Question

Consider a reaction $aG+bH\to Products$. When the concentration of both the reactants G and H is doubled, the rate increases by eight times. However, when a concentration of H fixed, the rate is doubled. The overall order of the reaction is:

• A. 0
• B. 1
• C. 2
• D. 3

Answer 1

The correct option is D 3

The rate law expression is $R=k\left[G{]}^a\right[H{]}^b$ ......(1)
The rate of reaction increases by a factor of 2 on doubling the concentration of 'G' .
The rate law expression becomes $R^{\prime }2R=k{2}^a\left[G{]}^a\right[H{]}^b$ ......(2)
Divide equation (2) with equation (1)
$\frac{2R}{R}=\frac{R^{\prime }=2R=k{2}^a\left[G{]}^a\right[H{]}^b}{k\left[G{]}^a\right[H{]}^b}$
Hence,
$2=2^a$ or $a=1$
The rate of freaction increases by a factor of 8 on doubling the concentration of 'G' and 'H'
The rate law expression becomes $k{2}^a\left[G{]}^a{2}^b\right[H{]}^b$ ......(3)
Divide equation (3) with equation (1)
$\frac{8R}{R}=\frac{k{2}^a\left[G{]}^a{2}^b\right[H{]}^b}{k\left[G{]}^a\right[H{]}^b}$
Hence,
$8=2^a{2}^b$ or $b=2$
The overall order of the reaction is $a+b=1+2=3$