Consider a multistep reaction where the slowest (rate-determining) step is: 2 NO_2(g) → NO_3(g) + NO(g). What is the best rate law for the overall reaction?

• A. rate = k[NO_3]^2
• B. rate = k[NO_2]^2
• C. rate = k[NO_2][NO_3]
• D. rate = k[NO_2]

Answer: (B)

Verified step by step guidance

1. Identify the rate-determining step (RDS) in the reaction, which is the slowest step controlling the overall reaction rate. Here, the RDS is given as: 2 NO_2(g) → NO_3(g) + NO(g).
2. Write the rate law expression based on the molecularity of the rate-determining step. Since the RDS involves two NO_2 molecules reacting, the rate law depends on the concentration of NO_2.
3. Express the rate law as: \(\text{rate} = k[\mathrm{NO}_2]^2\), where \(k\) is the rate constant and the exponent 2 corresponds to the stoichiometric coefficient of NO_2 in the RDS.
4. Understand that intermediates like NO_3 and products like NO do not appear in the rate law unless they are involved in the rate-determining step or affect the rate directly.
5. Conclude that the best rate law for the overall reaction is \(\text{rate} = k[\mathrm{NO}_2]^2\), reflecting the dependence on the reactant concentration in the slowest step.