Activity Coefficients of Hydrochloric Acid in Mixtures with Potassium Chloride in Methanol+ Water Solvents from Electro- motive Force Measurements at 298.15 M BY CHAN CHEE-YAN" AND KEAN H. KHOO Department of Chemistry, University of Malaya, Kuala Lumpur, Malaysia Received 2nd July, 1973 E.m.f. measurements of the cell, PtlHz I HCl(rnl), KCl(m,), methanol(X), waterlAgClIAg, have been made at 298.15 K for solvent compositions X = 0, 10,30,40 and 45 % (w/w) of methanol, the total ionic strength of each solution being 1 mol kg-'. The logarithm of the mean ionic molal activity coefficient of hydrochloric acid was found to vary linearly with potassium chloride molality for the systems in which the solvent mixture contained 0, 10 and 30 % methanol. For methanol composition above 30 %, the activity coefficient of the acid was a quadratic function of the salt concentration.Secondary medium effects are discussed in relation to differences in specific ionic interactions for the different electrolyte mixtures in water and in the mixed solvents. It has been shown 1 * from precise emf. measurements that for the system (HCl, NaCl, methanol, water) at constant ionic strength of 1 mol kg-1 the mean ionic molal activity coefficient, y of hydrochloric acid varies linearly with sodium chloride molal concentration according to eqn (1) at each solvent composition, ranging from 0 to 60 % (w/w) of methanol, at constant temperature : (1) where 1 and 2 refer to the x i d and the salt respectively. 7; is the mean ionic molal activity coefficient of the acid at the same total ionic strength but in the absence of the salt, and uI2 is an empirical parameter.A significant feature found for this system is that the parameter a I 2 is the same for each solvent mixture at constant temper- ature. It would be reasonable in this case, according to H ~ n e d , ~ to assume that the parameters in eqn (2), which represents the variation of the activity coefficient of the salt, would also be independent of solvent composition : Furthermore, this would lead to eqn (3).2* log y1 = log y;-a,,nz, log y 2 = log y;-a2,ln1 -pzlm:. (2) where m is the constant total ionic strength. Therefore, if the activity coefficient of one of the electrolytes is known in the methanol+water mixture, that of the second electrolyte may be calculated using eqn (3) from the activity coefficient ratio determined in water alone as the solvent. Harned reported that the values of the activity coefficients of lithium chloride and sodium chloride in methanol + water mixtures calculated by this method were in good 2728 ACTIVITY COEFFICIENTS OF HC1 AND NaCl agreement with experimental results but those for potassium chloride were not.Very few e.m.f. data for systems involving mixtures of electrolytes in mixed solvents are available for testing the general applicability of Harned's method. The present work gives the reason for the non-applicability of Harned's computation for t hc systems involving hydrochloric acid, potassium chloride, methanol, and water. The influence of methanol+ water solvent structure on the parameters attributed to specific ionic interactions is also discussed.EXPERIMENTAL E.m.f. measurements were made using a Pye Universal potentiometer with a Pye Scalamp galvanometer as a null detector. The experimental cell used is a slight modification of the one used by Kh00.