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

log k = 14.34 – 1.25 × 104K/T

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

Arrhenius equation is given by
k=AeEa/RT
lnk=lnA-EaRT
lnk=logA-EaRT
logk=logA-Ea2.303RT(i)

The given equation is
logk=14.31-1.25×104K/T(ii)
From equation (i) and (ii), we obtain
Ea2.303RT=1.25×104KT
Ea=1.25×104K×2.303×R
=1.25×104K×2.303×8.314JK-1mol-1
=239339.3jmol-1(approximaterly)
=239.34kJmol-1
Also, when t 1/2 = 256 minutes,
k=0.693t12
=0.693256
=2.707×10-3min-1
=4.51×10-5s-1
It is also given that, log k = 14.34 − 1.25 ×104K/T
log(4.51×10-5)=14.34-1.25×104KT
log(0.654-05)=14.34-1.25×104KT
1.25×104KT=18.686
T=1.25×104K18.686
=686.95K
=669K(approximately)