Isosteric heats of gas and liquid adsorption

The heat of adsorption is an indicator of the strength of the interaction between an adsorbate and a solid adsorbent. This parameter can be determined from the heat released in calorimetric experiments or from the analysis of adsorption isotherms at different temperatures. The latter, called isosteric heats of adsorption, are commonly used in the characterization of materials for gas- and liquid-phase adsorption. Although the equations for the determination of isosteric heats of adsorption from the gas phase are well-known, approximate equations are frequently used for liquid-phase adsorption. We present here the rigorous equations for determining the isosteric heats of gas- and liquid-phase adsorption and their relation to the commonly used approximate equations. These equations are used to compute the isosteric heats of liquid adsorption based on the adsorption isotherms obtained from simulations for two well-defined systems, one ideal and the other nonideal. The results of using the rigorous equations are compared with those from the approximate equations. The main conclusion is that the commonly used approximate equations provide reasonable, but not perfect, estimates of the isosteric heats of liquid adsorption using only the experimental adsorption isotherms. The more accurate rigorous equations require additional information, including the heat of vaporization and, for nonideal mixtures, the heat of mixing.