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* e^{(-Ea)/(RT)}`

Since, the rate for both the reaction are equal.

`K_1=K_2`

`A* e^{(-Ea_1)/(RT_1)}=A* e^{(-Ea_2)/(RT_2)}`

`(Ea_1)/(T_1)=(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:

`(Ea_1)/(T_1)=(Ea_2)/(T_2)`

`(75kJ/mol)/(T_1)=(49kJ/mol)/(298K)`

`T_1=456K`

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