Catalyzing carbon–nitrogen (C-N) coupling using small abundant nitrogenous molecules is of growing interest to lessen the environmental impact of the industrial process. High-entropy alloys hold the potential to have surface sites optimized for each of the coupling intermediates and by varying the alloy composition of the catalyst it provides tunability to the adsorption energy distribution. We model the C-N coupling using adsorption energies of CO and NO and assume that *CO couples with an *NO-reduced intermediate. As more mechanistic insight is needed, we limit the model to the coverage of pairs of *CO and *NO, providing a necessary but not sufficient condition for catalytic activity. Two limiting cases for simulating the adsorption process are presented: one considering thermodynamic equilibrium and one considering out-of-equilibrium conditions. A Monte Carlo method connecting the two limits is suggested which reproduce trends observed in experiments. By varying the partial pressure of NO, the shape of the pair coverage function in the composition space, as well as its optima, are altered. Our method finds a ternary AuCuPd optimum at equal CO/NO partial pressures and copper to be the optimum at low NO partial pressures.