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:
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In adsorption problems, always multiply the number of adsorbed molecules by the number of sites each molecule occupies.
The adsorption mechanism shows that one molecule of C\(_2\)H\(_4\) occupies two vacant sites (2V).
Therefore, each adsorbed C\(_2\)H\(_4\) removes 2 active sites from the vacant pool. Site balance:
Total active sites = Vacant sites + Occupied sites.
Since each C\(_2\)H\(_4\) occupies 2 sites:
\[
N_T = N_V + 2N_{C_2H_4}
\]
This matches option (B).