~ The experimental technique used was a combination of that used before and that used by Dowries.' Both silver-silver chloride and hydrogen electrodes were used in pairs and were similar to those used by Downes. They were prepared, stored and used in the same manner as before.4* The bias potentials of the silver-silver chloride electrodes used in the measurements were & 5 x V, or less, with reference to an aged reference silver-silver chloride electrode stored in 0.1 mol kg-1 hydrochloric acid aqueous solution. Each reported e.m.f.reading given in table 1 was the mean of four readings obtained from a pair of silver- silver chloride electrodes and a pair of hydrogen electrodes. The four readings of each set at any given time were within +3x The aqueous hydrochloric acid used was the constant-boiling mixture doubly-distilled from the A.R. grade acid. A.R. potassium chloride was recrystallised before use. Anhydrous methanol was obtained from A.R. methanol by distillation as before.6 Distilled water obtained from an all-glass still was re-distilled over alkaline potassium permanganate solution and the water used in the experiments was obtained by re-distillation of this conden- sate. Hydrogen and nitrogen purification were as before except that instead of using copper filings heated at 450°C for the removal of traces of oxygen, we used a commercial catalyst, labelled BASF BTS catalyst, heated at 140°C.The BTS catalyst proved to be just as efficient. Corrections of measured e.m.f. readings to a hydrogen partial pressure of 1 atm (101 325 N m-2) were made using data interpolated from the vapour pressure corrections at different temperatures tabulated by Akerlof et al.' for methanol+ water mixtures with an electrolyte ionic strength of 1 mol kg-l. The temperature was maintained at 298.15 Kk0.01 K. SolubiIity limitations of potassium chloride in the methanol+ water mixtures restricted the range of methanol composition to 0-45 % in this work. V of each other. RESULTS AND DISCUSSION The e.m.f. data are given in table 1, where Eis the e.1n.f.of the cell, PtlH21HCl(rnl), KCl(rn2), methanol(X), waterIAgClIAg, corrected to a hydrogen partial pressure of 1 atm, and m, +m, = 1 mol kg-l. The best-fit values of the parameters, a I 2 and Pl2, and of E" for each methanol composition, A', are computed by the method of least squares using eqn (4). Assuming for each mixture that we have log Y1 = 1% Y ; - % 2 ~ v - - P 1 2 4 , Y = ES2klog m, = 2ka,,m2 +2k/?,,m% + E" (4) where E" = (E&IArfC1-2k logy;), k = 0.059 158,' and EGIAgCl is the standard electrode potential in the given solvent. Table 1 gives values of AY, where A Y = Y(expt.) - Y(ca1c.). The values of Y(ca1c.) were from eqn (4) and the best-fit valuesC . - Y . CHAN AND K. H. KHOO 29 of a12, Pl2 and E". Values of E&iAgCI for each solvent mixture given in table 2 were derived from the best-fit values of E" using y'; data obtained elsewhere.s These agree favourably with those reported by Maya Paabo, Bates and Robinson.8 TABLE 1 .-E.m.f.DATA FOR THE SYSlEM (HCl(ml), KCl(mz), METHANOL(X), WATER) AT 298.15 K ; ml+rn2 = 1 mol kg-1 1 o5a ri 105a ri 1 0 5 ~ Y/ EIV Y(expt.)/V V ~ ~ 1 2 1 inolkg-1 E/V Y(expt.)/V V E/V Y(expt.)/V V X = O % x= 10% X = 3 0 % 0 0.1 0.3 0.4 0.5 0.7 0.8 0.9 0 0.1 0.3 0.4 0.5 0.7 0.8 0.9 0.233 20 0.236 53 0.244 27 0.248 83 0.254 23 0.268 54 0.279 71 0.298 13 0.233 20 2 0.233 82 0 0.235 11 0 0.23642 3 0.238 36 4 0.238 97 1 0.23571 -4 0.237 61 -6 0.227 90 0,227 90 -3 0.21998 0.223 43 0.239 13 0.229 97 0 0.231 46 0.243 83 0.23071 6 0.23620 0.249 15 0.231 34 2 0.241 65 0.274 71 0.233 36 0 0.267 58 0.293 20 0.234 04 0 0.286 15 0.263 56 0.232 63 -5 0.256 39 0.216 66 0.220 18 0.228 07 0.232 91 0.238 34 0.253 12 0.264 51 0.283 22 0.216 66 -4 0.21475 0.21475 2 0.21747 5 0.218 19 0.21548 -1 0.21891 -3 0.22624 0.21707 -1 0.22053 -2 0.23654 0.218 73 -1 0.222 19 -6 0.251 45 0.220 51 3 0.22406 1 0.281 44 0.222 28 -2 0.219 79 6 0.223 16 2 0.21998 3 0.222 30 0 0.22308 0 0.22546 3 0.226 23 1 0.220 72 -2 0.223 84 -3 0.22699 - 1 TABLE 2.