The rate law for the reaction $\mathrm{A}+\mathrm{B} \rightarrow \mathrm{C}$ at $25^{\circ} \mathrm{C}$ is…

The rate law for the reaction $\mathrm{A}+\mathrm{B} \rightarrow \mathrm{C}$ at $25^{\circ} \mathrm{C}$ is given by rate $=k[A][B]^2$. Calculate the rate of reaction if rate constant at same temperature is $6.25 \mathrm{~mol}^{-2} \mathrm{dm}^6 \mathrm{~s}^{-1}[[\mathrm{~A}]=1 \mathrm{M},[\mathrm{B}]=0.2 \mathrm{M}]$
  1. $0.25 \mathrm{~mol} \mathrm{dm}^{-3} \mathrm{~s}^{-1}$
  2. $0.5 \mathrm{~mol} \mathrm{dm}^{-3} \mathrm{~s}^{-1}$
  3. $0.75 \mathrm{~mol} \mathrm{dm}^{-3} \mathrm{~s}^{-1}$
  4. $1.25 \mathrm{~mol} \mathrm{dm}^{-3} \mathrm{~s}^{-1}$

Solution

$\begin{aligned} \text { Rate } & =\mathrm{k}[\mathrm{A}][\mathrm{B}]^2 \\ & =6.25 \mathrm{~mol}^{-2} \mathrm{dm}^6 \mathrm{~s}^{-1} \times 1 \mathrm{~mol} \mathrm{dm}^{-3} \\ & \quad \times 0.2 \mathrm{~mol} \mathrm{dm}^{-3} \times 0.2 \mathrm{~mol} \mathrm{dm}^{-3} \\ & =0.25 \mathrm{~mol} \mathrm{dm}^{-3} \mathrm{~s}^{-1}\end{aligned}$

Asked in: MHT CET 2023 (12 May Shift 2)

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