For the reaction a → b, if the reaction is first order with respect to a and the rate constant is k, which of the following is the correct rate law?

• A. rate = k[b]
• B. rate = k
• C. rate = k[a]^2
• D. rate = k[a]

Answer: (D)

Verified step by step guidance

1. Identify the order of the reaction with respect to species a. Since the problem states it is first order with respect to a, the rate depends linearly on the concentration of a.
2. Recall the general form of the rate law for a reaction that is first order in a reactant: \(\text{rate} = k [\text{reactant}]^1\).
3. Apply this to the given reaction a → b, where the reactant is a. The rate law becomes \(\text{rate} = k [a]\).
4. Understand that the rate depends on the concentration of the reactant a, not the product b, so \(\text{rate} = k [b]\) is incorrect.
5. Also, since the reaction is first order, the rate law cannot be \(\text{rate} = k [a]^2\) (which would be second order) or just \(\text{rate} = k\) (which would be zero order).