Transport in Aqueous Solutions of Group IIB Metal Salts at 298.15 K Part 6.-Irreversible Thermodynamic Parameters for Zinc Chloride and Verification of Onsager’s Reciprocal Relationships BY ANDREW AGNEW AND RUSSELL PATERSON* Department of Chemistry, University of Glasgow, Glasgow G12 SQQ Received 13th April, 1978 The isothermal vectorial transport properties of zinc chloride (conductance, transport number and salt diffusion coefficients) have been measured over the concentration range 0.1-3.5 mol dm-3 at 298.15 K. These data have been used to calculate mobility (&) and resistance (&) coefficients, using irreversible thermodynamic theory. Hittorf and concentration cell estimates of transport number have been used to verify the Onsager reciprocal relationships. The effects of self complexing in zinc chloride are illustrated by comparison with zinc perchlorate and other group IIB metal halides for which data are available. There is a scarcity of irreversible thermodynamic analyses on the transport properties of 2 : 1 salts, consequently there are few comparisons which can be made between pairs of salts, to illustrate the effects of self-complexing. Previous papers on cadmium iodide 1-5 showed unusual concentration dependence of transport coefficients.Because this salt is very strongly complexed, these coefficients could be predicted, at least in dilute solution, from its stability constants and by application of Onsager’s limiting laws expressed in irreversible thermodynamic form.6 Zinc chloride is a much less complexed salt ’ and there is no possibility of predict- ing its transport properties by such theories. It is, therefore, instructive to compare its transport properties with those of zinc perchlorate, which is completely dissociated at concentrations up to 3.0 mol dm-3.Although conclusions must be qualitative, complexing enhances all three mobility coefficients (La,, Lbb and Lab = &,a) in con- centrated solutions, while in dilute solutions up to 0.2 mol dm-3 when zinc chloride is almost completely dissociated the two salts are very similar, as might be expected. Certain features of the concentration dependence of self complexed salts of the group IIB halides, most dramatically illustrated by cadmium iodide, still remain but to a reduced degree for zinc chloride and also cadmium chloride which was studied previously by McQuillan.Experimental measurements of electrical conductance, salt diffusion coefficients and transport numbers have been made in the range 0.1-3.5 mol dm-3 as 25°C. It is shown that transport numbers estimated by Hittorf and concentration cell measure- ments agree within experimental error and consequently that the Onsager reciprocal relationships (Lab = Lba) hold in this system. EXPERIMENTAL Zinc chloride solutions were prepared from spectroscopically pure zinc oxide and AnalaR hydrochloric acid by the method described previously. ’ The stoichiometry of the salt solution was verified by analysis for zinc and chloride to a precision of kO.05 % for each 2896A . AGNEW AND R. PATERSON 2897 element. Density measurements were made and relationships between density, molarity (mol dm-3) and molality (mol kg-I) expressed as polynomials, table 1.Electrical conductance, salt diffusion coefficients and transport numbers were measured in the range 0.1-4.0 mol d ~ r t - ~ by the methods described earlier for cadmium iodide and zinc per~hlorate.