Transport in Aqueous Solutions of Group IIB (298.15 K) Part 3.-Isotopic Diffusion Coefficients for Cadmium-1 15 Ions in Iodide Metal Salts Aqueous Cadmium BY RUSSELL PATERSON" AND LUTFULLAH? Department of Chemistry, University of Glasgow, Glasgow G12 8QQ Received 6th May, 1977 Cadnlium isotopic diffusion coefficients (Daa) were determined in aqueous cadmium iodide in the concentration range 0.1-0.6 mol dm-3. Daa passes through two maxima, one below 0.1 mol dm-3, the other at 0.4 mol dm-3. Irreversible thermodynamic analysis shows that these maxima are due to positive fluctuations in the isotope-to-isotope coupling contributions to Daa. For these studies a modified diaphragm cell technique was developed. In previous papers 1 * the isothermal vectorial transport properties of aqueous cadmium iodide have been reported and analysed using the methods of irreversible thermodynamics.The anomalous transport properties of this salt are intimately connected with the degree to which it is self-complexed in solution. With a knowledge of the concentrations of these complexes, it has been shown that the transport behaviour could be predicted in dilute solutions.2 In this work the study of transport in cadmium iodide solutions has been extended to include isotopic diffusion ; diffusion coefficients have been measured for cadmium- 115 ions in cadmium iodide over the range 0.1-0.6 mol dm-3. For this purpose a new design of the Stokes diaphragm cell has been devised to provide simultaneous multi-cell determinations in a thermostat of normal dimensions. Isotopic diffusion coefficients for cadmium, D,,, have been shown to have a quite anomalous dependence upon the concentration of bulk salt, fig.3. The curve shows two maxima and all measured diffusion coefficients are larger than that at infinite dilution, Di, (7.12 x cm2 s-l). Comparison with other literature data shows that maxima in relatively concentrated solutions may be caused by the increasing presence of solvent-order destroying iom4 In concentrated cadmium iodide solutions, free iodide and the higher complexes CdI, and CdIi- may cause this effect. The maximum in dilute solutions has no precedent, however. Irreversible thermodynamic analysis of this data has been made, using previously determined binary mobility coefficients for cadmium (La,) and experimental diffusion coefficients, D,,, to determine isotope-isotope coupling coefficients. It is shown that these coupling coefficients are primarily responsible for the observed maxima in Daa.A theoretical analysis and prediction of the factors influencing isotope coupling in coinplexed electrolytes is deferred to the following paper.5 This, combined with earlier predictions of binary mobility coefficients allows the diffusion coefficients for cadmium to be calculated as a function of concentration in dilute solutions, including the first maximum in D,,, fig. 3. ? Present address : Institute of Physical Chemistry, University of Peshawar, Peshawar, Pakistan. 9394 TRANSPORT IN AQUEOUS SOLUTIONS EXPERIMENTAL The Stokes diaphragm cell technique provides a convenient and accurate method for determining diffusion coefficients in solution.Commonly a U-shaped permanent magnet is mounted coaxially with the diaphragm cell and, when rotated, it drives two internal magnetic stirrers, which are positioned above and below the diaphragm. Most variations of this method involve modifications to the stirring In general, the conventional rotating assembly or its slightly modified form is preferred. There are, however, certain disadvantages to the conventional methods. The diaphragm itself may be worn by the action of the stirrers rotating on its upper and lower surfaces. This effect can be allowed for by recalibration lo or avoided by adjusting the stirrers to that they do not quite touch the diaphragm when inuse.l The major experimental inconvenience is, however, the unwieldiness of the magnet assembly with its associated gearing and motor drive.It