The rate law equation for a reaction between $\mathrm{A}, \mathrm{B}$ and $\mathrm{C}$ is…

The rate law equation for a reaction between $\mathrm{A}, \mathrm{B}$ and $\mathrm{C}$ is $\mathrm{r}=\mathrm{k}[\mathrm{A}][\mathrm{B}][\mathrm{C}]^2$, what will be new rate of reaction if concentration of both A and B are doubled.
  1. $2 r$
  2. $4 \mathrm{r}$
  3. $6 \mathrm{r}$
  4. $8 r$

Solution

$\begin{aligned} & \mathrm{r}=\mathrm{k}[\mathrm{A}][\mathrm{B}][\mathrm{C}]^2 \\ & \mathrm{~A} \rightarrow 2 \mathrm{~A} \\ & \mathrm{~B} \rightarrow 2 \mathrm{~B} \\ & \mathrm{r}_{\text {new }}=\mathrm{k}[2 \mathrm{~A}][2 \mathrm{~B}][\mathrm{C}]^2 \\ & \frac{\mathrm{r}_{\text {new }}}{\mathrm{r}}=\frac{\mathrm{k}[2 \mathrm{~A}][2 \mathrm{~B}][\mathrm{C}]^2}{\mathrm{k}[\mathrm{A}][\mathrm{B}][\mathrm{C}]^2} \\ & \frac{\mathrm{r}_{\text {new }}}{\mathrm{r}}=2 \times 2, \mathrm{r}_{\text {new }}=4 \mathrm{r}\end{aligned}$

Asked in: MHT CET 2021 (23 Sep Shift 2)

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