How long will the catalyzed reaction take?

Question

The activation energy for a reaction is changed from 169 kJ/mol to 62.1 kJ/mol at 605 K by the introduction of a catalyst. If the uncatalyzed reaction takes about 2870 years to occur, about how long will the catalyzed reaction take? Assume the frequency factor A is constant and assume the initial concentrations are the same.

Answer 1

From first order kinetics: C/C₀ = e^-kt Taking ln of both sides and dividing by -k, you obtain

-ln(C/C₀)/k = t (Rate and time are inverse functions) The C is for "complete" reaction" and fixed for comparison.

t₂/t₁ = k₁/k₂

₌ Ae^(-E_A1/RT)/Ae^(-E_A2/RT) = e^((E_A2-E_A1)/RT)

t₂ = (2870 yr) e^((62.1 -169 kJ)(1000J/kJ)/((8.314 J/mole K)(605K))) = 1.69 x 10^-6 yrs = 53.3. secs.

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