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Question

In Arrhenius equation for a certain reaction, the values of A and Ea (activation energy) are 4×1013sec1 and 98.6 kJ mol1 respectively. If the reaction is of first order, at what temperature will its half life period be 10 minutes?

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Solution

According to Arrhenius equation,
k=AeEa/RT
or logek=logeAEaRT
or 2.303log10k=2.303log10AEaRT
For a first order reaction t1/2=0.693k
So, k=0.693600sec1(t1/2=10min=600sec)
=1.1×103sec1
Hence, log(1.1×103)=log(4×1013)98.6×1032.303×8.314×T
T=310.95 K

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