The variation of electrical potential across a semi-permeable membrane

Abstract

It was shown by Donnan that in certain cases the potential difference between two solutions of an electrolyte, separated by a membrane which is impermeable to the electrolyte, but permeable to the solvent, can be calculated. Thus suppose the solution (1) and (2) (1) Kֹ || Kֹ A' || A' c 1 , π 1 || c 2 , π 2 (2) of the electrolyte KA are separated by a membrane which does not permit the salt KA to pass, though freely permeable to other salts, with, say, the same cation K. We may then ascribe the potential difference set up at the membrane as due to the tendency of the Kֹ ions to equalise their concentrations. If we assume the permeable ions to obey the laws of ideal solutions, then π 2 -π 1 = RT/ n F log c 1 / c 2 , (i) where c 1 , c 2 , are the molar concentrations of the K ions, n their valency, R the gas constant, F the quantity of electricity associated with a gramme-equivalent of ionic matter, and π 1 , π 2 , positive potentials of the solutions. For univalent ions and 18° this reduces to π 2 , π 1 = 0·058 log ( c 1 / c 2 ) volts. If the permeable ions cannot be assumed to follow the laws of ideal solutions, we must substitute for c 1 and c 2 the quantities termed by G. N. Lewis the "activities," or else (as is readily done) obtain an equivalent equation, involving, instead of c 1 and c 2 the ordinary thermodynamic potentials of the ions. In the following paper an account is given of an attempt to test equation (i) by measurements of the potential difference between two aqueous solutions of potassium ferrocyanide, separated by a membrane of colloidal copper ferrocyanide.