Question

For a reaction, $A+B\to C+D$, if the concentration of $A$ is doubled without altering the concentration of $B$, the rate gets doubled. If the concentration of $B$ is increased by nine times without altering the concentration of $A$, the rate gets tripled. The order of reaction is:

• A. $2$
• B. $1$
• C. $\frac{3}{2}$
• D. $\frac{4}{3}$

Answer 1

The correct option is C $\frac{3}{2}$

For the reaction,
$A+B\to C+D$
$Rate=k\left[A{]}^{\alpha }\right[B{]}^{\beta }...\left(i\right)$
$2\times rate=k\left[2A{]}^{\alpha }\right[B{]}^{\beta }...\left(ii\right)$
$3\times rate=k\left[2A{]}^{\alpha }\right[9B{]}^{\beta }...\left(iii\right)$
From equations, $\left(i\right)$ and $\left(ii\right)$,
$\alpha =1$
From equations, $\left(i\right)$ and $\left(iii\right)$,
$\beta =\frac{1}{2}$
$\text{Order}=\alpha +\beta =1+\frac{1}{2}=\frac{3}{2}$