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For the reaction A + B → P with $\text{rate} = k[A][B]^2$, rate = $3.6 \times 10^{-2}$ mol dm⁻³ s⁻¹ when [A] = 0.2 M and [B] = 0.1 M. $k$ equals:

A$18$ mol⁻² dm⁶ s⁻¹
B$3.6$ mol⁻² dm⁶ s⁻¹
C$36$ mol⁻² dm⁶ s⁻¹
D$1.8$ mol⁻² dm⁶ s⁻¹
Answer & Solution
Correct answer: A. $18$ mol⁻² dm⁶ s⁻¹
$k = \text{rate}/([A][B]^2) = (3.6\times10^{-2})/(0.2 \times (0.1)^2) = (3.6\times10^{-2})/(0.002) = 18$ mol⁻² dm⁶ s⁻¹.
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