For A + B → products, doubling [A] alone doubles the rate, and doubling [B] alone makes the rate 4 times as great. When [A] = 0.10 and [B] = 0.20 mol dm−3 the rate is 2.0 × 10−3 mol dm−3 s−1. What is the value of k?
- Rate × 2 when [A] × 2: first order in A. Rate × 4 = 22 when [B] × 2: second order in B.
- Rate law: rate = k[A][B]2, third order overall.
- k = rate ÷ ([A][B]2) = (2.0 × 10−3) ÷ (0.10 × 0.202) = (2.0 × 10−3) ÷ (4.0 × 10−3) = 0.50.
Answer: k = 0.50 dm6 mol−2 s−1