Consider the reaction mechanism:Step 1: NO_2 + F_2 → NO_2F + FStep 2: NO_2 + F → NO_2FIf the second step is rate determining, what is the correct rate law expression for the overall reaction?

• A. rate = k[NO_2F][F]
• B. rate = k[NO_2]^2[F_2]
• C. rate = k[NO_2][F_2]
• D. rate = k[NO_2][F]

Answer: (D)

Verified step by step guidance

1. Identify the rate-determining step (RDS) in the mechanism, which is given as Step 2: \(\mathrm{NO_2 + F \rightarrow NO_2F}\). The rate law is based on this slowest step.
2. Write the rate law expression for the RDS using the reactants involved: \(\text{rate} = k[\mathrm{NO_2}][\mathrm{F}]\).
3. Recognize that the intermediate species \(\mathrm{F}\) is not usually present in the overall rate law, so express its concentration in terms of the initial reactants using the fast pre-equilibrium step (Step 1).
4. Write the equilibrium expression for Step 1: \(\mathrm{NO_2 + F_2 \rightleftharpoons NO_2F + F}\), and solve for \([\mathrm{F}]\) in terms of \([\mathrm{NO_2}]\) and \([\mathrm{F_2}]\).
5. Substitute the expression for \([\mathrm{F}]\) back into the rate law from Step 2 to get the overall rate law in terms of only the stable reactants, confirming the correct form.