Given the reaction a → b, if the rate constant k is 0.25 mol L^{-1} s^{-1} at 75 °C and the reaction is first order in a, what is the correct rate law for this reaction?

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

Answer: (D)

Verified step by step guidance

1. Identify the order of the reaction given in the problem. It states the reaction is first order in species a, which means the rate depends linearly on the concentration of a.
2. Recall the general form of the rate law for a first-order reaction: \(\text{rate} = k [\text{reactant}]\) where \(k\) is the rate constant and the reactant concentration is raised to the power of 1.
3. Since the reaction is first order in a, the rate law must be \(\text{rate} = k [a]\).
4. Check the units of the rate constant \(k\) to confirm the order. For a first-order reaction, \(k\) has units of \(s^{-1}\). However, the problem gives \(k\) as \$0.25\ \text{mol L}^{-1} s^{-1}$, which suggests a second-order rate constant. This discrepancy indicates the problem might have a typo or the units are not consistent with the order stated.
5. Despite the unit confusion, based on the problem statement that the reaction is first order in a, the correct rate law is \(\text{rate} = k [a]\).