Rate Equations

When diffusion is the rate-controlling step, in principle an equation can be written to elucidate experimentally derived plots of the fractional attainment of equilibrium with time for an ion exchange process. In practice this is difficult to achieve because the movement of one counterion (A) is coupled to the other (B), and this must be taken into account in both film- and particle-controlled exchange. A further complication arises in that water fluxes can play a significant part in affecting rates of exchange, especially for cations in the solid phase.

Detailed discussions on the appropriateness of the many equations available for kinetic interpretation of ion exchange results is beyond the scope of this article, and interested readers should consult the sources provided in the Further Reading section for further information.

So far as column data are concerned, the usual experiment method is to obtain a breakthrough curve, like those shown in Figure 4, where the appearance of the ingoing ion in the effluent is plotted against the volume of solution passed through the column. The effectiveness of the exchange can then be simply quantified in terms of the number of 'bed-volumes' passed through the column before the ingoing ion is detected in the effluent. This

Figure 3 The effect on the shape of the ion exchange profile caused by interrupting the time of exchange. (Reproduced from Harland, 1994, with permission.)

requires that the profile is reasonably sharp so that the breakthrough point can be estimated. The shape of the profile is a function of the selectivity; when KA;> 1, aA^ 1, the exchange front is sharp, and conversely when KA, aA«1 the front is more ill-defined (see Figure 4).

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