see table 7) show that if AM, = ( M ~ ) A - ( M ~ ) B is small the change in y2 is negligible, thus In a typical set of experiments using method (a) cell (I) was set up with a particular mixed-solvent system and electrolyte concentration [e.g.5% (w/w) DMSO; 1.0 mol dmP3 KCl] and diffusion allowed to proceed for ca. 24 h. To analyse the solutions the cell had to be dismantled, so that separate experiments lasting ca. 48 and ca. 72 h were also set up. Cell (11) was then studied over the same time intervals. For every experiment in cell (I), the corresponding AN: for use in eqn (1 6) was calculated from an experiment in cell (11) using eqn (1 7). AN,* was adjusted for any mismatches in the diffusion time or in Ap, between cells A and B assuming linearity in the time and in AM, over small ranges of these variables. Table 1 shows results of the experiments on cell (11) and table 2 the combination of these with the results from cell (I).For method (b) the value of M, on side A of the cell (I) is adjusted to make Ap, = 0. Now J,/J, = An,/An3 (22) (An,/An,) was plotted against t , and extrapolated to t , = 0. The results are also shown in table 2. In this experiment the matching of the p, was not perfect. The appropriate small corrections were made using the data of Erdey-Gruz et al.' Erdey-Gruz numbers, En&, are collected in table 2. TABLE RESULTS FOR CELL (11) AT 25 O C diffusion time S (M2)A (M2)B b l h ANJmol dm-3 dioxan 0.7299 1.0152 24 0.0285 46.5 0.0476 71 0.0575 DMSO 0.6736 0.7738 24 0.0 129 [5% (w/w>l 48 72 0.0246 0.03 12 glycine 0.3416 0.2099 24.5 1.45 (AN,) [2.5% (w/w)lD. FEAKINS, R. D. O'NEILL, w . E. WAGHORNE AND A.J . I. WARD 1439 TABLE 2.-RFSULTS FOR CELL (I) AT 25 OC 23 44 71 24 48 23.5 47.5 71.5 23.5 46.5 71.75 24 48 16 26.5 31.5 side A: 5% (w/w) dioxan+ 1 rnol dmP3 K T l - 0.0105 0.0252 - 0.0 147 0.1727 0.0125 0.036 1 - 0.0236 0.2794 0.0076 0.041 6 - 0.0340 0.3672 0.0133 0.0238 -0.0105 0.1800 0.0086 0.0 179 -0 0093 0.1443 0.0113 0.0127 -0.0014 0.1727 0.0147 0.02 15 - 0.0068 0.2384 0.01 50 0.0241 - 0.009 1 0.3632 0.0045 0.0065 - 0.0020 0.0934 0.0057 0.0098 - 0.0041 0.1730 0.008 1 0.01 20 - 0.0039 0.1921 - 0.0020 - 0.0080 0.0060 0.2858 - 0.00 1 4 -0.0122 0.0 108 0.41 36 side A : 5 % (w/w) DMSO+ 0.5 rnol dm-3 H+CI- 0.0004 - 0.0028 0.0032 0.1036 0.0004 - 0.0042 0.0046 0.1460 - 0.0003 - 0.0044 0.0041 0.1660 side A: 5% (w/w) dioxan+ 1.0 rnol dm-3 R b T - side A: 5% (w/w) dioxan+0.5 rnol dm-3 Rb+C1- side A: 5% (wfw) DMSO+ 1.0 mol dm-3 K+CI- side A: 5% (w/w) DMSOfO.5 mol dm-3 K W - side A: 5% (w/w) DMSO+ 1.0 mol dm-3 H+C1- - 0.085 - 0.084 - 0.093 - 0.058 - 0.064 - 0.008 - 0.029 - 0.025 - 0.02 1 - 0.024 - 0.020 0.021 0.026 0.03 1 0.032 0.024 side A: 2.5% (w/w) glycine + 1 .O mol dmP3 Na+CI- 23 0.0105 1.349 - 1.244 0.1439 - 8.6 side A: 8.558% (w/w) allyl alcohol+0.5 rnol dm-3 K+Cl- side B: 10.001 % (w/w) allyl alcohol 17.5 0.275 0.0574 4.8 24 0.394 0.0792 5.0 48.25 0.890 0.1399 6.4 AnJAn, was extrapolated to t , = 0 and corrected to correspond to the system 8.847% (w/w) ally1 alcohol in side A. This gave Xn& = 2.7.1440 WASHBURN NUMBERS TABLE 2.-(continued) 0.75% 10% ally1 raffinosea 5% dioxan alcohol 5% DMSO 2.5% glycine - K+Cl- 10 8.1 2.7 1.7 Na+CI- RbfC1- H+CI- - - - - - 8.6 - - - - 5.7 - - 2.2 - - - a Ref.