-vALUES OF THE PARAMETERS, CClz and /?I*, AND EiglAgC1 Xi:< crlz/mol 1 kg P12/mol-2 kg2 E"IV Y F 8 E 2 g InscllV (0.222 34) 10 0.0573+0.0005 0 0.227 93 f O.OO0 03 0.783 0.215 4 (0.215 5) (0.203 1) 0.009 92 0.216 70 0.683 0.197 1 (0.196 8) 0.214 73 0.668 0.194 0 (0.194 1) 0 0.0543+0.0004 0 0.233 1 8+ 0.000 03 0.809$- 0.001 0.222 29 30 0.0662+ 0.0002 0 0.219 95+0.000 01 0.715 0.202 7 40 0.0601 45 0.0636 0.008 28 ft EAglAgcl values in parentheses are from ref.(8). HARNED'S METHOD Values of the parameters, a1 and p1 2 , varied significantly with solvent composition (see table 2). This clearly indicates that Harned's method as discussed previously cannot be applied to the system (HCI, KCI, methanol, water) as the critical assumption of constancy in cxl2 and Pl2 for the various solvent mixtures is not valid in this case. From tables 1 and 2 it is seen that the logarithm of the activity coefficient of hydrochloric acid is a linear function of potassium chloride molality for X = 0, 10 and 30 % methanol, but above 30 % methanol it is a quadratic function of the salt30 A C T I V I T Y COEFFICIENTS OF HCl AND NaCl molality. Akerlof et al.' have shown that the linear equation for hydrochloric acid in the system (HCl, NaCl, methanol, water) at constant temperature fitted their experi- mental data over the whole range of X = 0-60 % methanol.In view of this fact, the deviations from linearity as observed for the system (HCl, KCl, methanol, water) for methanol composition above 30 % could possibly indicate that at the higher methanol compositions, ion association between potassium and chloride ioiis may be just significant but is slight enough to be accounted for by the inclusion of the Dl2n?; term as in eqn (4) where no association is assumed. SECONDARY MEDIUM EFFECTS The secondary medium effect for a given electrolyte in a given electrolyte-mixed solvent system is defined by the quotient J / ~ ? , where the subscripts w, s denote water and the mixed solvent, respectively. We have shown that for hydrochloric acid at constant ionic strength in the systems studied, 1% wY1 = 1% wY;-wa12f1l2 ( 5 ) and We can then write X/ %(w/w) methanol FIG.1.-Plots of -A(or12, Pl2, ~ n ~ ) ~ , ~ against solvent composition X . A, m2 = 0 mol kg-' ; B, m2 = 0.3 rnol kg-' ; C , m2 = 0.5 mol kg-' ; D, uz2 = 0.7 mol kg-' ; E, m2 = 0.9 mol kg-' ; F, m2 = 1 mol kg-', trace concentration of HCl.C . - Y . CHAN AND K. H. KHOO 31 The sum of the terms on the right in eqn (7) gives the difference between the second- ary medium effect for hydrochloric acid in the presence of a given concentration of potassium chloride at constant total ionic strength and that for the acid alone at the same total ionic strength for the same solvent.This quantity, denoted by A(alz, Pl2, m2)w,s, would be some function (though uncertain) of the specific ionic interactions ''9 of the two electrolytes in water and in the mixed solvent. Its variation with solvent composition for different potassium chloride concentrations, m2, are given by the plots in fig. 1. The plots show marked inflexions in the region of methanol composi- tion between X = 25 and 40 %. Solvent structure changes with composition in mixed solvent systems and effects of such changes on certain properties (e.g. acid-base behaviour, ionic transport) of single electrolytes dissolved in alcohol+water mixtures have been known l 2 9 l3 to result in observed extrema in the variation of these properties with solvent composition.The extrema are considered to occur in the region of composition in which the order- disorder relationships 12* l3 in the structure of the mixed solvent are