Question

Consider the data given below for the reaction:

\[\ce{A + B-> Product}\]

S. No.	conc. of [A] mol L-1	conc. of [B] mol L-1	Rate; mol L-1 sec-1
1.	0.1	0.1	4.0 × 10-4
2.	0.2	0.2	1.6 × 10-3
3.	0.5	0.1	1.0 × 10-2
4.	0.5	0.5	1.0 × 10-2

Answer the following questions.

1. What is the order of reaction with respect to A and B?
2. Calculate the rate constant.
3. Determine the reaction rate when the concentration of A and B are 0.2 mol L^-1 sec^-1 and 0.35 mol L^-1 sec^-1 respectively.

Answer 1

(i) Order with respect to [A] is 2 and with respect to [B] is 0.

(ii) Using any of the experimental data, we can now calculate the rate constant. 

`"Rate" = "k"["A"]^2["B"]^0`

`4.0 xx 10^(-4) = "k"[0.1]^2`

`4.0 xx 10^(-4) = "k"[0.01]`

`"k" = (4.0 xx 10^(-4))/0.01`

k = 4.0 × 10^-2 mol^-1 Ls^-1

∴ Rate constant k is 4.0 × 10^-2 mol^-1 Ls^-1

(iii) To determine the reaction rate when the concentration of A is 0.2 mol L^-1 and the concentration of B is 0.35 mol L^-1 we can use,

The rate law for the reaction:

`"Rate" = "k"[A]^2[B]^0`

Substituting the given concentration of A into the rate law:

Rate = k[A]²

`"Rate" = (4.0 xx 10^(-2))(0.2)^2`4.0

`"Rate" = (4.0 xx 0^(-2))(0.04)`

Rate = 1.6 ×  10^-3 mol L^-1 s^-1

∴ reaction rate when the concentration of A is 0.2 mol L^-1 and the concentration of B is 0.35 mol L^-1 is 1.6 ×  10^-3 mol L^-1 s^-1