Question

The activation energy for a reaction is changed from 184 kJ/mol to 60.5 kJ/mol at 600. K by the introduction of a catalyst. If the uncatalyzed reaction takes about 2537 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

Answer:

The catalyzed reaction will take 1,41 s

Explanation:

The rate constant for a reaction is:

$k = A e^{-\frac{Ea}{RT}}$

Assuming frequency factor is the same for both reactions (with and without catalyst) it is possible to obtain:

${\frac{k1}{k2}} = e^{-\frac{Ea_{2}-Ea_{1}}{RT}}$

Replacing:

${\frac{k1}{k2}} = e^{-\frac{60,5kJ/mol-184kJ/mol}{8,314472x10^{-3}kJ/molK*600k}}$

${\frac{k1}{k2}} = 5,64x10^{10}$

That means the reaction occurs 5,64x10¹⁰ faster than the uncatalyzed reaction, that is 2537 years / 5,64x10¹⁰ = 4,50x10⁻⁸ years. In seconds:

4,50x10⁻⁸ years×$\frac{365days}{1year}$×$\frac{24hours}{1day}$×$\frac{3600s}{1hour}$ = 1,41 s

I hope it helps!