Ethylene adsorbs on the vacant active sites V of a transition metal catalyst according to the following mechanism.

If \(N_T\), \(N_V\) and \(N_{C_2H_4}\) denote the total number of active sites, number of vacant active sites and number of adsorbed C\(_2\)H\(_4\) molecules, respectively, the balance on the total number of active sites is given by: