A complex reaction is established to follow the mechanism: (fast equilibrium, ), followed tightly by — Chemical Kinetics Chemistry Question
Question
A complex reaction is established to follow the mechanism: $NO + Br_2 \rightleftharpoons NOBr_2$ (fast equilibrium, $K_{eq} = 2.0 \text{ M}^{-1}$), followed tightly by $NOBr_2 + NO \xrightarrow{k_2} 2NOBr$ (slow, $k_2 = 1.5 \text{ M}^{-1} \text{ s}^{-1}$). The overall integrated rate law takes the exact form $\text{Rate} = k_{eff} [NO]^2 [Br_2]$. Calculate the absolute numeric value of $k_{eff}$ in $\text{M}^{-2} \text{ s}^{-1}$.
💡 Solution & Explanation
Based strictly on the designated slow step, $\text{Rate} = k_2[NOBr_2][NO]$. Using the fast equilibrium to resolve the intermediate, $K_{eq} = \frac{[NOBr_2]}{[NO][Br_2]} \Rightarrow [NOBr_2] = K_{eq}[NO][Br_2]$. Substituting this gives $\text{Rate} = k_2 (K_{eq}[NO][Br_2]) [NO] = (k_2 K_{eq}) [NO]^2 [Br_2]$. Thus, the effective overall rate constant $k_{eff} = k_2 \times K_{eq} = 1.5 \times 2.0 = 3.0 \text{ M}^{-2} \text{ s}^{-1}$.