The rate equation for the gaseous phase reaction 2 AB + B₂ $\to$ 2 AB₂, is observed to be

$\text{ Rate }=k[\mathrm{AB}{]}^2\left[{\mathrm{B}}_2\right]$

Possible mechanism(s) consistent with this rate equation is/are:

In mechanism each step is elementary whose rate law can be written directly from stoichiometric coefficients of reactants. Rate of reaction = rate of slowest step.
Rate law should not contain concentration of intermediate. It
may contain concentration of reactant, product and catalyst.

1. Rate = k[AB]₂ [B₂]

2. Rate = rate of slowest step = $k\left[{\mathrm{B}}_2\right]\left[{\mathrm{A}}_2{\mathrm{B}}_2\right]=$$\mathrm{k}\left[{\mathrm{B}}_2\right]{\mathrm{K}}_{\mathrm{e}}\left[\mathrm{AB}\right]\left[\mathrm{AB}\right]={\mathrm{k}}^{\mathrm{\prime }}[\mathrm{AB}{]}^2\left[{\mathrm{B}}_2\right]$

3. $\text{ Rate }=k\left[\mathrm{AB}\right]\left[{\mathrm{B}}_2\right]$

4. Rate = rate of slowest step = $k\left[\mathrm{AB}\right]\left[{\mathrm{AB}}_3\right]=$$\mathrm{k}\left[\mathrm{AB}\right]{\mathrm{K}}_{\mathrm{eq}}\left[\mathrm{AB}\right]\left[{\mathrm{B}}_2\right]={\mathrm{k}}^{\mathrm{\prime }}[\mathrm{AB}{]}^2\left[{\mathrm{B}}_2\right]$