The reaction $2 \mathrm{~A}+\mathrm{B}+\mathrm{C} \longrightarrow \mathrm{D}+\mathrm{E}$ is found to. be…

The reaction $2 \mathrm{~A}+\mathrm{B}+\mathrm{C} \longrightarrow \mathrm{D}+\mathrm{E}$ is found to. be first order in A , second order in B and zero order in C . What is the effect of increasing concentration of all reactants twice?
  1. Rate of reaction increases 8 times.
  2. Rate of reaction increases 24 times.
  3. Rate of reaction increases 36 times.
  4. Rate of reaction remains unaffected.

Solution

$\begin{aligned} & \text { Rate }=\mathrm{k}[\mathrm{~A}][\mathrm{B}]^2[\mathrm{C}]^0 \\ & (\text { Rate })_1=\mathrm{k} \times[2 \mathrm{~A}] \times[2 \mathrm{~B}]^2 \times[2 \mathrm{C}]^0 \\ & =8 \mathrm{k}[\mathrm{~A}][\mathrm{B}]^2[\mathrm{C}]^0 \\ & \therefore \quad \frac{(\text { Rate })_1}{\text { Rate }}=\frac{8 \mathrm{k}[\mathrm{~A}][\mathrm{B}]^2[\mathrm{C}]^0}{\mathrm{k}[\mathrm{~A}][\mathrm{B}]^2[\mathrm{C}]^0}=8 \\ & \therefore \quad(\text { Rate })_1=8 \times \text { Rate } \end{aligned}$ i.e., rate of reaction increases 8 times.

Asked in: MHT CET 2024 (09 May Shift 2)

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