Question

A popular chemical demonstration is the "magic genie" procedure, in which hydrogen peroxide decomposes to water and oxygen gas with the aid of a catalyst. The activation energy of this (uncatalyzed) reaction is 70.0 kJ/mol. When the catalyst is added, the activation energy (at 20.ºC) is 42.0 kJ/mol. Theoretically, to what temperature (ºC) would one have to heat the hydrogen peroxide solution so that the rate of the uncatalyzed reaction is equal to the rate of the catalyzed reaction at 20.ºC? Assume the frequency factor A is constant, and assume the initial concentrations are the same. Temperature = __ºC

Answer 1

Answer : The temperature for non-catalyzed reaction will be, $215^oC$

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 = 70.0 kJ/mol

$Ea_2$ = activation energy for catalyzed reaction = 42.0 kJ/mol

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

$T_2$ = temperature for catalyzed reaction = $20^oC=273+20=293K$

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

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

$\frac{70.0kJ/mol}{T_1}=\frac{42.0kJ/mol}{293K}$

$T_1=488K=488-273=215^oC$

Therefore, the temperature for non-catalyzed reaction will be, $215^oC$