Question

From the following data, show that the decomposition of hydrogen peroxide is a reaction of the first order:

t (min)	0	10	20
V (ml)	46.1	29.8	19.3

Where t is the time in minutes and V is the volume of standard KMnO₄ solution required for titrating the same volume of the reaction mixture.

Answer 1

k = `2.303/"t" log  (["A"_0])/(["A"])`

k = `(2.303/"t") log ("V"_0/"V"_"t")`

In the present case, V₀ = 46.1 ml.

The value of k at each instant can be calculated as follows:

t (min)	Vt	k = `(2.303/"t") log ("V"_0/"V"_"t")`
10	29.8	k = `2.303/10 log (46.1/29.8)` = 0.0436 min−1
20	19.3	k = `2.303/20 log (46.1/19.3)` = 0.0435 min−1

Thus, the value of k comes out to be nearly constant. Hence it is a reaction of the first order.