Question

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

Expt No	[A]	[B]	rate (mol $d{m}^{-3}{s}^{-1}$)
1	0.2	0.2	2
2	0.2	0.4	4
3	0.6	0.4	36

The rate law for the above reaction is :

• A. $r=K\left[A{]}^2\right[B]$
• B. $r=K\left[A\right][B{]}^2$
• C. $r=K\left[A{]}^3\right[B]$
• D. $r=K\left[A{]}^2\right[B{]}^2$

Answer 1

The correct option is A $r=K\left[A{]}^2\right[B]$

From second and third experiment, we observe that when the concentration of $B$ is kept constant at $0.4$ M and the concentration of $A$ is trebled from $0.2$ M to $0.6$ M, the rate increases 9 times from 4 to 36. Hence, the order of the reaction with respect to $A$ is 2.
From first and second experiment, we observe that when the concentration of $A$ is kept constant at 0.2 M and the concentration of $A$ is doubled from 0.2 M to 0.4 M, the rate doubles from 2 to 4. Hence, the order of the reaction with respect to $B$ is 1.
The rate law for the reaction is $r=K\left[A{]}^2\right[B]$