Q36 / 150 · MHT CET 2021 (23 Sep Shift 1) · Chemistry

A reaction is first order with respective to A and second order with respective to $B$. What is the effect on reaction rate if concentration of B is increased 3 times?

  • A
    Rate increases 6 times
  • Correct answer
    B
    Rate increase 9 times
  • C
    Rate increase 2 times
  • D
    Rate increase 3 times

Solution

Rate law of reaction, $$ \mathrm{r}=\mathrm{k}[\mathrm{A}]^{\prime}[\mathrm{B}]^2 $$ If concentration of $\mathrm{B}$ is increased 3 times, $$ \begin{aligned} & \mathrm{B} \rightarrow 3 \mathrm{~B} \\ & \mathrm{r}_{\mathrm{New}}=\mathrm{k}[\mathrm{A}][3 \mathrm{~B}]^2 \\ & \frac{\mathrm{r}_{\mathrm{New}}}{\mathrm{r}}=\frac{\mathrm{k}[\mathrm{A}][3 \mathrm{~B}]^2}{\mathrm{k}[\mathrm{A}][\mathrm{B}]^2} \\ & \frac{\mathrm{r}_{\mathrm{New}}}{\mathrm{r}}=3^2 \\ & \mathrm{r}_{\mathrm{New}}=9 \mathrm{r} \end{aligned} $$ Rate increase 9 times.

Hence, the correct answer is option: 'B'.

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