When the addition of the differential amount of component $i$ $\mathrm{d}{n}_i^{\sigma }$ or $\mathrm{d}{n}_i^{\text{s}}$ is effected at constant pressure $p$, the differential molar enthalpy of adsorption, ${\mathrm{\Delta }}_a{H}_i^{\sigma }$ or ${\mathrm{\Delta }}_a{H}_i^{\text{s}}$ also called the isosteric enthalpy of adsorption ($q^{\text{st}}$) is defined as: $${\mathrm{\Delta }}_a{H}_i^{\sigma }=-q^{\text{st},\sigma }=U_i^{\sigma }-H_i^{\text{g}}$$ $${\mathrm{\Delta }}_a{H}_i^{\text{s}}=-q^{\text{st},\sigma }=H_i^{\sigma }-H_i^{\text{g}}$$ where $H_i^{\text{s}}=(\frac{\partial H^{\text{s}}}{\partial n_i^{\text{s}}}{)}_{T,p,m,n_j^{\text{s}}}$ and $H_i^{\text{g}}$ is the partial molar enthalpy of component $i$ in the gas phase, i.e. $(\frac{\partial H^{\text{g}}}{\partial n_i^{\text{g}}}{)}_{T,p,n_i^{\text{g}}}$