~ Conductances were precise to k0.07 % due largely to uncertainties in chemical analysis, Transport numbers were determined by both Hit torf and concentration cell measurements : the latter by the technique described in the previous paper,g the former using the cell devised by Pika1 and Miller lo and used for cadmium iodide studies.l Since both silver-silver chloride and zinc amalgam electrodes are availableY7 a pair of each of these electrodes was used in each half cell.The combinations of measured cell potentials thus available allowed transport numbers for both zinc and chloride to be obtained inde- pendently and thus the internal self consistency of calculation methods could be verified. Y X P C mlC C ~ " ~ 1 0 5 c+ 11~x105 c+ K ~ 1 0 3 c K ~ 1 0 3 c K ~ 1 0 3 c Ta EB Ta Tb Tb t+ C f4 In m f4 In m n i - 0 TABLE PO POLYNOMIAL EXPRESSIONS OF THE FORM Y = aiXi Y X P C m l c C ~ " ~ 1 0 5 c+ ~ " ~ 1 0 5 c+ K ~ 1 0 3 c Kx103 c K ~ 1 0 3 c Ta EB Ta EB # In m d In m ao 0.998 163 1.001 665 97 1.210 34 2.391 04 0.186 215 2.315 346 0.400 527 394 39.739 47 -0.0619 570 07 -0.591 500 235 1.067 168 72 0.368 596 453 0.804 233 821 0.888 220 402 a3 O.OOO781 1 - - 6.177 83 -0.468 191 146.196 3 32.095 9 4.688 44 206.950 41 1 152.171 747 - 124.410 775 -209.520 195 0.060 243 047 2 0.012 894 265 5 -0.675 845 636 a1 0.117 757 0.020 885 006 0 - 1.327 79 -3.164 110 196.497 2 171.946 4 70.617 46 11.373 037 3 -1.360 161 87 1.751 358 27 - 11.517 490 1 - 0.068 31 5 774 4 - 0.054 496 535 9 -0.554 994 617 - 4.657 07 - -0.332 509 - - 0,007 024 276 45 0.004 447 122 71 0.210 629 967 concentration a2 lmol dm-3 -0.007 632 4 0.005 566 622 84 3.916 32 2.240 799 -212.075 2 -119.111 1 - 27.374 62 19.414 685 4 - 94.555 407 7 -25.409 334 9 95.658 985 5 -0.155 357 189 -0.009 445 978 77 0.967 938 651 0.1-4.0 0.1-4.0 0.1-1.5 1.2-3.9 0.01-0.3 0.25-1.1 1 .O-4.7 0.025-0.096 (V) 0.096-0.115 (V) 0.025-0.096 (V) 0.096-0.1 15 (V) 0.09-3.65 1.6-4.5-(111) 0.3-1.6 (m) concentration range as /mol dm-3 - 0.1-4.0 0.1-4.0 - 1.294 86 0.1-1.5 - 1.2-3.9 - 0.01-0.3 - 0.25-1.1 - - 1.0-4.7 0.025-0.096 (V) 0.096-0.1 15 (V) - - - 0.025-0.096 (V) - 0.096-0.1 15 (V) 0.09-3.65 - 0.3-1.6 (m) - 1.6-4.5 (m) - The preparation of zinc amalgam electrodes has been described earlier.' Silver-silver chloride electrodes, of the thermoelectrolytic type, were prepared as recommended by Ives and Janz.ll Both types of electrode had bias potentials of < 0.02 mV when placed in zinc chloride solutions. Salt diffusion coefficients were determined by the Rayleigh interferometric method, described by Chapman and Newman.12 Details of experiments are similar to those described for zinc perchlorate studies and had experimental uncertainty of k0.3 %.2898 TRANSPORT IN AQUEOUS SOLUTlONS RESULTS AND DISCUSSION TRANSPORT NUMBERS Transport numbers determined by the Hittorf method, had a precision of kO.01 which reflected difficulties encountered using zinc amalgam electrodes in these solutions.g In several instances light deposits of zinc oxide or oxychloride were formed on the anode and in such cases only cathodic half-cell results are given, table 2.TABLE ~.-HITTORF TRANSPORT NUMBER DETERMINATIONS mi %I mb m: mr C/mol dm-3 lmol kg-1 (of solution) 0.157 69 0.423 03 0.624 59 0.879 73 1.360 69 2.020 64 2.494 53 2.745 07 3.367 80 WC 28.593 28.218 25.116 30.256 31.522 33.720 34.054 34.495 36.524 0.155 14 0.403 95 0.583 78 0.802 05 1.187 48 1.669 33 1.986 20 2.144 68 2.516 60 W" I g 26.507 28.242 25.640 29.41 9 31.985 33.121 35.681 - - 0.155 28 0.403 86 0.583 71 0.801 75 1.187 34 1.669 36 1.985 57 2.146 12 2.516 78 2PliO /(mol x lO-3)-1 1.371 1 0.231 89 0.273 40 0.354 76 0.518 82 0.465 57 0.370 69 0.372 85 0.406 14 0.155 07 0.403 99 0.583 95 0.802 24 1.668 53 1.986 67 2.516 57 - - ti 0.347 0.316 0.278 0.225 anodic - - 0.015 - 0.091 - 0.235 - 0.135 77 0.502 61 0.487 42 0.738 84 1.187 41 1.618 80 1.922 06 2.082 76 2.462 29 tl: 0.336 