Arrhenius equation is given by,
k = Ae -Ea/RT
⇒ In k = In A - Ea/RT
⇒ In k = Log A - Ea/RT
⇒ Log k = Log A - Ea/2.303RT .......(i)
The given equation is
Log k = 14.34 - 1.25 x 104 K/T ........(ii)
From equation (i) and (ii), we obtain
Ea/2.303RT = 1.25 x 104 K/T
⇒ Ea = 1.25 x 104 K x 2.303 x R
= 1.25 x 104 K x 2.303 x 8.314 J K-1 mol-1
= 239339.3 J mol-1 (approximately)
= 239.34 kJ mol-1
Also, when t1/2= 256 minutes,
k = 0.693 / t1/2
= 0.693 / 256
= 2.707 x 10-3 min-1
= 4.51 x 10-5 s-1
It is also given that, log k= 14.34 - 1.25 x 104 K/T
= 668.95 K
= 669 K (approximately)