Cells with a liquid junction potential

Consider two half-cells having identical electrodes dipping into their respective solutions containing the same electrolyte but at different mean ion activities. Electrical contact between the half-cells is made by the two solutions meeting at a junction. Such a cell may be represented by 

At the right-hand electrode, for the passage of 1 faraday, 1 equivalent of M ions will be deposited. However, migration of t+ equivalents of M across the junction will to some extent make good the loss of M by the deposition process. Similarly, at the left-hand electrode, although 1 equivalent of M dissolves as M ions, t+ equivalents migrate out of the region towards the cathode. This behaviour is summarized below. 

For this process the free energy change per faraday is 

It should be stressed that the transport number which appears in the equation for the cell e.m.f. is that of the ionic species with respect to which the electrodes are not reversible. For the general case where the electrolyte species provides v ions of which there are u+ cations and v anions. Equation (5.31) takes the forms 

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