Question

$aA+bB\to$ Product, $dx/dt=k\left[A{]}^a\right[B{]}^b$. If concentration of $A$ is doubled, rate is four times. If concentration of $B$ is made four times, rate is doubled. What is relation between rate of disappearance of $A$ and that of $B$?

• A. $-\left\{d\right[A\left]/dt\right\}=-\left\{d\right[B\left]/dt\right\}$
• B. $-\left\{d\right[A\left]/dt\right\}=-\left\{4d\right[B\left]/dt\right\}$
• C. $-\left\{4d\right[A\left]/dt\right\}=-\left\{d\right[B\left]/dt\right\}$
• D. $Noneofthese$

Answer 1

The correct option is B $-\left\{d\right[A\left]/dt\right\}=-\left\{4d\right[B\left]/dt\right\}$

$aA+bB\Rightarrow$ Product

Rate = $K\left[A{]}^a\right[B{]}^b$

On doubling A

Rate $\to 4$ times

$\Rightarrow a=2$

On making concentration of B four times

Rate $\to 2$ times

$b=1/2$

$\because ROR=\frac{-1}{a}\frac{d\left[A\right]}{dt}=-\frac{1}{b}\frac{d\left[B\right]}{dt}$

$\frac{-d\left[A\right]}{dt}=-4\frac{d\left[B\right]}{dt}$