For a first order reaction A ⟶ P, the temperature (T) dependent rate constant (k) was found to follow the equation log k = -2000(1/T) + 6.0. The pre-exponential factor A and the activation energy Ea, respectively, are
(IIT-JEE, 2009)k=Ae−Ea/RT
or log k = log A - Ea2.303RT
log k = -2000 (1T) + 6.0
On comparison, we get
log A = 6
or A = 106s−1
∴ Ea2.303R=2000
or Ea = 2.303 x 8.314 x 2000
=38.3kJmol−1