(1 1). THERMODYNAMICS AND WASHBURN NUMBERS (a) Previous determinations1 of Washburn numbers for alkali-metal chlorides have involved two stages. The thermodynamics of transfer of the salts from water to the mixed solvents had normally already been determined using cells with amalgam electrodes, cell (111) (III) Here m, = m,; m, is now in mol (kg mixed solvent)-'. Washburn numbers were then found by combining these results with measurements on cell (IV): (IV) In cell (IV) m, and m, are normally chosen to make (a+), = (a+),; see below. (b) At the relatively low concentrations of organic component used-here, ion-selective electrodes are expected to give reliable results, and in the present work the following cells were used instead of cell (111): (V) (VI) AE= EvI-Ev (24) Ag-AgC1 I MCl(m,), S I M(Hg) I MCl(m,), W I AgC1-Ag.Ag-AgCl 1 MCl(m,), W I MCl(m,), S I AgC1-Ag. G(M) I MCl(rn,), W 1 AgCl-Ag G(M) I MCl(m,), S I AgCl-Ag. For a few experiments m, was made equal to m,, as in cell (111); the e.m.f. when corrected for the asymmetry potentials of the glass electrodes is the same as would be obtained from cell (111) and was used in the same way. (c) In most cases the same solutions were used in cells (V) and (VI) as in cell (IV). This is the method originally described by Feakins;14 it simplifies the calculation of the Wash burn numbers. The e.m.f. of cell (IV) is given by E = (2RT/F) t, d In a _+ + (RT/F) ww d In aw. (25) JSW Here a+ is the mean ion activity of the electrolyte, referred to the molal standard state in purewater, a, is the activity of water referred to a standard state of pure water, and t , is the cationic transport number.1, = i++flx) In eqn (25) where f+ is the mean of t , on either side of the boundary and x a variable specifyingD. FEAKINS, R. D. O'NEILL, w . E. WAGHORNE AND A. J. I. WARD 1441 the position of a point in the boundary. In the present experiments t, varied negligibly across the boundary and and (a,), were equal or nearly so; this allows the term inf(x) to be neglected and eqn (25) becomes rw rw E = (2RT/F)i+ J S dlna*+(RT/F)J S w,dlna,. But - Thus writing W AE[eqn(24)] = (2RT/fl{ S dlna*. x = (RT/F)]ww,dlnuw. S E=-t+AE+x Choice of z (a+)s also makes the first term of eqn (26) small and means that t, need not be known precisely.Table 3 gives E, x and AE values from cells (1V)-(VI). Values of xo, obtained by extrapolation of x to infinite dilution,' are given in table 4. The AE values were treated in the usual way to give AE; values; these are shown in table 5. The Washburn numbers in table 6 were calculated-using the Raoult's law activity coefficients in table 7. Table 8 gives cationic transport numbers at infinite dilution determined as explained in Part 1 .' Table 9 shows values of nO, obtained by combining wO, with En;. ELIMINATION OF ASYMMETRY POTENTIALS We assume that the e.m.f. of a cell such as (V) with a glass electrode can be represented at a time t, after the immersion of the electrode as = WE&(a)+fa(t,) - (2RT/F) In (a+)%.