0.309 0.281 0.239 0.118 - 0.022 -0.109 -0.132 - 0.227 cathodic 0.176 35 0.304 17 0.678 60 0.867 45 1.721 70 2.050 98 2.572 65 - - 1: (av.) 0.342 0.313 0.279 0.232 0.118 - 0.01 8 - 0.100 -0.132 - 0.231 G 0.354 0.316 0.279 0.225 "3.116 - 0.024 - 0.105 --0.142 - 8.226 mi, nz&, m:, mc and rnt represent the original solution concentration, the final concentrations of middle compartment on cathodic and anodic sides, respectively and concentration in the cathodic and anodic compartments at the end of the experiment.These concentrations are expressed as mol kg-l of solution. t t are transport numbers obtained by interpolation from cell data using the poly- nomials of table 1. For comparison, and to verify Onsager's reciprocal relationships, transport numbers were determined by potentiometric measurements using concentration ce1ls.l In this instance the four electrode positions in each half-cell were occupied by pairs of zinc amalgam and silverlsilver chloride electrodes. Bias potentials between pairs of like electrodes, which were never > 0.02mVY could be monitored during con- centration cell measurements. Four independent cell measurements could be made in any experiment, listed below as cells A, B, C, D and E Ag+AgCl IZnC1, aql [ZnCl, aql AgCl+Ag Ag + AgCl JZnCl, aql Zn + Zn,Hg IZnC1, aql AgCl+ Ag Zn + Zn,Hg IZnCl, aql AgCl + Ag (A> (B) (C) c2 c1 c2 c1 CA. AGNEW AND R.PATERSON 2899 Zn+Zn,Hg IZnC1, aql IZnC1, aql Zn+Zn,Hg Zn + Zn,Hg IZnC1, aql Ag + Cl IZnCl, aql Zn + Zn,Hg. (D) (El C1 c2 C1 c2 In principle the potentials of all cell combinations might be obtained with con- centration C1 kept constant at 0.044 143 mol dm-3, while C, was varied from 0.098 to 4.4 mol dm-3. In practice, since large concentration differences are to be avoided, due to heats of mixing, the same net effect was obtained by covering the concentration range in stepwise fashion to obtain the data of table 3. Integral transport numbers Ta and Tb (for zinc and chloride, respectively) were obtained from eqn (1) and (2) ?'ABLE 3.-POTENTIALS OF ZINC CHLORIDE CONCENTRATION CELLS REFERRED TO A DILUTE SOLUTION OF 0.048 143 mol dmV3 0.041 44 0.098 36 0.215 70 0.252 08 0.434 59 0.694 70 0.742 33 0.863 91 1.031 31 1.356 25 1.361 68 1.821 16 2.009 26 2.020 21 2.524 92 2.981 51 2.992 8 3.402 39 3.558 94 3.631 69 4.447 36 0 0.016 08 0.032 80 0.035 95 0.048 24 0.058 29 0.059 84 0.063 23 0.067 68 0.074 35 0.074 60 0.083 63 0.087 15 0.087 35 0.097 53 0.107 26 0.107 03 0.116 54 0.119 27 0.122 03 0.142 95 0 0.009 72 0.018 76 0.020 63 0.026 63 0.030 73 0.031 50 0.032 58 0.033 90 0.035 03 0.035 26 0.036 20 0.036 40 0.035 96 0.034 77 0.033 62 0.033 54 0.032 04 0.032 78 0.030 99 0.026 61 0 0.025 93 0.051 62 0.056 71 0.075 01 0.089 33 0.091 56 0.096 11 0.101 69 0.109 77 0.110 13 0.120 09 0.123 79 0.123 57 0,132 52 0.141 10 0.140 79 0.148 86 0.152 04 0.153 26 0.169 61 - 0.3751 0.3635 0.3638 0.3550 0.3440 0.3440 0.3390 0.3334 0.3191 0.3202 0.3015 0.2940 0.2910 0.2624 0.2383 0.2382 0.2152 0.2156 0.2022 0.1569 I 0.6202 0.6355 0.6340 0.6431 0.6526 0.6535 0.6579 0.6656 0.6773 0.6774 0.6964 0.7040 0.7069 0.7359 0.7602 0.7602 0.7829 0.7844 0.7962 0.8428 - - - 0.995 0.359 0.360 0.999 0.345 0.347 0.998 0.343 0.347 0.998 0.314 0.319 0.997 0.266 0.271 0.998 0.269 0.262 0.997 0.236 0.238 0.999 0.187 0.188 0.996 0.110 0.113 0.998 0.108 0.110 0.998 0.015 0.016 0.998 -0.018 - 0.018 0.998 - 0.020 -0.019 0.998 -0.107 -0.107 0.999 -0.178 -0.178 0.998 -0.177 -0.177 0.998 -0.234 -0.234 1.000 -0.245 -0.247 0.998 -0.262 -0.262 1.000 -0.325 -0.326 For the data given, experimental values of T,+Tb average 0.998, with standard deviation 0.001, rather than unity.Differential