Exercise 4 | Chemical Kinetics: Mechanisms

What is the activation energy Ea of a reaction whose reaction-rate constant k increases by a factor of 100 upon increasing the temperature from 300K to 400K?

Arrhenius equation: k = Ae-Ea/RT

Exp 1: reaction-rate constant = k1 and T1 = 300K
k1 = Ae-Ea/RT1

Exp 2: reaction-rate constant = k2 = 100 k1 and T2 = 400K
k2 = Ae-Ea/RT2

 

k2 / k1 = Ae-Ea/RT2 / Ae-Ea/RT1

k2 / k1 = e-Ea/RT2 + Ea/RT1

ln (k2 / k1) = EaR 1T1 - 1T2

⇒ Ea = ln 100 × 8.3141300 - 1400 = 4.59 x 104 J = 45.9 kJ