Question

For a reaction : $A + B \rightarrow$ 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 $\left( mol \,dm ^{-3} \,s ^{-1}\right)$
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

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