Answer : The temperature for non-catalyzed reaction needed will be 456 K
Explanation :
Activation energy : The energy required to initiate the reaction is known as activation energy.
According to the Arrhenius equation,
[tex]K=A\times e^{\frac{-Ea}{RT}}[/tex]
Since, the rate for both the reaction are equal.
[tex]K_1=K_2[/tex]
[tex]A\times e^{\frac{-Ea_1}{RT_1}}=A\times e^{\frac{-Ea_2}{RT_2}}[/tex]
[tex]\frac{Ea_1}{T_1}=\frac{Ea_2}{T_2}[/tex] ..........(1)
where,
[tex]Ea_1[/tex] = activation energy for non-catalyzed reaction = 75 kJ/mol
[tex]Ea_2[/tex] = activation energy for catalyzed reaction = 49 kJ/mol
[tex]T_1[/tex] = temperature for non-catalyzed reaction = ?
[tex]T_2[/tex] = temperature for catalyzed reaction = [tex]25^oC=273+25=298K[/tex]
Now put all the given values in the above formula 1, we get:
[tex]\frac{Ea_1}{T_1}=\frac{Ea_2}{T_2}[/tex]
[tex]\frac{75kJ/mol}{T_1}=\frac{49kJ/mol}{298K}[/tex]
[tex]T_1=456K[/tex]
Therefore, the temperature for non-catalyzed reaction needed will be 456 K
