Write the rate law for the following mechanism:Step 1: NO₂ + NO₂ → NO₃ + NO    (slow)
Step 2: NO₃ → NO + O₂    (fast)

• A. rate = k[NO₂]
• B. rate = k[NO₃]
• C. rate = k[NO₂]²
• D. rate = k[NO₃][NO]
• E. rate = k[NO][O₂]

Answer: (C)

Verified step by step guidance

1. Identify the slow step in the mechanism, as it determines the rate law for the overall reaction. In this case, Step 1 is the slow step: NO2 + NO2 → NO3 + NO.
2. Write the rate law based on the slow step. The rate law is determined by the reactants involved in the slow step. Since Step 1 involves two NO2 molecules, the rate law is: rate = k[NO2]^2.
3. Recognize that the fast step does not directly affect the rate law of the overall reaction, but it completes the mechanism. Step 2: NO3 → NO + O2 is fast and does not appear in the rate law.
4. Understand that intermediates like NO3, which are produced and consumed within the mechanism, do not appear in the rate law for the overall reaction.
5. Conclude that the rate law for the overall reaction is based solely on the slow step, resulting in: rate = k[NO2]^2.