Considering the rate law, rate = k[a]^2[b], which of the following statements is correct?

• A. The overall order of the reaction is 2.
• B. The reaction is second order with respect to a and first order with respect to b.
• C. Doubling the concentration of a will double the rate.
• D. The reaction is first order with respect to a and second order with respect to b.

Answer: (B)

Verified step by step guidance

1. Identify the rate law given: \(\text{rate} = k[\text{a}]^{2}[\text{b}]\). This shows how the rate depends on the concentrations of reactants a and b.
2. Determine the order with respect to each reactant by looking at the exponents: the order with respect to a is 2 (because of \([\text{a}]^{2}\)), and the order with respect to b is 1 (because of \([\text{b}]^{1}\)).
3. Calculate the overall order of the reaction by adding the individual orders: overall order = 2 (from a) + 1 (from b) = 3.
4. Analyze the effect of doubling the concentration of a on the rate: since the rate depends on \([\text{a}]^{2}\), doubling [a] will increase the rate by a factor of \$2^{2} = 4$, not just double it.
5. Based on these observations, conclude that the correct statement is: 'The reaction is second order with respect to a and first order with respect to b.'