The suggested mechanism for the halogenation reaction is: (fast, equilibrium constant ); (slow, rate — Chemical Kinetics Chemistry Question
Question
The suggested mechanism for the halogenation reaction $CHCl_3(g) + Cl_2(g) \rightarrow CCl_4(g) + HCl(g)$ is: $Cl_2 \rightleftharpoons 2Cl^\bullet$ (fast, equilibrium constant $K_{eq}$); $CHCl_3 + Cl^\bullet \rightarrow HCl + CCl_3^\bullet$ (slow, rate constant $k$); $CCl_3^\bullet + Cl^\bullet \rightarrow CCl_4$ (fast). Which of the following statement(s) is/are correct based on this mechanism?
💡 Solution & Explanation
The slow step dictates the rate: $\text{Rate} = k[CHCl_3][Cl^\bullet]$. From the fast equilibrium, $K_{eq} = \frac{[Cl^\bullet]^2}{[Cl_2]}$, so $[Cl^\bullet] = K_{eq}^{1/2} [Cl_2]^{1/2}$. Substituting gives $\text{Rate} = k K_{eq}^{1/2} [CHCl_3][Cl_2]^{1/2}$. Therefore, the order w.r.t. $CHCl_3$ is 1, and w.r.t. $Cl_2$ is 0.5. Overall order is $1.5$. Since it has multiple steps, it is complex, not elementary.