- (28) It is assumed that is characteristic of the particular electrode a and is analogous to the same quantity with a classical electrode. The functionfa(tl) represents the tendency, small with the electrodes used here, for the potential of the electrode to drift with time. Suppose that we use a second electrode p in cell (VI), then sEp = %;(D) +fp(tl) - (2RT/F) In (a&):. (29) The cells are set up simultaneously and at the time t, the electrodes are transferred between the two cells. After a further time t, we have "EB = + f p ( t J - (2RVF) In (a*)% (30) = 'E;(a>+fa(t,)-(2RT/F)ln (a+);. (31) wEa-sEa = WE&(a)-SE0,(a)+fa(t,)-fa(t,)-(2RT/F)ln [(a*>%/(a,)El (32) wEp-sEp = WE;CB)-SE;(P)+.fB(fz)-fg(t,)-(2RT/F) In [(4w4;1 (33) Now = AEa (say) and = AEp (say).Normally t , was equal to t,, and with wE&(a) - SE&(a) = - sEz(p) = AE; (say) we expect AEa = AEB; the agreement was normally to kO.1 mV or better.1442 WASHBURN NUMBERS TABLE 3.-AE/mV FROM CELLS (v) AND (VI), EQN (24); E/mV AND )"mV FROM CELL (Iv) (a) 20% ally1 alcohol m,/mol kg-l m,/mol kg-l AE Li+Cl- 1.000 01 0.998 31 27.18 0.801 47 0.802 86 27.00 0.400 26 0.400 56 27.94 0.200 27 0.200 31 27.96 0.149 81 0.149 94 28.41 0.050 00 0.050 12 29.06 m,/mol kg-' m,/mol kg-' E X 1.299 46 1.001 39 0.501 09 0.199 90 0.147 90 0.100 06 0.050 06 Li+Cl- 0.829 39 0.99 0.98 0.619 77 1.26 1.24 0.291 65 1.53 1.54 0.110 86 1.86 1.88 0.082 32 1.84 1.87 0.054 10 2.35 2.26 0.024 49 3.54 2.05 m,/mol kg-l m,/mol kg-l AE E X 1.000 07 0.800 70 0.389 97 0.200 41 0.150 07 0.100 02 0.050 00 0.020 03 1.000 06 0.799 10 0.401 04 0.199 95 0.149 86 0.100 03 0.049 97 0.999 82 0.399 89 0.200 06 0.149 91 0.099 81 0.049 95 0.020 00 0.512 22 0.399 76 0.191 96 0.093 56 0.069 93 0.056 29 0.023 05 0.009 59 0.496 06 0.393 16 0.193 94 0.094 20 0.070 52 0.047 03 0.023 49 0.607 59 0.235 63 0.115 72 0.086 11 0.056 97 0.028 33 0.011 27 Na+Cl- 1.21 0.79 1.90 0.26 0.45 0.34 0.44 2.37 K+C1- - 0.66 - 0.47 - 0.07 -0.55 -0.51 - 0.59 -0.57 NHlCl- -0.30 0.28 0.32 0.26 0.24 0.43 0.27 1.27 1.56 1.48 2.35 2.42 2.58 2.76 2.1 1 1.73 1.74 1.85 2.39 2.42 2.68 2.94 1.43 1.37 1.48 1.59 1.64 1.74 1.87 1.72 1.86 2.22 2.45 2.60 2.71 2.93 3.05 1.41 1.51 1.81 2.12 2.17 2.39 2.66 1.28 1.51 1.64 1.72 1.76 1.95 2.01D.FEAKINS, R, D. O'NEILL, w .E. WAGHORNE AND A. J . I. WARD 1443 TABLE 3.-(continued) (6) 5% glycine m,/mol kg-l rn,/mol kg-l AE E X 0.199 98 0.160 08 0.119 93 0.100 06 0.080 01 0.049 95 0.030 01 0.010 00 0.199 96 0.160 01 0.120 05 0.010 04 0.079 99 0.050 09 0.030 04 0.010 01 0.199 97 0.158 84 0.123 04 0.102 29 0.080 14 0.044 02 0.030 35 0.010 16 0.199 94 0.157 83 0.119 26 0.098 31 0.080 50 0.050 38 0.029 87 0.204 49 0.163 78 0.123 82 0.102 82 0.082 83 0.052 02 0.031 01 0.010 47 0.204 93 0.166 23 0.124 11 0.103 62 0.083 59 0.052 59 0.031 76 0.010 71 0.206 18 0.164 13 0.124 66 0.103 54 0.082 50 0.051 61 0.030 75 0.010 05 0.204 99 0.164 05 0.123 55 0.103 11 0.083 88 0.053 89 0.031 66 Li+Cl- - 1.02 - 0.63 -0.50 - 1.05 - 1.23 - 0.93 - 1.66 - 1.09 Na+Cl- 0.02 0.44 -0.14 -0.17 0.07 -0.11 - 0.09 -0.19 K+Cl- 0.65 0.55 - 0.69 - 0.84 - 0.39 5.46 - 1.79 - 3.74 0.74 1.05 0.57 0.96 0.52 1.32 0.39 Cs+Cl- 0.05 0.09 0.04 0.16 0.14 0.19 0.41 0.35 0.04 -0.1 1 0.10 0.1 1 0.06 0.1 1 0.14 0.17 -0.21 -0.13 0.40 0.53 0.28 - 2.62 1.02 1.95 -0.24 -0.41 - 0.22 -0.39 -0.15 - 0.53 -0.10 - 0.26 -0.11 -0.12 -0.17 - 0.25 -0.10 -0.12 - 0.0 1 0.05 0.06 0.05 0.05 0.09 0.06 0.10 0.10 0.1 1 0.14 0.06 0.12 0.09 0.03 0.15 0.13 0.13 0.11 0.06 0.09 0.11 0.13 0.09 TABLE 4.