is seldom convenient to operate more than one cell in a normally sized thermostat. For the above reasons the design of both the stirrers and their driving mechanism was reconsidered. Two bar magnets were mounted on a small Perspex turbine, which enclosed the diffusion cell. The turbine was rotated by a jet of water pumped from the thermostat bath itself. Since the turbine unit is compact, several cells may be used simultaneously in a relatively small thermostat bath. A unit capable of accommodating four such cells fitted into a thermostat (64 x 46 x 41 cm3) and was driven by a single pump. THE DIAPHRAGM CELL A Pyrex glass standard filter tube with sintered glass disc (porosity No.4; 3790/68, Jobling Pyrex, London) was used to construct the cell. The upper stirrer within the cell was made by enclosing a soft iron wire in a medium walled Pyrex glass tube and attaching FIG. 1 .-Schematic representation of the diaphragm cell, including internal stirrers. Also shown are the top plug, with internal capillary and air-leak and the bottom plug made to the design of Mills and Woolf, ref. (9), with A, body of fibreglass-impregnated Teflon ; B, stainless steel valve ; C, brass adjustment knob ; D, locking nut ; E, side vents ; F, plugs and G, O-rings of neoprene rubber.R . PATERSON AND LUTFULLAH 95 two side blades at right angles to form a flat four-bladed unit, fig. 1. These blades were slightly shorter than the internal diameter of the filter tube.A central shaft of Pyrex glass was sealed to the stirrer blades. This passed through a glass collar and its end was melted to form a small spherical knob which rested on the flanged top of the collar, fig. 1. The collar was then fused to the side wall of the cell with a short length of glass rod, such that the stirrer blades rotated centrally in the cell, some 2mm above the upper surface of the diaphragm. The stirrer in the bottom compartment was constructed similarly, except that the solid sphere on the central rod was adjacent to the stirrer blades, thus holding them at the same distance below the diaphragm. A diagram of the cell and stirrer units is given in fig. 1. The action of the stirrers in both compartments was tested to ensure smooth rotation.The ends of the filter tube were terminated with B-19 standard ground glass joints. The top plug was of standard design and contained a central capillary, terminated with a B-7 ground glass socket, fig. 1. The useable capacity of the cell was marked as the upper limit of this internal capillary. In use, the top B-7 socket was fitted with a very fine drawn out glass capillary. In this way the cell was not completely sealed, and thus allowed for volume changes due to mixing (when calibration experiments involving potassium chloride solutions were made). The bottom plug, fig. 1, was constructed to the design of Mills and Woolf and incorporated a valve mechanism to ensure 1 complete filling of the lower compartment. FIG. 2.-Schematic representation of the water-driven turbine and H its casing.Turbine rotor: (C) cuts made into the turbine rotor for magnets, (M) ; (H) central hole ; (P) paddle drilling around the periphery. Turbine casing: (B) base which is filled with mercury to a depth of 3 mm in use; (I), inner wall ; (0), outer wall ; (N), nozzle imput for pump water ; (H), central hole to fit around diaphragm cell ; (L), lugs for mounting turbine assembly upon supporting tray.96 TRANSPORT I N AQUEOUS SOLUTIONS TURBINE UNITS AND SUPPORTING TRAY The turbine is shown diagrammatically in fig. 2. It was constructed from a solid Perspex disc (95 mm in diameter and 25 nim thick) through which was bored a central hole 52 mm in diameter. A standard 3” (9.5 mm) drill was then used to machine twelve tangential paddle grooves, each to a maximum depth of 5 mm from the circumference of the turbine.Two rectangular slots 20 mm deep and 13 min square were cut sym.etrically into the inner side of the turbine, to hold two permanent bar magnets. These