For the reaction A + B → P, the following initial-rate data were obtained: | [A]/M | [B]/M | Initial rate (M/s) | |---|---|---| | 0.4 | 0.2 | 4.0 × 10⁻⁵ | | 0.6 | 0.2 | 6.0 × 10⁻⁵ | | 0.8 | 0.4 | 3.2 × 10⁻⁴ | The rate law is:
Arate = $k[A]$
Brate = $k[A]^2[B]$
Crate = $k[A][B]^2$
Drate = $k[A][B]$
Answer & Solution
Correct answer: C. rate = $k[A][B]^2$
Rows 1→2: [A] × 1.5, [B] same, rate × 1.5 ⇒ order in A = 1. Rows 1→3: [A] × 2, [B] × 2, rate × 8. Doubling [A] contributes ×2 (since order in A = 1); remaining factor 4 = 2² is from [B] ⇒ order in B = 2. Rate = $k[A][B]^2$ (overall order 3).
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