A reaction has a rate constant of 0.0117 s-1 at 400.0 k and 0.689 s-1 at 450.0 k. calculate the activation energy in kilojoules for this reaction.

By definition we have to:

LOG (k2 / k1) = (-Ea/R) * (1/T1-1/T2)

Where,

k1 = 0.0117 s-1

K2 = 0.689 s-1

T1 = 400.0 k

T2 = 450.0 k

R is the ideal gas constant

R = 8.314 KJ / (Kmol * K)

Substituting

ln (0.0117/0.689) = - Ea / (8.314) * ((1/400) - (1/450))

Clearing Ea:

Ea = 122 kJ

answer

the activation energy in kilojoules for this reaction is

Ea = 122 kJ