magnets were wrapped in p!astic tape and push-fitted into their positions. The turbine casing was of an open-top construction made from 35 mm lengths of 3 mm walled Perspex tubes with outer diameters of 50 and 100mm respectively. A circular sheet of Perspex formed the base of the casing. This too was bored centrally to the dimen- sions of the inner tube, giving a central hole in the turbine casing through which the diaphragm cell could pass. Prior to sealing the wall of the casing to the base, the surface of the inner wall was accurately machined so that the turbine fitted closely into the casing, but still rotated freely.The gap between the outer rim of the turbine rotor and the outer casing was 1.5 111111. A 6 mm hole in the side wall of the casing, in line with the paddle drillings on the turbine, was fitted with a 3 mm (i.d.) nozzle and provided access for a flow of water directed tangentially at the turbine rotor. No corresponding exit tube was required. In use, water pumped into the rotating turbine left by way of the gap between the turbine rotor and the outer casing. Three Perspex lugs were attached to the base of the turbine casing to fix this unit reproducibly upon its tray (described below). To provide an almost frictionless surface for the turbine rotor the turbine casing was filled to a depth of 3 mm with mercury.Four such turbines were mounted on a common tray in the thermostat. This tray was constructed from Perspex sheet (12 mm thick) reinforced with rectangular Perspex bars. The tray was perforated with 5 mm holes to allow circulation of bath liquid. Four holes, matching those of the turbines were drilled symmetrically in the tray, allowing four diffusion cells, with turbines, to be mounted in fixed positions. The tray itself was supported by four adjustable legs and could be levelled in the thermostat bath. Each diaphragm cell was held in a vertical position in the central hole of the turbine unit, using clamps attached to aluminium rods mounted on the Perspex tray. Initial adjustments were made to ensure that the cell diaphragms were horizontal and that the internal stirrers were driven smoothly by the turbine.Thereafter each cell could be removed and replaced reproducibly. WATER CIRCULATION The four turbines were driven from a single circulatory pump (Shandon, Gallenkamp, London). A variety of such pumps were used with success. To drive four turbines from this single pump, a simple distributor was constructed. This consisted of a 100ml Pyrex bulb with five 3 mm glass tubes joined to its lower end. Of these the entry tube was placed vertically below the bulb. The other four tubes were in axial positions and distributed the flow to the turbines. Each of these outflows was controlled by a TF 2/18 “ Rotafio ” tap. The central bulb of the distributor was half-filled with air when in use, and provided both a reservoir of backing pressure and served to dampen pressure fluctuations from the water pump.By adjustment of the “ Rotaflo ” taps, stirring speeds in the diaphragm cells could be held constant at rotation speeds from 10-100 rpm. OPERATION Thermostat control was obtained using a conventional mercury-toluene coiled glass thermo-regulator in conjunction with an electronic relay mechanism (type 42, Gallenkamp, London). The thermostat water was heated by two 150 W light bulbs activated by the thermo-regulator and cooled by tap-water passing through cooling coils immersed in the thermostat. In this way temperature was maintained at 298.15+0.01 K. VOLUME DETERMINATIONS Volumes of the cell compartments were determined by weight calibrations, using carbon tetrachloride.That of the diaphragm was determined independently after dropwise additionR . PATERSON AND LUTFULLAH 97 of carbon tetrachloride to the sintered glass diaphragm in an otherwise dry cell, held horizontally. The volumes of top ( VT) and bottom ( VB) compartments were each some 55 cm3 and that of the diaphragm ( VD) some 1.5 cm3. Compartment volumes