-vALUES OF Xo/mV AT 25 "c Xo/mV interval water to : Li+Cl- Na+Cl- K+CI- Rb+Cl- Cs+Cl- NHaCl- 20% ally1 alcohol 2.46 3.21 2.85 - 2.09 - - 0.09 - 5% glycine -0.01 0.08 0.11 10% dioxana 1.12 1.21 0.88 -0.04 -0.12 - a Ref.(3).1444 WASHBURN NUMBERS TABLE 5.-vALUES OF AEE/mV AT 25 OC AEi/mV interval water to : Li'Cl- Na+Cl- K+Cl- Cs+Cl- NHiCl- 20% allyl alcohol 32.1 39.8 37.9 - 29.8 5% glycine - 4.92 -4.80 - 4.45 -4.34 - TABLE VALUES OF w&/mol Faraday-' w",mol Faraday-l intervala water to : Li+Cl- Na+Cl- K+C1- RbW- Cs+W NH,+Cl- H+C1- 20% allyl alcohol 1.34 1.83 1.70 - - - 5% glycine 0.00 0.15 0.18 - - 10% dioxanb 2.01 2.17 1.58 -0.08 -0.21 - - 10% DMSO" 0.87 2.24 1.50 2.01 1.35 - 1.18 - 0.15 - 0.48 at 1.4% raffinosed 2.3 1.3 0.7 - 0.3 0.8 0.4 a For comparison with En& (table 2) the w& are assumed to be applicable to the mid-point of the interval, e.g.at 10% allyl alcohol; ref. (3); ref. (4); ref. (12). TABLE 7.-RAOULT'S LAW ACTIVITY COEFFICIENTS AT 25 OC species fw 10% dioxana 20% allyl alcohol6 10% DMSO" 5% glycined 1.0040 1.007 0.998 0.989 a Ref. (3); M. Ewert, Bull SOC.Chim. Belges, 1936, 45, 493; ref. (4); H. D. Ellerton, G. Reinfelds, D. E. Mulcahy and P. J. Dunlop, J. Phys. Chern., 1964, 68, 398. TABLE 8.-cATIONIC TRANSPORT NUMBERS, t y , AT INFINITE DILUTION AT 25 OC solution L i T - Na+Cl- K T l - C s T - NH,fCl- water 0.336 0.396 0.49 1 0.501 0.490 20% (w/w) allyl alcohol 0.342 0.409 0.498 - 0.498 5% (w/w) glycine 0.326 0.390 0.488 0.495 -D. FEAKINS, R. D. O'NEILL, w. E. WAGHORNE AND A. J. I. WARD 1445 We note, though, that AE = gAEa + AEa> = AEZ -(2RT/F) In [(a*):/(a*)g] + Cfa(t1) -fa(tJ +fg(tJ -fg(tl)]- (34) The last term of eqn (34) also vanishes iffa(t) =fb(t) even if t , # t,; the mean of AEa and AEB may therefore represent an improvement on either value alone. EXPERIMENTAL Measurements of Washburn number and ionic transport number were as before.' Units with four interconnecting half-cells were used, which, in various combinations, enabled the measurement of two Washburn and two ionic transport numbers.A similar unit was used for glass-electrode measurements. With silver-silver chloride electrodes in position in two of the half-cells, the e.m.f. of cell (IV) was measured; this ensured the equilibration of these electrodes. Each silver-silver chloride half-cell could then be connected with a glass electrode half-cell in water or mixed solvent as appropriate, enabling the e.m.f. values of cells (V) and (VI) to be determined. Two glass electrodes (Corning monovalent cation electrodes) were prepared according to the manufacturers' instructions, then left soaking in 0.00 1 mol dmP3 solutions of the appropriate alkali-metal chloride overnight.They were rinsed with the cell solutions and introduced into their half-cells. After 30 min, connecting taps between glass and silver-silver chloride half-cells were opened for long enough to record the readings of e.m.f. of cells (V) and (VI). The glass electrodes were then removed and interchanged between the cell compartments after appro- priate washings; the e.m.f.s were again measured after 30 min. They were treated as explained above to eliminate asymmetry and time-dependent potentials. Cells with glass electrodes were interfaced to an impedance-matching device (Knick, Berlin) interfaced in turn to the Hewlett-Packard 