A toy model solved by statistical mechanics for teaching reaction kinetics beyond ideality

Chemical equilibrium is fully characterized by thermodynamics, while the rates of chemical reactions can be calculated for ideal solutions by using mass-action equations. The evaluation of the rates of reactions in a non-ideal system is instead much more complex, even at equilibrium, being dependent on the microscopic features of the interactions: no universal theory exist. Here we propose a toy model to help students understand such complexity. It is formulated by means of statistical mechanics and aims at the evaluation of the exchange reaction rate at equilibrium. The toy model can be solved by the students, with various types of interactions, as an exercise. The results prove that no general rule connects the reaction rates to the thermodynamic quantities, such as the activity coefficients, dramatically proving the complexity and richness of the field.