were obtained reproducibly to rfI0.015 cm3 and those of the diaphragms to k0.003 cm3. DIFFUSION EXPERIMENTS The cells were filled by the “ vacuum thump ” method ;lo all solutions were filtered and degassed before use. Once the diaphragm was filled with solution using this vacuum method the bottom compartment was filled using the valve arrangment in the bottom plug (fig.l), which avoided trapping of air bubbles. The upper compartment could then be filled either with solvent (for calibration experiments, using potassium cnloride) or with the same solution (for isotopic diffusion experiments). For calibration, 0.50 mol dmW3 potassium chloride in the lower compartment diffused into pure solvent (water). In these experiments a prediffusion time of two hours was allowed to establish a uniform concentration gradient across the diaphragm. The duration of this prediffusion was estimated by Gordon’s approximation.12 It has been shown that Gordon’s estimate may overestimate the prediffusion time, but varying the length of the prediffusion time within reasonable limits has been shown to contribute no significant error.g At the end of the prediffusion the top plug was removed and the upper compartment emptied using pipettes with side holes, to prevent disruption of the diaphragm gradient.The top compart- ment was filled with pure water (25°C) once more after several rinsings. At this final filling the diffusion run proper was considered to be initiated; the top plug was replaced and the volume of the top compartment adjusted to the calibration mark in the upper capillary. A typical calibration experiment lasted 46-48 h. At the end of the experiment the upper and lower solutions were sampled and analysed by conductimetric analyses of weight-diluted samples .g For isotopic diffusion experiments the cell was entirely filled with an inactive solution of the required concentration. Diffusion experiments were initiated by injection of a small sample of the same solution traced with isotope into the top compartment. For this purpose “ Hamilton ” microsyringes, fitted with “ Chaney ” adaptors were used.Volumes added were 0.1 cm3 or less and, after addition, the excess volume was removed. This method is classed as a solvent-filled diaphragm rneth~d,~ since at time zero the diaphragm and bottom solution are sled with inactive solution and only the top compartment contains the labelled diffusing species. Diffusion experiments for cadmium-115 were allowed to proceed for 72-80 h. The isotopic content of each compartment was assayed by withdrawing accurately- known volumes for radioactive counting. Normal counting precautions were used, but to eliminate coincidence and quenching effects high activity samples were diluted with inactive solution, and upper and lower compartments were counted at similar activity levels.Samples were counted using standard scintillation procedures in 10cm3 aliquots of a dioxane-based liquid scintillator. The 1-4 dioxane solvent was purified by refluxing with ferrous sulphate (log) and sodium metabisulphate (log) per dm3 of dioxan for 1 h. If this precaution was not observed, colour quenching was severe due to production of iodine in the radioactive samples. Triplicate samples were counted and counting efficiency of G0.3 % was obtained. PREPARATION OF ISOTOPIC SOLUTION Radioactive cadmium chloride (115CdC12 as) in 0.1 mol dm-3 hydrochloric acid was obtained from the Radiochemical Centre, Amersham, England.Labelled cadmium iodide was obtained from this solution by an electrolysis technique. The electrolysis cell consisted of a Pyrex glass U-tube with a central porous disc (porosity 4). Each half cell had a capacity of approximately one ml and each was fitted with a platinum electrode, 3 mm square, electroplated with a heavy deposit of cadmium metal. The electrolysis solution was 0.1 mol dm3 cadmium chloride acidified with hydrochloric acid ; hydrazine dihydrochloride was added as depolariser. One cadmium plated