Answer:
The catalyzed reaction will take 1,41 s
Explanation:
The rate constant for a reaction is:
[tex]k = A e^{-\frac{Ea}{RT}}[/tex]
Assuming frequency factor is the same for both reactions (with and without catalyst) it is possible to obtain:
[tex]{\frac{k1}{k2}} = e^{-\frac{Ea_{2}-Ea_{1}}{RT}}[/tex]
Replacing:
[tex]{\frac{k1}{k2}} = e^{-\frac{60,5kJ/mol-184kJ/mol}{8,314472x10^{-3}kJ/molK*600k}}[/tex]
[tex]{\frac{k1}{k2}} = 5,64x10^{10}[/tex]
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×[tex]\frac{365days}{1year}[/tex]×[tex]\frac{24hours}{1day}[/tex]×[tex]\frac{3600s}{1hour}[/tex] = 1,41 s
I hope it helps!
