Henry's Law as a Limit for an Isotherm Model Based on a Statistical Mechanics Approach

The fundamental integral equation for isotherms derived from statistical mechanics was applied to the analysis of adsorption under low concentrations (or pressures). The model considers adsorption on an energetically heterogeneous surface characterized by an energy distribution function in the semiexponential formN(Q) = (m/RT)e−mQ/RTand by the individual adsorption of each site obeying the Langmuir isotherm. The expression derived guarantees a linear relationship of the covering degree,q,and the concentration,C,that is,q=HC(Henry's law), under the condition of low values of concentration. In this derivationH=mb0/(m− 1) is Henry's constant, whilem> 1 andb0are parameters to be adjusted to experimental data.