transport numbers, t,C and tg were calculated using eqn (3) and(4)lO t," = Ta+ E B dTa/dEB tg = Tb+ E B dTb/dEB. (3) (4) For this purpose T, and Tb were expressed as polynomials of E B (table 1) and differ- entiated. Agreement between these two calculations is excellent, as shown by the comparison of t: from eqn (3) and (1 - ti) from eqn (4), table 3. Hittorf and con- centration cell transport numbers are equal, within the experimental uncertainty of kO.01 for Hittorf and k0.005 for concentration cell measurements, table 3, fig. 1. These data may be compared with those of Harris and Parton l3 obtained from2900 TRANSPORT I N AQUEOUS SOLUTIONS concentration cells (0.5-4.0 mol kg-l) and additional points in more dilute solution reported by Robinson and Stokes,14 fig.1. There is good agreement between our data and those literature sources, especially at concentrations above 1 .O mol kg-'. Only two of these data points are significantly in disagreement with our data. Those at 0.5 mol kg-l (the lowes'i data point of Harris and Parton) and at 1.0 mol kg-l. The transport number for zinc in zinc chloride becomes zero at 2.0 mol kg-l (1.89 mol dm-3) and thereafter becomes negative. This inversion occurs at - 2.5 rnol kg-I for zinc bromide and - 3.5 mol kg-l for zinc iodide, reflecting the more com- plexed nature of the chloride salt.Our own earlier work on complexation showed that zinc chloride was not strongly complexed in dilute solution in contrast with aqueous cadmium iodide l5 for which cationic transport number (ta) becomes zero at 0.3 mol dm-3.1 Electrical conductance and salt diffusion coefficients (0,) were obtained by the methods described above to precisions of k0.03 and kO.5 %, respectively, given in tables 1-4 and at rounded concentrations, table 5. IRREVERSIBLE THERMODYNAMICS As shown previously,2* l6 the incidence of self-complexing or ion association does not affect the formal representation of the linear phenomenological equations of the salt a,,b,,, eqn (5)-(8). Ja = LaaXa+LabXb ( 5 ) Jb = LbaXa+LbbXb xa = RaaJa + RabJb or in inverse form where Ja and Jb are the total flows of zinc and chloride (mol cm-2 s-l) and Xa and X, their conjugate forces defined as the negative gradients of electrochemical potential of the free ions (J cm-l s-l).The dimensions of mobility coefficients Llk are mo12 J-1 cm-l s-l and for resistance coefficient, Rik, J cm s mo1-2. For cadmium iodide, in which self complexing is extensive in dilute solution, the component coupling coefficients between complexes and free ions have been identified and esti- mated, using classical theories limited to dilute solutions.2* For zinc chloride these methods of estimation are no longer valid since the major features caused by self-complexing occur at concentrations far above the limits of usefulness of current predictive theories. The comparison of zinc chloride and zinc perchlorate and zinc chloride and the complexed halides of other group IIB metals serve, however, to illustrate the effects of complexing upon transport coefficients and may be coin- pared with cadmium iodide, for which predictive analysis is available.2 The transport data measured are presented at rounded concentrations in table 5.There is agreement between Hittorf and concentration cell determinations of transport numbers as shown above, table 2 and fig. 1. In consequence the Onsager reciprocal relationships are obeyed, L a b = (The uncertainty in this assumption is examined below.) Since concentration cell measurements provided more accurate data, these trans- port numbers (tz) are used in table 5. As Miller l7 has shown, the mobility coefficients Llk may be obtained from [eqn ( 5 ) and (6)].eqn (9) -' r sk - tft,"A rirkDv , i = a, b N 103F2ZiZk 103RT rr,z,(d In y/d In m); . k = a, b. + - (9)A . AGNEW AND R . PATERSON 290 1 To evaluate the activity term of eqn (9) the osmotic coefficients (4) of Robinson and Stokes l4 were used, eqn (10) 0.6 0.3 0.2 0.1 2 0.0 - 0.1 i I '. FIG. 1.