The rate constant for the first-order decomposition of H_{2}O_{2} 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})

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#### Solution

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 H_{2}O_{2} 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 × 10^{5}

Concept: Temperature Dependence of the Rate of a Reaction

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