# The Rate Constant for the First-order Decomposition of H2O2 is Given by the Following Equation - Chemistry

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

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

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

(Given: R = 8.314 JK–1 mol–1)

#### Solution

Given:

Order of the reaction = First order

t1/2 = 200 minutes = 200 × 60 = 12,000 seconds

The relation between t1/2  and k is given by

t1/2 = 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

Ea = 1.91 × 105

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