Rate of reaction, $\mathrm{A}+\mathrm{B} \rightarrow$ product, is $7.2 \times 10^{-2} \mathrm{moldm}^{-3}…

Rate of reaction, $\mathrm{A}+\mathrm{B} \rightarrow$ product, is $7.2 \times 10^{-2} \mathrm{moldm}^{-3} \mathrm{~s}^{-1}$ at $[\mathrm{A}]=0.4 \mathrm{~mol} \mathrm{dm}^{-3}$ and $[B]=0.1 \mathrm{~mol} \mathrm{dm}^{-3}$. The reaction is first order in A and second order in B. Calculate rate constant.
  1. $14 \mathrm{~mol}^{-2} \mathrm{dm}^6 \mathrm{~s}^{-1}$
  2. $12 \mathrm{~mol}^{-2} \mathrm{dm}^6 \mathrm{~s}^{-1}$
  3. $18 \mathrm{~mol}^{-2} \mathrm{dm}^6 \mathrm{~s}^{-1}$
  4. $20 \mathrm{~mol}^{-2} \mathrm{dm}^6 \mathrm{~s}^{-1}$

Solution

$\begin{aligned} & \text {Rate }=\mathrm{k}[\mathrm{A}][\mathrm{B}]^2 \\ & \begin{aligned} \mathrm{k} & =\frac{\text { Rate }}{[\mathrm{A}][\mathrm{B}]^2}=\frac{0.072 \mathrm{~mol} \mathrm{dm}}{[0.4][0.1]^2} \\ & =18 \mathrm{~mol}^{-2} \mathrm{dm}^6 \mathrm{~s}^{-1}\end{aligned}\end{aligned}$

Asked in: MHT CET 2024 (16 May Shift 1)

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