3450A multi-function meter used as a digital voltmeter .DIFFUSION MEASUREMENTS Most of the details are due to Mills and W00lf.l~ The diffusion cell was mounted in a water-bath at 25.000+0.005 O C , * itself kept in a water-bath at 24.4k0.1 O C . The four pumps used to circulate the water, and the stirrer-motor for the cell, were mounted on the laboratory wall. The thermostat baths rested on a granite slab supported on an oil-drum filled with water to reduce vibrations. The design of the cell was that of Stokeslj although slightly simplified. The cylindrical cell was divided into upper and lower compartments (50 cm3) by a 4 cm, no. 4, sintered glass disc. In operation, stirrers made of lengths of iron wire encased in glass just touched the diaphragm above and below and were rotated (1 revolution per s) by magnets fixed to the external stirrer motor. The cell-holder was designed to reproduce the position of the cell with respect to these magnets.Runs involving a solution of salt in mixed solvent initially separated from mixed solvent of the same composition illustrate the general procedure. The mixed solvent, being the less dense, was used to fill the upper compartment and the frit, and the electrolyte solution the lower compartmen t. The compartments were filled in such a way as to minimise thermal gradients in the cell at the start of the experiment; this included taking the solutions from a bath at 25.05 "C where they had stood for 1-2 days to remove excess dissolved air. After diffusion, the solution (diffusion solution) in the upper compartment was removed with a pipette and titrated conductometrically against a silver nitrate solution itself just standardised against the original electrolyte solution.This gave An,. To determine the change in solvent composition a solution was prepared having the same molar concentration of electrolyte as the diffusion solution, but with the original proportions * The Celsius temperature is the excess of the thermodynamic temperature over 273.15 K.1446 WASHBURN NUMBERS of water and non-aqueous component. The difference in refractive index between this and the diffusion solution was measured using an interferometer (VEB Carl Zeiss Jena model LI3). The interferometer had previously been calibrated with solutions of known composition. Between two solutions of different solvent composition but of the same molar concentration of electrolyte the refractive index difference is, over a small range of composition, both independent of electrolyte concentration and also linear in M,.Glycine (Merck) was recrystallised twice from conductivity water. Ally1 alcohol (prop- 2-en-1-01) (Hopkin and Williams Synthesis Grade) was dried (CaSO,) then fractionally distilled. Salts were Johnson Matthey ' Specpure' or Merck ' Suprapur' grades and hydrochloric acid B.D.H. 'CVS hydrochloric acic N'. Conductance water,16 dioxan" and DMS04 were as before. DISCUSSION The n& values for the various ion constituents are shown in table 9. The systems have been selected from the results available to correspond to the lowest concentration of non-electrolyte studied in each case.In principle, if several w$ are available with one common ion, only one Zn& is needed to obtain all the ionic n&. If a second Zn& is available, tests of consistency are possible; the alternative sets generated by using nO, for Rb+Cl- for 5% dioxan and for H+Cl- for 5% DMSO are shown. The differences between these and the sets based on EnO, for K+Cl- are equivalent to an average error of 0.35 on n$. This is also roughly what would be expected from the scatter of results in table 2. We shall assume a notional precision of 1. TABLE 9.