electrode was mounted in each half-cell, which was then filled with the solution used for plating. To the cathodic compartment a 1-498 TRANSPORT I N AQUEOUS SOLUTIONS suitable quantity of radioactive cadmium chloride was added and cadmium-115 plated on to the cathode.When most of the activity had been transferred to this electrode, the cell solution was replaced by one of inactive cadmium iodide. The polarity of the cell was reversed and cadmium-115 iodide solutions were obtained at the desired activity. The radioactive cadmium electrode could be used to prepare a number of such solutions, as required. RESULTS AND DISCUSSION The cell constants (p) of the four diffusion cells were determined by standard rneth~ds,~. 9* lo using the gradient-filled initial state in which 0.50 mol dm-3 potassium chloride in the lower compartment was allowed to diffuse into pure solvent in the upper, after a prediffusion time during which a linear gradient had been established across the diaphragm. Barnes l3 has taken account of the fact that a true steady state diffusion condition is not created by this method and this treatment has been extended by Mills, Woolf and Watts l4 to include three initial conditions in the diaphragm.These are the gradient-filled, solvent-filled and solution-filled conditions. Only the first two are of interest in this study, since the gradient-filled condition applies to calibration experiments, using potassium chloride and solvent-filled corresponds to the conditions of isotopic diffusion. The radioactive solution is added to the upper compartment only, and so the diaphragm and lower compartment are filled with inactive solution at time zero. This latter condition is particularly convenient for isotopic studies since it involves a minimum of handling of radioactive solutions.The two methods must, therefore, be shown to be compatible. For calibration by the gradient-filled method the cell constant is defined by eqn (1) where O C B is the concentration at time zero (after prediffusion) in the bottom compartment. C, and CB are those obtained after time t / s . O C B is not obtained directly, but from these latter concentrations by eqn (2) The integral diffusion coefficient D may be obtained from literature sources using the data of Stokes 1 5 9 recently refined by Mills and Woolf.' Stirring speeds for the Stokes diaphragm cell are usually chosen in the range 50-60 r.p.m. Since modified stirrers were used in our cells, the effect of stirring rate upon cell calibration was investigated. Cell constants (j?) were obtained at 30, 60 and 85 r.p.m., for which the ratios /3/pG0 r.p.m.were 0.991, 1.000 and 0.999 respectively. The cell constant was thus unaffected by stirring speeds in the range 60-85 r.p.m. A speed of 60 r.p.m. was used for all subsequent work. Cell constants for the four cells employed, ranged from 0.44 to 0.51 and were reproducible to For isotopic experiments employing the solvent-filled initial state,14 the isotopic "CB = CB + C ~ V T +4VD)/(VB + + VD). (2) GO.1 %. diffusion coefficient, D is defined by eqn (3) (3) 1 D = - In [ OCB(l - n/6)/(cB - cT)] Pt The cell constant, /3, is identical to that defined in eqn (l), but an additional term, (1 - A/6), appears in the logarithmic term, where A is the volume ratio 2 VD/( V, + VB) : the volume of the diaphragm compared with the average volumes of the top andR .PATERSON AND LUTFULLAH 99 bottom compartments. For a successful application of Barnes' theory,13 ;t is assumed to be small. For the cells of this study 3, ranged from 0.024-0.028, which is within acceptable limits. TABLE 1 .-ISOTOPIC DIFFUSION COEFEICIENTS FOR 22Naf IONS IN SODIUM CHLORIDE (298.15 K), USED FOR CALIBRATION TEST conceatra tion C/mol dm-3 sodium chloride I I1 I11 diffusion coefficients, D X 105/cm2 s-1 0.40 1.279 1.278 1.283 I, From this work using the solvent-filled diaphragm technique and cell constant (B) from potassium chloride diffusion (0.50 mol dm-3) into water (experimental uncertainty k 0.5 %). 