undergoing the most pronounced changes. Similar solvent structural effects are manifested by the inflexions in the plots in fig. 1. Ionic interactions have been conveniently, but arbitrarily, separated into non- specific ionic interactions of the type considered in the well-known Debye-Huckel theory for very dilute solutions and specific ionic interactions including ion-solvent interactions different from the Debye-Huckel type.l' Thus in eqn (8) which gives the activity coefficient for hydrochloric acid in a mixed so1vent,14 the term logyyH is assumed to account for non-specific ionic interactions and the term bTm for specific ionic interactions.log 7 1" = - Am'/( 1 + 4.3Bmf) - log (1 + 0.002mm) + bim = log yYH+b$,2 (GI where A , B are the Debye-Huckel constants on the molal scale, M the mean molecular weight of the solvent and bi is the empirical specific ionic interaction parameter for hydrochloric acid. From eqn (7) and (8), we can write where m = rn, +m2 = 1 mol kg-l. Thus the secondary medium effect for hydro- chloric acid is given by the sum of the contributions of the effects of change in solvent composition on the Debye-Huckel non-specific ionic interactions and the specific ionic interactions in the electrolyte mixture. Values of for the various methanol compositions have been computed using data on the values of A , B, M , and 7; reported el~ewhere,'~ interpolating data where necessary.Fig. 2 shows that no marked characteristics are observed for the variation of log(wyyH/sy:H) with solvent composition, but for - A(bi, a12, Pl2, m2)w,s versus solvent composition the plots show distinct maxima in the same region of solvent composition as for the plots in fig. 1 where inflexions occurred. The positions of the maxima appear to be shifted in the direction of higher methanol concentration with increasing concentration of potassium ions. Thus it appears that solvent structural effects are reflected in the parameters used to account for specific ionic interactions but not in the commonly used deb ye-Huckel term whose variation with solvent composition is considered as merely a variation with solvent dielectric constant and density.32 ACTIVITY COEFFICIENTS OF HCl AND NaCl 0 10 2 0 3 0 4 0 5 0 X] %(w/w) methanol FIG.2.-A-G, plots of -A@;, a12, Pl2, m2)w,sagainst solvent composition X . A, m2 = 0 mol kg-' ; B, mz = 0.1 mol kg-' ; C, m2 = 0.3 mol kg-l ; D, m2 = 0.5 rnol kg-' ; E, m2 = 0.7 rnol kg-' ; F, m2 = 0.9 mol kg-I ; G, m2 = 1 mol kg-', trace concentration of HCI. 0- . -, plot of Iog(,yya/ SyyH) against solvent composition X. We thank Mr. W. W. Koh and Mr. S. H. Yeow for their assistance. G. Akerlof, J. W. Teare and H. Turck, J. Amer. Chetn. Soc., 1937, 59, 1916. H. S. Harned and R. A. Robinson, Multicomponent Electrolyte Solutions (Pergamon, Oxford, 1968), p. 96. €3. S. Harned, J. Phys. Chem., 1962, 66, 589. C. J. Downes, J. Phys. Chem., 1970, 74, 2153. D. Feakins and K. H. Khoo, J. Chem. SOC. A , 1970, 361. 1969), p. 469. Maya Paabo, R. G. Bates and R. A. Robinson, Anal. Chem., 1965,37,463. ref. (7), p. 354. York, 1967), p. 515. ref. (2), p. 10. and Francis, London, 1968), p. 59. 4K. H. Khoo, J. Chem. SOC. A, 1971, 1177. ' R. A. Robinson and R. H. Stokes, Electrolyte Solutions (Butterworths, London, 2nd edn., l o H. S. Harned and B. B. Owen, The Physical Chemistry of Electrolytic Solutions (Reinhold, New l2 R. G. Bates, Hydrogen-Bonded Solvent Systems, ed. A. K. Covington and P. Jones (Taylor l 3 F. Franks and D. J. G. Ives, Quart. Reu., 1966,20, 1. l4 ref. (lo), p. 472. l5 R. G. Bates and R. A. Robinson, Chemical Physics of Ionic Solutions, ed. B. E. Conway and R. G. Barradas (Wiley, New York, 1966), p. 211.