Question

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

Answer 1

Experiment no.	G (Mol/L)	H (Mol/L)	Rate $Mol{L}^{-1}tim{e}^{-1}$
1	a	b	r
2	2a	2b	8r
3	2a	b	2r

Applying, $r=k\left[G{]}^x\right[H{]}^y...\left(i\right)$
$8r=k[2G{]}^x.[2H{]}^y$
$8r=k{.2}^{x+y}[G{]}^x.[H{]}^y$
Substituting the value of $r$ from equation (i)
$8k[G{]}^x.[H{]}^y=k{.2}^{x+y}\left[G{]}^x\right[H{]}^y$
$2^{x+y}=8$
$\Rightarrow 2^{x+y}=2^3$
$\Rightarrow x+y=3$
Overall order is $3$.