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Question

The rate constant for the first order decomposition of H2O2 is given by the following equation:
logk=14.341.25×104K/T

Calculate Ea for this reaction and at what temperature will its half-period be 256 minutes?

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Solution

The expression for the rate constant is as follows:
logk=14.341.25×104K/T...(i)

Comparing it with Arrhenius equation, we get-
logk=logAEa2.303RT
Therefore,Ea2.303R=1.25×104

Ea=1.25×104×2.303×8.314

The activation energy =Ea=239339J/mol=239.339kJ/mol
Half life period, t1/2=256min=256×60 sec
k=0.693t1/2

k=0.693256×60sec

k=4.51×105/s

Substitute in equation (i), we get-

log4.51×105=14.341.25×104K/T

4.35=14.341.25×104K/T

T=669 K

Hence, the temperature at which the half-life period is 256 minutes is 669 K.

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