Respuesta :
Answer:
The catalyzed reaction will take time of [tex]5.11\times 10^{-8} years[/tex].
Explanation:
According to the Arrhenius equation,
[tex]K=A\times e^{\frac{-Ea}{RT}}[/tex]
The expression used with catalyst and without catalyst is,
[tex]\frac{K_2}{K_1}=\frac{A\times e^{\frac{-Ea_2}{RT}}}{A\times e^{\frac{-Ea_1}{RT}}}[/tex]
[tex]\frac{K_2}{K_1}=e^{\frac{Ea_1-Ea_2}{RT}}[/tex]
where,
[tex]K_2[/tex] = rate of reaction with catalyst
[tex]K_1[/tex] = rate of reaction without catalyst
[tex]Ea_2[/tex] = activation energy with catalyst = 59.0 kJ/mol = 59000 J/mol
[tex]Ea_1[/tex] = activation energy without catalyst = 184 kJ/mol = 184000 J/mol
R = gas constant
T = temperature = [tex]600K[/tex]
Now put all the given values in this formula, we get:
[tex]\frac{K_2}{K_1}=e^{\frac{184,000 kJ-59000 kJ}{R\times 300}}=7.632\times 10^{10}[/tex]
The reaction enhances by [tex]7.632\times 10^{10}[/tex] when catalyst is present.
Time taken by reaction without catalyzed = 3900 years
Time taken by reaction with catalyzed = x
[tex]x=\frac{3900 year}{7.632\times 10^{10}}=5.11\times 10^{-8} years[/tex]
The catalyzed reaction will take time of [tex]5.11\times 10^{-8} years[/tex].