11, From Mills, Woolf and Watts [ref. (14) and (9)] by the methods used in I, (uncertainty k0.5 %). 111, From Mill's review, ref.(16) (original reference J. Amer. Chem. SOC., 1955, 77, 6116), using the gradient-filled technique, (uncertainty f 0.5 %). To test these equations, the isotopic diffusion coefficient for 22Na+ in aqueous sodium chloride (0.40 mol dm-3) was measured and compared with literature data.g* l 6 Excellent agreement was obtained within the experimental uncertainty of measurement (20.5 %), see table 1. ISOTOPIC DIFFUSION COEFFICIENTS FOR CADMIUM-1 15 I N AQUEOUS CADMIUM IODIDE With the calibration methods thus justified, diffusion coefficients for cadmium-1 15 in aqueous cadmium iodide were determined in the range 0.1-0.60 rnol dm-3. Results are given in table 2 and fig. 3. TABLE 2.-ISOTOPIC DIFFUSION COEFFICIENTS FOR CADMIUM-1 15 IONS IN AQUEOUS CADMIUM IODIDE (DaJ TOGETHER WITH MOBILITIES AND ISOTOPE-ISOTOPE COUPLING TERMS DEFINED IN EQN (6) DaaX 10-3IRT Laa/CE a (C,'/CiC,*) Lza x 1012 x 1012 x 1013 CE Dsa X 106 /mol dm-3 /cmz s-1 /mol em* J-1 s-1 x 10-3 0.0 0.1 0.15 0.20 0.30 0.40 0.50 0.60 7.122 7.860 *7.436 7.422 *7.898 8.114 7.884 *7.164 2.8730 3.1708 2.9997 2.9941 3.1861 3.2732 3.1804 2.8904 2.8730 3.0370 2.9788 2.8940 2.7390 2.63 18 2.5706 2.5478 O.OO0 - 1.338 - 0.209 - 1.001 -4.471 - 6.41 6 - 6.098 - 3.426 a ref.(2). The experimental uncertainty in D, is k0.5 %. Data starred in column 2 were averaged values from duplicate experiments which agreed to k0.5 %. The units of Ls8 [obtained from ref. (2)] and Lza are mo12 J-' cm-l s-l. Since the estimated uncertainty in LalCT is f 1 % the isotope-isotope coupling term, in the final column, is uncertain to 2 0.4 x 10-13 units.The concentration dependence of the diffusion coefficient for cadmium (Daa) is remarkably complex. It is notable that all experimental diffusion coefficients in the experimental range are larger than the value at infinite dilution, D$,, (7.12 x cm2100 TRANSPORT IN AQUEOUS SOLUTIONS s-l) obtained from eqn (4), using Matheson's estimate of the equivalent ionic con- ductance of cadmium at infinite dilution, A:, (53.5 cm2 Sz-l equiv-l).l' In the experimental range, D,, passes through a minimum (at 0.2mol ~ l m - ~ ) rises to a maximum (at 0.4 mol dm-3) and falls once more to a lower value at 0.6 mol dm-3. (Duplicate experiments made at 0.15, 0.30 and 0.60 niol dm-3 were reproducible to k0.5 %).No data are available at concentrations below 0.1 mol dm-3 because of the concentration limitations of the diaphragm method, but it is obvious that the diffusion coefficient must pass through a maximum value between 0.1 mol dm-3 and infinite dilution. t 6.0 1 I t I 0.0 0.2 0.4 0.6 - dC FIG. 3.-Isotopic diffusion coefficients for cadmium-115 in aqueous cadmium iodide at 298.15 K, Daa, 0. The contribution to Daa from the binary mobility coefficient term is RTLaa/CT from eqn (6), 0. [ L a values were obtained from ref. (2)]. The shaded area representing the difference between DU and RTLaaICT is a measure of the isotope-isotope coupling term, - RTLza CT/CX'.* of eqn (6) ; table 2. The dimensions of RTLaa/CT and RTLza Cz/CiC,' are those of the diffusion coefficient, Da,/cm" s-l when concentrations CT, Cz and C.* are in mol ~ r n - ~ .Hertz, Holz and Mills have shown that maxima in ionic diffusion coefficients may be obtained when solvent-order producing ions are present. Such effects occur only at high concentrations; iodide ion has shown to be effective. It is possible that the second maximum in fig. 3 arises from such solvation effects caused by increasing concentrations of free iodide and the order-destroying complexes CdI; and CdI;-. (The distribution of species is shown in fig. 4 of Paper 2 2). Olsztajn, Turq and Chemla,l* in their studies of isotopic diffusion of cadmium and zinc ions in potassium chloride, observed that diffusion coefficients increased with concentration of supporting electrolyte.No maxima were observed, but