- aqueous 0.5 1.0 2.0 l/c -Zinc transport numbers (fa) as a function of the square root of the molar concentration for zinc chloride: 0, data derived from concentration cells, table 3 ; A, data from Hittorf measurements, table 2 ; 0, literature data from ref. (13) and (14). To evaluate the activity term, 4 was expressed as a polynomial in lnm over two ranges 0.1-1.6 and 1.6-4.4 mol kg-l. The activity term was also evaluated in dilute solution from the mean molal activity coefficients obtained previously (up to 1.0 mol kg-l), table 1.Agreement between these two calculations was excellent for all but 0.1 and 0.2 mol kg-I. Since these were at the lower limit of osmotic data where curve fitting procedures might be expected to be suspect, activity coefficient estimates TABLE 4.-EXPERIMENTAL SALT DIFFUSION COEFFICIENTS, Dv, FOR ZINC CHLORIDE D,X 105/cm2 s-1 1.048 1.01 8 1.005 1.002 0.995 0.979 C/mol dm-3 0.0499 0.1748 0.2477 0.2796 0.3254 0.6137 D, x 105/cm2 s-1 0.967 0.975 0.971 1.007 1.012 1.042 C/mol dm-3 0.7442 0.7651 0.9096 1.283 1.312 1.811 D,X 105/cm2 S-1 1.050 1.127 1.206 1.204 1.248 1.271 C/mol dm-3 1.831 2.357 2.995 3.095 3.442 3.9072902 TRANSPORT I N AQUEOUS SOLUTIONS were considered the more accurate for these concentrations.At 1.5 mol dm-3 osmotic coefficients pass through a minimum and so at this concentration and at 2.0 mol dm-3 the activity term was estimated graphically from a plot of C$ against In m, rather than from the polynomials of table 1. Irreversible thermodynamic transport coefficients are given in table 6 and the additional frictional coefficients, -CoRao, -CoRbo and the resistance coefficient for water Roo, were obtained from the identity, eqn (1 1)18 CiRil, = 0 k = a,b,O. (1 1) i=a,b,O TABLE s.-ISOTHERMAL TRANSPORT DATA FOR ZINC CHLORIDE AT ROUNDED CONCENTRATIONS C /mol dm-3 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 .o 1.5 2.0 2.5 3 .O 3.5 rn /mol kg-1 0 0.1004 0.2012 0.3024 0.4042 0.5066 0.6095 0.713 0.817 0.922 1.028 1.569 2.135 2.728 3.352 4.008 A /cm2 R-1 equiv-1 129.15 89.31 80.43 73.33 67.77 62.56 57.89 53.72 49.98 46.64 43.65 32.74 25.91 21.09 17.48 14.67 ta* 0.409 0.360 0.350 0.336 0.320 0.303 0.284 0.264 0.243 0.221 0.198 0.084 - 0.020 -0.106 -0.177 - 0.245 Dv/crnz s-1 1.2090 1.031 1.005 0.993 0.986 0.982 0.980 0.979 0.980 0.982 0.985 1.01 6 1.070 1.140 1.201 1.248 (I*) 1 .ow 0.8500 0.8414 0.8359 0.8204 0.8045 0.7898 8.7768 0.7655 0.7558 0.7477 0.7800 0.8872 1.0339 1.1991 1.4363 * Transport numbers from concentration cell measurements were used, table 3.TABLE 6.-IRREVERSIBLE THERMODYNAMIC COEFFICIENTS FOR ZINC CHLORIDE C /mol dm-3 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 .o 1.5 2.0 2.5 3 .O 3.5 1.41 8 1.127 1.067 1.021 0.995 0.975 0.960 0.948 0.940 0.935 0.932 0.882 0.81 1 0.748 0.688 0.608 0.000 0.526 0.625 0.719 0.824 0.933 1.037 1.135 1.229 1.317 1.399 1.616 1.650 1.616 1.543 1.408 Lbb/N x 1012 8.200 7.187 6.871 6.670 6.598 6.550 6.527 6.520 6.523 6.537 6.558 6.451 6.138 5.738 5.295 4.778 NRaa x 10-12 0.705 0.919 0.990 1.060 1.122 1.188 1.258 1.333 1.412 1.494 1.579 2.095 2.720 3.417 4.187 5.192 - NRab x 10-11 0.000 0.672 0.900 1.143 1.401 1.691 1.999 2.322 2.659 3.009 3.369 5.247 7.312 9.623 12.200 15.302 NRbb x 10-11 1.220 1.441 1.537 1.623 1.691 1.767 1.850 1.938 2.034 2.136 2.244 2.864 3.595 4.453 5.443 6.603 -CoRao x 10-11 3.527 3.922 4.052 4.159 4.206 4.247 4.292 4.344 4.400 4.461 4.527 5.229 6.288 7.461 8.737 10.656 - CoRbo x 10-11 1.220 1.105 1.087 1.051 0.990 0.922 0.850 0.777 0.704 0.631 0.559 0.241 - 0.061 -0.358 - 0.657 - 1.048 CO /mol dm-3 55.35 55.29 55.18 55.06 54.93 54.79 54.65 54.49 54.34 54.17 54.00 53.06 52.00 50.87 49.68 48.48 N = 2C is the equivalent concentration, (equiv dm-3) and Co is the molar concentration of wate, (mol dm-3). The dimensions of Ljk and Rik coefficients are mo12 J-l cm-' s-l and J c m ~ r n o l - ~ r respectively.A .AGNEW AND R . PATERSON 2903 Mobility coefficients L,,/N, Lbb/N and Lab/N are shown in fig. 2, 3 and 4. For zinc chloride, self complexing becomes significant only above 0.1 mol dm-3. Com- parison of intrinsic mobility coefficients for zinc (L,,/N) in chloride and perchlorate salts shows that there is no significant difference between the two salts up to and including 0.2 mol dm-3, fig. 2. Above this concentration L,,/N decreases less steeply in the chloride salt.In cadmium iodide and cadmium chloride * La,/N passes through a minimum. For zinc chloride this minimum is absent, but an 1.5 1.0 0.5 0.0 0.0 0.5 1.0 1.5 2.0 2.5 3.0 1/N FIG. 2.-Comparison of the intrinsic mobilities of zinc ions (Laa/N) in zinc chloride, 0 ; andlzinc perchlorate solutions, 0. The dimensions of Laa are given in table 6. (33 05 1.0 1.5 2.0 2.5 dN FIG. 3.-Intrinsic mobilities for chloride ions (Lbb/N) in zinc chloride, ; compared with those ob- served for chloride in barium chloride," - - - - - , * in cadmium chloride8 (insert, 0 ) ; and with perchlorate ion in zinc perchlorate, 0 .' The dimensions of Lbb are given in table 6. 1-922904 TRANSPORT I N AQUEOUS SOLUTIONS inflexion remains. The minimum in L b b / N , common to these self-complexed salts is still observed with chloride in zinc chloride, fig.3, although it is once more less pronounced than for the cadmium salts cited. Zinc perchlorate behaves as a fully dissociated salt and variation of its transport parameters with concentration is unremarkable and similar to barium chloride for which analysis is available,17 fig. 3. For the coupling coefficient L a b / N , comparison with barium chloride and zinc perchlorate (fig. 4) shows that in dilute solution its concentration dependence in zinc chloride is similar to a dissociated salt. As coinplexing becomes important, con- tributions to the coupling coefficient from complexes give additional increases, which are clearly obvious when comparison is made with zinc perchlorate and barium chloride, fig.4. It is this additional increase in Lab, due to contributions from the direct mobility coefficients of the complexes,2* which raises L a b until at above 2.0 mol dm-3 [zaZbLa,I > ZZL,, and so the zinc transport number becomes negative, eqn (12)17 where z,”Laa + ZaZbLab 01 t: = dN FIG. 4.--Coupling coefficients Lab/N for zinc chloride, @ ; zinc per~hlorate,~ 0 ; and barium chloride,” - . - - -. The dimensions of Lab are given in table 6. In part 5 increasing ion-to-water frictional coefficients were observed for both zinc and perchlorate ions as concentration was increased. In zinc chloride the zinc-to-water frictional coefficient (fa* / 12, I) increases less markedly than in zinc perchlorate while the chloride-to-water frictional coefficient, in contrast to perchlorate, decreases steadily and ultimately passes through zero and becomes negative, following the sign inversion for ta, eqn (13)16 The remaining independent friction, that between cation and anion, &,/[&I = fba/lZbl = - N & / I z a z b I , is much larger in zinc chloride than in the perchlorate salt.A .AGNEW AND R . PATERSON 2905 Again as with Lab/N the magnitude of this parameter is greatly enhanced by com- plexation. That these effects are due to increasing complexation of the salt can be seen by comparison of interionic frictional coefficients in cadmium chloride * and cadmium iodide.2 TABLE 7.