-NUMBER OF MOLES OF WATER TRANSPORTED WITH RESPECT TO THE ORGANIC COM- PONENT AT INFINITE DILUTION, n&/moll mol;' nk/mol, mol;' raffinose dioxan ally1 alcohol DMSO gl ycinea ion 0.75% 5% 10% 5% 2.5% Li + Na+ K+ Rb+ cs+ NHt H+ c1- 15.5 11.0 9.7 9.2 5.6 5.7 2.2 2.0 - - - - - 1.4 4.2 2.4 ~ ~~~ ~ 3.5 1.2 - 7.3 4.1 4.6 - 5.0 2.7 2.4 - 3.5 3.3 2.0 - 0.7 - - - - - - 2.1 - - - 0.3 - 0.7 - 3.6 The above are all based on Zn& for K+CI-. The absolute accuracy (notional) is & 1 ; the relative accuracy among the cations is much better.The following sets were found using Zn& for Rb'Cl- for 5% dioxan and Zn& for H+Cl- for 5% DMSO. n&/moll mol;' organic component Li+ Na+ K+ Rb+ Cs+ H+ CI- 2.9 - dioxan 5% 12.0 9.8 6.1 2.8 2.5 DMSO 5% 0.0 3.7 1.9 2.7 1.4 -0.9 -1.3 a Data from ref. (9) give En& = 5 +_ 1 for K+Cl-. This would raise the above values by ca. 1 unit.D. FEAKINS, R . D. O’NEILL, w . E. WAGHORNE AND A. J. I. WARD 1447 In 1959 Miller’l determined the phenomenological coefficients in the ternary system raffinose+water+K+Cl- and gave sufficient information to enable Zn& to be calculated at a raffinose concentration of 0.75 % (w/w).Previously Longsworthla had determined w& at a mean raffinose concentration of 1.4% (w/w). Any variation in w& is normally small over such a range and the values were taken to apply also at 0.75% and the individual n& calculated. The results will be discussed in more detail in later publications, but some preliminary observations can be made. When only the Washburn numbers were available it was difficult to compare the effects of the various cosolvents on the solvation of the ions, but with the individual n& much more progress can be made. We recall3 that (35) independently of any model of the flow process or solvation.A( = v,/v,) is the molar ratio of solvent components in the bulk mixture and I( = Nw/Ns) the corresponding ratio in the transported solvent; N = Nw + N,, and is the average number of solvent molecules of both kinds carried by the ion. The ratio 1/A is a measure of the extent of preferential solvation and If preferential solvation is by water, l/A > 1 and 0 < n& < N ; in the limit of strong preferential solvation by water, n& = N . If preferential solvation is by the non-aqueous component, l/A < 1, n& < 0; in the limit of strong preferential solvation by the non-aqueous component, ng = N . The value n& = 0 means that 1 = A, i.e. that the ion carries the mixed solvent exactly in the proportions present in the bulk.In the present highly aqueous media the ions will move much more water than com- ponent 2 even if 1/A -c 1. Consider now the behaviour of systems at high concentrations (A) of water. As 1/n+o ng = M l -(A/,)] (37) In an admittedly oversimplified mass-action treatment3 All is independent of A but is related to an equilibrium constant which depends on the relative strengths of interaction