Question

The rate constant for the first-order decomposition of H₂O₂ is given by the following equation:

`logk=14.2-(1.0xx10^4)/TK`

Calculate E_a for this reaction and rate constant k if its half-life period be 200 minutes.

(Given: R = 8.314 JK^–1 mol^–1)

Answer 1

Given:

Order of the reaction = First order

t_{1/2 =} 200 minutes = 200 × 60 = 12,000 seconds

The relation between t_1/2  and k is given by

t_1/2 = 0.693/k

k = 0.693/12000 = 5.7 × 10⁻⁵

The rate constant for the first-order decomposition of H₂O₂ is given by

`logk=14.2-(1.0xx10^4)/TK...................(i)`

By Arrhenius equation

`log k=logA-E_a/(2.303RT)...............(ii)`

Comparing (i) and (ii), we get

E_a = 1.91 × 10⁵