Question

For the reaction $2A\to B+3C;if-\frac{d\left[A\right]}{dt}=k_1[A{]}^2;\frac{d\left[B\right]}{dt}=k_2[A{]}^2;\frac{d\left[C\right]}{dt}=k_3[A{]}^2$ the correct reaction between $k_1,k_{2}and{k}_3$ is :

• A.
  $k_1=k_2=k_3$
• B.
  $2k_1=k_2=3k_2$
• C.
  $4k_1=k_2=3k_2$
• D.
  $\frac{k_1}{2}=k_2=\frac{k_3}{3}$

Answer 1

The correct option is D

$\frac{k_1}{2}=k_2=\frac{k_3}{3}$
(d) Rate of reaction

$=-\frac{1}{2}\frac{d\left[A\right]}{dt}=\frac{d\left[B\right]}{dt}=\frac{1}{3}\frac{d\left[C\right]}{dt}or\frac{k_1[A{]}^2}{2}=\frac{k_2[A{]}^2}{1}=\frac{k_3[A{]}^3}{3}\frac{k_1}{2}=k_2=\frac{k_3}{3}$