The integral equation (IE) approach coupled with a rectangular adsorption energy distribution and Mean Field Approximation (MFA) is used to describe the adsorption of single gases and their binary mixture on a heterogeneous solid surface. In particular, it is important to stress that all theoretical expressions shown are the exact solution of IE approach. During the analysis of single-gas adsorption isotherms also accompanying calorimetric effects are investigated. The problem of correlations between the best-fit parameters describing energetic heterogeneity and energy of intermolecular interactions is discussed. The predictions of the theory are compared with the experimental literature data. It is shown that the new theoretical adsorption isotherms give the results that are very close to the experimental data.