Question

The decomposition of dinitrogen pentaoxide has an activation energy of 102 kJ/mol and ΔH°rxn = + 55 kJ/mol. What is the activation energy for the reverse reaction?

Answer 1

Answer: The activation energy of the reverse reaction is 47 kJ/mol

Explanation:

The chemical equation for the decomposition of dinitrogen pentaoxide follows:

$N_2O_5\rightleftharpoons 2NO_2+\frac{1}{2}O_2$

We are given:

Activation energy of the above reaction (forward reaction) = 102 kJ/mol

Enthalpy of the reaction = +55 kJ/mol

As, the enthalpy of the reaction is positive, the reaction is said to be endothermic in nature.

To calculate the activation energy for the reverse reaction, we use the equation:

$E_a_{\text{(forward)}}=E_a_{\text{(backward)}}+|\Delta H|$

where,

$E_a_{\text{(forward)}}$ = Activation energy of the forward reaction = 102 kJ/mol

$E_a_{\text{(backward)}}$ = Activation energy of the backward reaction = ?

$\Delta H$ = Enthalpy of the reaction = +55 kJ/mol

Putting values in above equation, we get:

$102=E_a_{\text{(backward)}}+55\\\\E_a_{\text{(backward)}}=(102-55)=+47kJ/mol$

Hence, the activation energy of the reverse reaction is 47 kJ/mol