We consider dimerization: \[2\,\text{A }{\mathop{\rightleftharpoons}\limits_{k_2}^{k_1}} \text{ B}\] When we assume that the forward and backward reaction are elementary reactions, then according to the law of mass action we can write down the following system of differential equations for the concentrations of A and B: \[ \left\{\begin{aligned} \frac{\dd[\text{A}]}{\dd t} &= -2k_1[\text{A}]^2 +2k_2[\text{B}]\\ \\ \frac{\dd[\text{B}]}{\dd t} &=k_1[\text{A}]^2-k_2[\text{B}]\end{aligned} \right.\]

A concrete example of the above equilibrium reaction is the dimerization of the brown nitrogen dioxide to the colourless gas dinitrogen tetraoxide and the backward dissociation: \[2\,\text{NO}_2\text{ }{\mathop{\rightleftharpoons}\limits_{k_2}^{k_1}} \text{ N}_2\text{O}_4\]