Adsorption isotherms in ion exchange reactions. Further treatments and remarks on the application of the Langmuir isotherm

Abstract

In a previous work, the author gave an adsorption isotherm for the general case of single-site heterovalent exchange and simpler approximate equations having linear forms involving the same plot used for the Langmuir isotherm. The present work gives a substantiation of these equations by calculations involving some potential practical examples. It also extends the equations to the case of two-site (multisite) heterovalent exchange and considers the evaluation of the different ion exchange parameters. Further discussion is given on the hazards of the application of the Langmuir equation to ion exchange reactions. For homovalent exchange, instead of the Langmuir isotherm, use of the single-site isotherm or two-site isotherm of Boyd et al., as treated in our previous work, is recommended. This isotherm is graphically represented by the same plot used for the Langmuir isotherm. It is more instructive, avoids confusion and allows for equilibrium constant calculations. In the case of heterovalent exchange, the equations given in the previous work for single-site adsorbents and in the present work for two-site (multisite) ones should invariably be used to obtain correct results.