Question

Hydrogen peroxide decomposes spontaneously to yield water and oxygen gas according to the following reaction equation. 2H202(aq) →2H20(/) + 02(g) The activation energy for this reaction is 75 kJ/mol. In the presence of a metal catalyst the activation energy is lowered to 49 kJ/mol. At what temperature would the non-catalyzed reaction need to be run to have a rate equal to that of the metal-catalyzed reaction at 25°C?

Answer 1

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,

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

Since, the rate for both the reaction are equal.

$K_1=K_2$

$A\times e^{\frac{-Ea_1}{RT_1}}=A\times e^{\frac{-Ea_2}{RT_2}}$

$\frac{Ea_1}{T_1}=\frac{Ea_2}{T_2}$ ..........(1)

where,

$Ea_1$ = activation energy for non-catalyzed reaction = 75 kJ/mol

$Ea_2$ = activation energy for catalyzed reaction = 49 kJ/mol

$T_1$ =  temperature for non-catalyzed reaction = ?

$T_2$ = temperature for catalyzed reaction = $25^oC=273+25=298K$

Now put all the given values in the above formula 1, we get:

$\frac{Ea_1}{T_1}=\frac{Ea_2}{T_2}$

$\frac{75kJ/mol}{T_1}=\frac{49kJ/mol}{298K}$

$T_1=456K$

Therefore, the temperature for non-catalyzed reaction needed will be 456 K