Chapter 20, Problem 20.75E

A proposed mechanism for the gas-phase chlorination of methane is

$\begin{array}{c}{\text{Cl}}_{\text{2}}+{\text{CH}}_{\text{4}}\to {\text{CH}}_4\text{Cl}+\text{Cl}\cdot \\ {\text{CH}}_4\text{Cl}\to {\text{CH}}_3\cdot +\text{HCl}\\ {\text{CH}}_3\cdot +{\text{Cl}}_{\text{2}}\to {\text{CH}}_3\text{Cl}+\text{Cl}\cdot \\ \text{Cl}\cdot +{\text{CH}}_4\to {\text{CH}}_3\cdot +\text{HCl}\end{array}$

Suppose the first step is the RDS. What is the expected rate law in terms of the original reactants, ${\text{Cl}}_{\text{2}}$ and ${\text{CH}}_4$? How would you determine if this mechanism might be a potentially correct (or, for that matter, a potentially incorrect) one?