Hitherto, transport numbers of ions through ion-exchange membranes have mostIy been obtained indirectly from measurements of membrane potentials under conditions of zero current. A method is now described for measuring the transport numbers directly with current densities and concentration differences similar to those prevailing in a multicompartment electrodialysis cell.At high current densities and in an unstirred system the ions can be transported through Permaplex C-10 and A-10 membranes at a faster rate than they can diffuse and be transported through the solution and up to the membrane faces. When, as a result, the interfacial layer has become sufficiently depleted in ions the current is carried by H+ and OH-ions (derived from the water) and lower transport numbers result. Stirring the solution results in normal transport numbers.At low current densities the transport numbers of Na+ and Clare independent of stirring, and their dependence upon current density and upon the difference of concentration between the two sides of the membrane can be explained on the hypothesis that both concentration diffusion and electrical transport occur simultaneously through the membrane. The straight lines obtained on plotting transport number against the reciprocal of the current density indicate that the decrease of transport number with current density is due to concentration diffusion. Extrapolation to infinite current density gives the values 0.98, 0.95, 0.95 and 0.95 for the true transport numbers of Na+ through Permaplex C-10 at concentrations of 0-1, 1.0, 2.0 and 2.95 N NaCl (all against 0.1 N), and the slopes of the lines enable the concentration diffusion coefficient of NaCl to be calculated. For Permaplex C-10 this is 8.1 x 10-8 cm2 sec-1.
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