  The statistical thermodynamics of binary mixtures of polyatomic species was
developed on a generalization in the spirit of the lattice-gas model and the
quasi-chemical approximation (QCA). The new theoretical framework is obtained
by combining: (i) the exact analytical expression for the partition function of
non-interacting mixtures of linear $k$-mers and $l$-mers (species occupying $k$
sites and $l$ sites, respectively) adsorbed in one dimension, and its extension
to higher dimensions; and (ii) a generalization of the classical QCA for
multicomponent adsorbates and multisite-occupancy adsorption. The process is
analyzed through the partial adsorption isotherms corresponding to both species
of the mixture. Comparisons with analytical data from Bragg-Williams
approximation (BWA) and Monte Carlo simulations are performed in order to test
the validity of the theoretical model. Even though a good fitting is obtained
from BWA, it is found that QCA provides a more accurate description of the
phenomenon of adsorption of interacting polyatomic mixtures.
