Given the following elementary steps: Step 1: A + B → C + D (fast) Step 2: C + B → D (slow), what is the overall rate law for the reaction?

• A. Rate = k[A][B]^2
• B. Rate = k[A][B]
• C. Rate = k[A]^2[B]
• D. Rate = k[C][B]

Answer: (D)

Verified step by step guidance

1. Identify the rate-determining step: The slowest step in a reaction mechanism is the rate-determining step. In this problem, Step 2 (C + B → D) is the slow step, so it determines the rate of the overall reaction.
2. Write the rate law based on the rate-determining step: The rate law is determined by the reactants involved in the rate-determining step. For Step 2, the reactants are C and B, so the rate law is Rate = k[C][B].
3. Consider the fast equilibrium assumption: In some mechanisms, the fast step reaches equilibrium quickly, affecting the concentration of intermediates. However, in this problem, the fast step does not affect the rate law derived from the slow step.
4. Verify the consistency of the rate law with the given options: Compare the derived rate law Rate = k[C][B] with the provided options to ensure it matches one of them.
5. Understand the role of intermediates: C is an intermediate formed in Step 1 and consumed in Step 2. The rate law includes intermediates when they are part of the rate-determining step.