Answer:
The ratio is 2:1
Explanation:
The relation between activation energy, temperature and reaction constant is formulated as Arrhenius equation, which is:
[tex]lnK=ln(A)-\frac{E_{a}}{RT}[/tex]
Where
K = rate constant
A= frequency factor
T= temperature (K)
R= gas constant
Here A and R both are constant for the two given conditions
So
[tex]lnK_{cat}=ln(A)-\frac{E_{cat}}{RT_{cat}}\\\\lnK_{uncat}=ln(A)-\frac{E_{uncat}}{RT_{uncat}}\\[/tex]
Equating the two
[tex]lnK_{cat}+\frac{E_{cat}}{RT_{cat}}=lnK_{uncat}+\frac{E_{uncat}}{RT_{uncat}}[/tex]
[tex]lnK_{cat}-lnK_{uncat}=\frac{E_{uncat}}{RT_{uncat}}-\frac{E_{cat}}{RT_{cat}}\\ln(\frac{K_{cat}}{K_{uncat}})=\frac{E_{uncat}}{RT_{uncat}}-\frac{E_{cat}}{RT_{cat}}[/tex]
[tex]ln([tex]\frac{K_{cat}}{K_{uncat}}=2[/tex])=\frac{14000}{8.314X362}-\frac{11900}{8.314X362}=0.698[/tex]
Taking antilog