the increasesR . PATERSON AND LUTFULLAH 101 were tentatively ascribed to the presence of increasing concentrations of the order- destroying complexes CdCli- and ZnCla- in these solutions. The maximum for D,, in dilute solutions has no parallel in published data on binary electrolytes. Some dissociated electrolytes in fact show minima due to the steep decrease from infinite dilution value predicted by the Onsager limiting law. It is obvious that the complexed nature of cadmium iodide precludes direct application of Onsager theory. This theory is, however, developed to include complexed electrolytes in the following paper.5 IRREVERSIBLE THERMODYNAMICS Sufficient experimental data are available to make a formal irreversible thermo- In earlier papers 1 9 9 2o it was shown that the isotopic diffusion coefficient of an dynamic analysis of the cadmium diffusion results.ion of species a in a solution of salt (a, b) may be represented by eqn (5) In eqn (5) Cz is the total concentration of species a (mol dm-3) and C,* and C,O are the concentrations of isotopically labelled and unlabelled ions, such that C,* + C,O = C z . (With RTexpressed as J mol-l and La, as mo12 J-1 cm-l s-l, D,, is expressed as cm2 s-l). La,, the binary mobility coefficient of cadmium, is known from earlier studies.2 The remaining isotope-isotope coupling coefficient Lza may, therefore, be calculated, table 3. At infinite dilution the isotope term -L:aCf/CfC,O in eqn ( 5 ) is zero, and so the diffusion coefficient is determined solely by the intrinsic mobility L,JC:.It is pertinent, therefore, to examine the degree to which this parameter determines D,, when the concentration is increased, and how important are the coupling interactions between the labelled and unlabelled cadmium species in that solution. It is obvious from table 3 and fig. 3 that both maxima in D,, are due to positive fluctuations in the isotope-isotope coupling term in eqn (5). a method was developed for predicting all transport properties of the unlabelled salt, including the function L,,/Cz, which appears in eqn (5). In the following paper in this series, this treatment has been extended to include isotopic experiments in self complexed electrolytes. Isotope-isotope coupling is predicted and the diffusion coefficients (D,,) calculated for cadmium iodide in dilute solutions. In Paper 2 We are grateful to the Pakistan Ministry of Education for a grant to Lutfullah. R. Paterson, J. Anderson and S. S. Anderson, J.C.S. Furaduy I, 1977,73, 1763, Part 1. R. Paterson, J. Anderson, S. S. Anderson and Lutfullah, J.C.S. Furaday I, 1977, 73, 1773, Part 2. R. A. Robinson and R. H. Stokes, Electrolyte Solutions (Butterworth, London, 2nd edn, 1968). H. Hertz, M. Holz and R. Mills, J. Chim. phys., 1974, 71, 1355. R. Paterson and Lutfullah, J C.S. Faraduy I, 1978,74, 103, Part 4. J. M. Nielson, A. W. Adamson and J. W. Cobble, J. Amer. Chem. SOC., 1952, 74, 446. ’ J. B. Lewis, J. Appl. Chern., 1955, 5, 228. * F. A. L. Dullien and L. W. Shemilt, Canad. J. Chem. Eng., 1961,39,242. R. Mills and L. A. Woolf, The Diaphragm Cell (Australian National University Press, Canberra, 1968). lo G. J. Janz and G. E. Mayer, Diflusion of Electrolytes : Principles and Practice of the Diaphragm Cell Technique ( U . S . Office of Saline Water, Report, 1966). l1 S. K. Jalota and R. Paterson, J.C.S. Faraday I, 1973, 69, 1510. l2 A. R. Gordon, Ann. N. Y. Acad. Sci, 1945,46,285.102 TRANSPORT IN AQUEOUS SOLUTIONS l3 C. Barnes, Physics, 1934, 5,4. l4 R. Mills, L. A. Woolf and R. 0. Watts, A.I. Chem. Eng. J., 1968, 14, 671. l5 R. H. Stokes, J. Amer. Chem. SOC., 1951, 73, 3527. l6 R. Mills, Rev. Pure Appl. Chem. (Australia), 1961, 11, 78. R. A. Matheson, J. Phys. Chem., 1962, 66,439. M. Olsztajn, P. Turq and M. Chemla, J. Chim. phys., 1970,67,217. l9 J. Anderson and R. Paterson, J.C.S. Faraday I, 1975, 71, 1335. 2o S. Liukkonen, Actu Polytechnica Scand., Chemistry Incl. Metallurgy Series No. 113, Helsinki, 1973. (PAPER 7/769)