By Angus McDougall (auth.)
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02 V). 3 which becomes i = io + ioZIXVF /RT - io + io(1-IX)ZVF /RT == iozVF /RT Thus, in these conditions the current density is linearly related to the overpotential. 05 V). In these circumstances the reverse reaction has a rate negligible compared with that of the forward reaction. 303RT IXzF and b= ~ io and are clearly dependent on the particular electrode reaction. The exchange current density, io' can be readily evaluated from a graph of experimental The rates of electrode processes 41 results.
9 we have V=RT zF In(~) lL - I thus giving the overpotential-current relation for mass transfer by diffusion of ions only. If ionic transport (that is, movement due to an applied electric field) is also a contributor to the concentration of ions at the electrode surface, then the relations obtained so far must be modified somewhat. H 2 + OH- -+ H 20 + e- then the current density is equal to the sum of two types of mass transferthe diffusion contribution DzF(c o - ce )/[) and the ionic transport contribution t _ i, where t _ is the transport number of the anion (hydroxide in the example).
It decreases with increase in viscosity and with decrease in temperature; a typical value at ordinary temperatures is about 10- 9 m 2 s - 1. urn for vigorously stirred systems. When ce = 0, that is, when every ion arriving at the electrode surface immediately reacts, then the limiting current density is given by . DzFc o IL = - - (jL o is assumed not to change across the diffusion layer, and it is found to vary little with concentration. 9) By regarding the change of concentration across the diffusion layer as producing an overpotential V we may, by assuming thermodynamic behaviour and the type of equation obtained in chapter 3 for dependence of electrode potential on ionic concentration, write V=RTlnc o zF ce (Of course the system is in no sense at equilibrium but there is some excuse for applying this sort of argument to a steady state condition.