Question

For a reaction : $A+B\to$ Products, the rate of the reaction at various concentrations are given below :
The rate law for the above reaction is

Expt No	[A]	[B]	rate $\left(mold{m}^{-3}{s}^{-1}\right)$
1.	0.2	0.2	2
2.	0.2	0.4	4
3	0.6	0.4	36

• A. $r=k[A{]}^2[B]$
• B. $r=k[A][B{]}^2$
• C. $r=k[A{]}^3[B]$
• D. $r=k[A{]}^2[B{]}^2$

Answer 1

Answer: (A)

Let order of reaction wrt $A$ and $B$ is $m$ and $n$ respectively. Then

rate $=k[A{]}^m[B{]}^n$

$2=k[0.2{]}^m[0.2{]}^n...(i)$

$4=k[0.2{]}^m[0.4{]}^n...(ii)$

$36=k[0.6{]}^m[0.4{]}^n...(iii)$

On comparing Eqs. (i) and (ii), we get

$\frac{4}{2}=\frac{[0.4{]}^n}{[0.2{]}^n}$

$\Rightarrow 2=2^n$

$\Rightarrow n=1$

Again on comparing Eqs. (ii) and (iii), we get

$\frac{36}{4}=\frac{[0.6{]}^m}{[0.2{]}^m}$

$\Rightarrow 9=3^2=3^m$

$\Rightarrow m=2$

$\therefore$ Rate law for the given reaction will be

$r=k[A{]}^2[B]$