The uncatalyzed pathway for a gas-phase reaction has an activation energy of 85 kJ/mol. A catalyst provides an alternative pathway whose activation energy is lowered by 25 kJ/mol. At 300 K, roughly how many times larger is the rate constant of the catalyzed pathway?

Core Concept

The Arrhenius expression k = Ae^(-Ea/RT) shows that k scales with e^(-Ea/RT), so lowering Ea multiplies k by e^(dEa/RT). Here d(Ea/RT) = 25000 J/mol divided by (8.314 x 300) = about 10. The ratio is therefore e^(10), roughly 2 x 10^4. Because the barrier sits inside an exponent, a modest energy saving produces a tens-of-thousands-fold rate gain.