For a reaction $\mathrm{A}+\mathrm{B} \rightarrow$ product, if $[\mathrm{A}]$ is doubled keeping [B]…

For a reaction $\mathrm{A}+\mathrm{B} \rightarrow$ product, if $[\mathrm{A}]$ is doubled keeping [B] constant, the rate of reaction doubles. Calculate the order of reaction with respect to $A$.
  1. $0$
  2. $1 / 2$
  3. $1$
  4. $2$

Solution

$\begin{array}{ll} & \mathrm{A}+\mathrm{B} \longrightarrow \text { Product } \\ & \text { Rate }^{\mathrm{k}[\mathrm{A}]^x[\mathrm{~B}]^{\mathrm{y}}} \\ & \text { Rate }_1=\mathrm{k}[2 \mathrm{~A}]^x[\mathrm{~B}]^{\mathrm{y}} \\ \therefore \quad & \frac{\text { Rate }_1}{\text { Rate }}=\frac{\mathrm{k} 2^x[\mathrm{~A}]^x[\mathrm{~B}]^y}{\mathrm{k}[\mathrm{A}]^x[\mathrm{~B}]^{\mathrm{y}}}\end{array}$ $\begin{array}{ll} \therefore & \frac{2 \times \text { Rate }}{\text { Rate }}=2^x \\ \therefore & 2^x=2 \\ \therefore & x=1 \end{array}$ $\therefore \quad$ Order of reaction with respect to $A=1$

Asked in: MHT CET 2023 (11 May Shift 2)

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