The Rate-Process Expression for Equivalent Conductivity

The net charge transported per second aaoss a unit area (i.e., the current density j) is 

Upon inserting the expression (4.212) for the drift velocity into Eq. (4.164), it is clear that 

A picture of the hyperbolic sine relation between the ionic current density and the electric field that would result from Eq. (4.213) is shown in Fig. 4.69. 

In all these cases, two significant approximations can be made. One is the high-field Tafel type (see Chapter 7) of approximation, in which the absolute magnitude of the exponents IpAl in Eq. (4.213) [i.e., the argumentpX of the hyperbolic sine in Eq. (4.213)] is much greater than unity. Under this condition ofpX 1, one obtains sinh pX because one can neglect comparison with e . Thus (Fig. 4.71) 

In electrolytic solutions, however, the conditions for the high-field approximation are not often observed. The applied field X is generally relatively small, in which case pX l and the following approximation can be used  

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