QJEEAdv07Che342: JEE Advanced 2007 Chemistry - Class 12 JEEAdv07Che342 Solution: Consider a reaction aG + bH Products. When concentration of…

The rate law expression is

$\mathrm{R}=k[\mathrm{G}]^{a}[\mathrm{H}]^{b}$ ...... (i)

The rate of reaction increases by a factor of 2 on doubling the concentration of ' $\mathrm{G}$ '.

The rate law expression becomes

$\mathrm{R}^{\prime}=2 \mathrm{R}=k 2^{a}[\mathrm{G}]^{a}[\mathrm{H}]^{b}$ ..... (ii)

Divided equation (ii) with eqn. (i)

$\begin{aligned}\frac{\mathrm{R}^{\prime}}{\mathrm{R}} & =\frac{2 \mathrm{R}}{\mathrm{R}}=\frac{k 2^{a}[\mathrm{G}]^{a}[\mathrm{H}]^{b}}{k 2[\mathrm{G}]^{a}[\mathrm{H}]^{b}} \\2 & =2^{a} \\a & =1\end{aligned}$

The rate of reaction increases by a factor of 8 on doubling the concentration of $\mathrm{G}$ and ' $\mathrm{H}$ '.

The rate law expression becomes

Rate $=\mathrm{R}^{\prime \prime} k 2^{a}[\mathrm{G}]^{a} 2^{b}[\mathrm{H}]^{b}$ ..... (iii)

Divide equation (iii) with equation (i)

$\begin{aligned}\frac{8 \mathrm{R}}{\mathrm{R}} & =\frac{k 2^{a}[\mathrm{G}]^{a} 2^{b}[\mathrm{H}]^{b}}{k[\mathrm{G}]^{a}[\mathrm{H}]^{b}}\end{aligned}$

$8=2^a2^b$

or $b=2$

The overall order of reaction is

$a+b=1+2=3$