of the two solvent species with the ion of interest. Thus n& would not be expected to approach a common value for a given ion, independent of the non- electrolyte, as 1/A -+ 0, but rather to be characteristic of each solvent system. The following model was developed in more detail in earlier parts. For simplicity we shall discuss only cation solvation.Each organic molecule considered here has a suitable lone pair of electrons which can interact with a cation in an ‘acid-base’ type of interaction and thus compete with water for the primary solvation of the cation. Consider first the ground state of the ion or the equilibrium distribution of solvent molecules around the ion. Evidence from gas-phase studies or from the thermodynamics of ion solvation suggests that all the species here are expected to be more ‘basic’ than water in ionic s o l ~ a t i o n . ~ ~ ~ This does not necessarily mean that preferential solvation is by the organic component. The difference in strength between the ion-molecule interactions might be reduced by averaging of the basicity over both components of the mixture by a co-operative mechanismlg and the generally smaller size of water favours its incorporation in the primary solvation shell.Even where N1448 WASHBURN NUMBERS (see later) is large enough to correspond to the movement of more than one shell, the first is likely to be dominant in determining l / A . When the ion moves under the influence of a gradient in electrical or chemical potential another effect becomes important. Here it is helpful to envisage the equilibrium distribution for a given ion as being an average over a number of distributions of different energies for all the ions of that type. The co-operative mechanism referred to above may have the effect of making quite different distributions rather close in energy. Some of these distributions may lead to lower activation energies for flow than others and ions involved in these will carry the current preferentially. In particular, ion-water complexes, being the smaller, may move more readily than complexes incorporating organic molecules.The last effect may be particularly important in the key raffinose+water system. Earlier it was suggested that even though cations may well interact strongly with raffinose at equilibrium, they will be unlikely to move it on flow. Thus the transition state involves marked preferential solvation by water. Then n& approaches N closely [eqn (35)]; and if so low a concentration of raffinose has little effect on the structure of water, then the N are also the numbers of molecules of water transported by the ions in pure water, that is, the dynamic solvation numbers. TABLE IO.-VALUES OF 112 ASSUMING N = nO, FOR RAFFINOSE+ WATER ion dioxan 5% allyl alcohol 10% DMSO 5% gl ycine 2.5% Li+ 3.4 Na+ K+ CI- 2.3 - - 1.3 1.7 1.9 0.9 1.1 1.9 1.6 0.9 0.69 0.66 0.62 0.54 N cannot be less than the highest value of n& found for any system as 1/J.