Which of the following is a possible rate law for the reaction: a + b → c, if the reaction is first order in a and second order in b?

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

Answer: (B)

Verified step by step guidance

1. Understand that the rate law expresses the reaction rate as a function of the concentration of reactants raised to their respective orders. Here, the reaction is first order in 'a' and second order in 'b'.
2. Write the general form of the rate law using the given orders: rate = k [a]^m [b]^n, where m is the order with respect to 'a' and n is the order with respect to 'b'.
3. Substitute the given orders into the rate law: since the reaction is first order in 'a', m = 1, and since it is second order in 'b', n = 2. So, rate = k [a]^1 [b]^2.
4. Compare this expression to the options provided to identify which matches the form rate = k [a][b]^2 exactly.
5. Conclude that the correct rate law must have the concentration of 'a' raised to the first power and the concentration of 'b' raised to the second power, matching the option rate = k[a][b]^2.