Chemistry: 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?

Hydrogen peroxide decomposes spontaneously to

Winechou

09.01.2022

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

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