-+ 0. For the moment, then, the best available Nfor pure water are then; for the raffinose +water system. We note that an earlier assumption3 of N(Li+) = 7 was wrong, and in general the ions move many more solvent molecules than hitherto assumed. Thus N(C1-) = 4, and N(K+) = 6; values close to zero had been suggested earlier. The earlier arguments were speculative and can now be ignored. Turning now from raffinose to the other non-aqueous components, we see that in the series dioxan, allyl alcohol, DMSO and glycine, there is an increasing tendency for the non-aqueous component to be transported.In the case of dioxan, there is a significant drop in n& only for Li+. The incorporation of allyl alcohol is, however, significant for all three cations studied, perhaps because of its less demanding steric requirements, and DMSO emerges as a strong ligand, particularly for Li+ and H+, the latter actually transporting DMSO in preference to water. This result, which is in keeping with n.m.r. evidence, had been reached earlier4 though on weaker grounds. All ions transport glycine in preference to water. Glycine is a zwitterion and the fully developed charges at each end of the molecule are likely to interact strongly with the ions. In all cases, the degree of preferential solvation by either component is small. ThisD. FEAKINS, R. D. O’NEILL, w. E. WAGHORNE AND A. J. I. WARD 1449 may be seen by calculating the ratios l / A with the assumption that N = nO, for the raffinose+water system. The results, in table 10, show ratios that differ little from unity. We thank Prof. M. Chemla, Dr J. M’Halla and Dr T. H. Lilley for discussions. Dr Elvira Kugler kindly provided details of some of the early experiments in Budapest. We thank the Irish Department of Education and University College, Dublin, for scholarships (to R. D. OW.) D. Feakins and J. P. Lorimer, J. Chem. SOC., Faraday Trans. I , 1974, 70, 1888. J. N. Agar, in The Structure of Electrolytic Solutions, ed. W. J. Hamer (Wiley, New York, 1959), p. 218. D. Feakins, K. H. Khoo, J. P. Lorimer, D. A. O’Shaughnessy and P. J. Voice, J . Chem. Soc., Faraday Trans. I , 1976, 72, 2661. D. Feakins and D. A. O’Shaughnessy, J. Chem. SOC., Faraday Trans. I , 1978, 74, 380. D. Feakins, E. de Valera, P. J. McCarthy, R. D. O’Neill aqd W. E. Waghorne, J. Chem. SOC., Chem. Commun., 1978, 218. [Note that the numbers given in this paper are incorrect and are corrected in ref. (6) and in the present paper.] D. Feakins, R. D. O’Neill, W. E. Waghorne and A. J. 1. Ward, J. Chem. SOC., Chem. Commun., 1979, 1029. ’ T. Erdey-Gruz, A. Hunyar, E. Pogany and A. Vali, Acta Chim. Acad. Sci. Hung., 1948, 1, 7; T. Erdey-Gruz, Transport Phenomena in Aqueous Solutions (Hilger, London, 1974), p. 486 and references therein. G. Ortmanns, Ber. Bunsenges Phys. Chem., 1965, 69, 2336. L. A. Woolf, D. G. Miller and L. J. Gosting, J. Am. Chem. Soc., 1962, 84, 317. lo J. M’Halla, P. Turq and M. Chemla, J. Chem. SOC., Faraday Trans. 1, 1981, 77, 465. l 1 D. G. Miller, J. Phys. Chem., 1959, 63, 570. l2 L. G. Longsworth, J. Am. Chem. SOC., 1947, 69, 1288; [see also ref. (3)J. l 3 R. Mills and L. A. Woolf, The Diaphragm Cell (Australian National University, Canberra, 1968). l 5 R. H. Stokes, J. Am. Chem. SOC., 1950, 72, 763. D. Feakins, J . Chem. SOC., 1961, 5308. D. Feakins and P. J. Voice, J. Chem. SOC., Faraday Trans. I , 1973, 69, 171 1. H. P. Bennetto, D. Feakins and K. G . Lawrence, J. Chem. SOC. A, 1968, 1493. L. G. Longsworth, J. Am. Chem. SOC., 1947, 69, 1288. l9 D. Feakins and P. Watson, J. Chem. SOC., 1963, 4734. (PAPER 1/61 1)