-TEST OF ONSAGER'S RECIPROCAL RELATIONSHIP FOR ZINC CHLORIDE Lab error limit (+It N N in ratio LblLbB - Lab - Lsb- Lba x 1012 x 10'2 C/mol dm-3 t,h* t: 0.1577 0.4230 0.6246 0.8797 1.3607 2.0206 2.4945 2.745 1 3.3678 0.342 0.313 0.279 0.232 0.118 - 0.01 8 - 0.100 -0.132 - 0.23 1 0.354 0.316 0.279 0.225 0.116 - 0.024 - 0.105 - 0.143 - 0.226 -0.108 -0.021 0.000 0.036 0.007 0.017 0.01 1 0.021 -0.008 0.590 0.856 1.065 1.300 1.575 1.651 1.616 1.582 1.440 0.94 0.97 1 .oo 1.03 1.01 1.01 1.01 1.01 0.99 0.22 0.12 0.09 0.06 0.04 0.03 0.02 0.02 0.02 * t,h are Hittorf data from table 2.f 8(Lab/&) defined in Part 5 are based on the probable experimental uncertainty of 0.015 units in ( t t - ti). 1 .o 2 .o 3 .O z/N FIG. 5.-Ion-to-water frictional coefficientsho/JZil :fao/lZal zinc-to-water friction in zinc chloride, 0 ; and zinc perchlorate, 0. fbo/zb, chloride-to-water friction in zinc chloride: ; and perchlorate-to- water friction in zinc perchlorate, 0.ONSAGER RECIPROCAL RELATIONSHIPS The equality, within experimental error, of transport numbers t t and t:, has been used as sufficient reason to assume the validity of the Onsager reciprocal relationships Lab = &a. It is, however, instructive to assess the degree to which this equality may be justified. The experimental uncertainties in tk and t: were kO.01 and k0.005, respectively.2906 TRANSPORT I N AQUEOUS SOLUTIONS Using eqn (14)-(17) of the previous paper,9 the data of table 7 were obtained. Onsager's reciprocal relationships are verified to much closer limits than for zinc perchlorate. The probable error limit on the ratio LablLba is now only a few percent even although the probable experimental error (st:+&;), 0.015, is similar to that assumed for zinc perchlorate (0.01). Even although this parameter is rather higher than might be expected due to difficulties with the zinc amalgam electrodes in Hittorf determinations the probable error limit d(Lab/Lba) is only 2 % in the most concentrated solutions. As noted previously, in zinc perchlorate where similar problems bear,9 this degree of uncertainty could only be achieved if 6(tg+ ti) were +O.OOl due to low coupling coefficients L,b/N and large conductivities. R. Paterson, J. Anderson and S. S. Anderson, J.C.S. Faraday I, 1977, 73, 1763. R. Paterson and Lutfullah, J.C.S. Furuduy I, 1978,74,93. R. Paterson and Lutfullah, J.C.S. Faraduy I, 1978, 74, 103. R. Paterson, Faraday Disc. Chem. Soc., 1977, 64, 304. M. J. Pikal, J. Phys. Chem., 1971, 75, 3124. A. J. McQuillan, J.C.S. Furaduy I, 1974, 70, 1558. A. Agnew and R. Paterson, J.C.S. Faraduy I, 1978, 74, 2885. lo M. J. Pikal and D. G. Miller, J. Phys. Chem., 1970, 74, 1337. Reference Electrodes ed., D. J. G. Ives and G. J. Jam (Academic Press, N.Y., 1961). T. W. Chapman, Ph.D. Thesis (University of California at Berkeley, 1967). ' R. Paterson, J. Anderson, S. S. Anderson and Lutfullah, J.C.S. Faruduy I, 1977, 73, 1773. ' Lutfullah, H. S. Dunsmore and R. Paterson, J.C.S. Furuduy I, 1976,72,495. l3 A. C. Harris and H. M. Parton, Trans. Faraduy Suc., 1940, 36, 1139. l4 R. A. Robinson and R. H. Stokes, Electrolyte Solutions (Butterworth, London, 1968). Lutfullah and R. Paterson, J.C.S. Faruduy I, 1978,74,484. l6 S. K. Jalota and R. Paterson, J.C.S. Faruduy I, 1973, 69, 1510. D. G. Miller, J. Phys. Chem., 1966, 70, 2639. L. Onsager, Ann. N.Y. Acad. Sci., 1945, 46, 241. (PAPER 8/704)