Question

The formation of ${H_2}{O_2}$​ in the upper atmosphere follows the mechanism:
${H_2}O\,\, + \,\,O\,\, \to \,\,2OH\, \to \,\,{H_2}{O_2}$ $\Delta H\,\, = \,\,72kJmo{l^{ - 1}}$ , ${E_a}\,\, = \,\,77kJmo{l^{ - 1}}$ .
Then, ${E_a}$ for the backward reaction will be $(per\,\,mol)$ :
(A) $- 149kJ$
(B) $+ 149kJ$
(C) $- 5kJ$
(D) $+ 5kJ$

Answer 1

In order to answer this question, you must be aware of basic laws of thermodynamics. Firstly, enlist the given quantities and then use the basic formulae for evaluating ${E_a}$ for the backward reaction will be $(per\,\,mol)$ . The activation energy for the backward reaction is equal to the sum of the activation energy of the forward reaction and the enthalpy change of the reaction. Take care of the units and make accurate calculations and then select the correct option.

Complete step-by-step solution: Step 1: In this step, we will enlist all the given quantities:
$\Delta H\,\, = \,\,72kJmo{l^{ - 1}}$ , ${E_a}\,\, = \,\,77kJmo{l^{ - 1}}$ (forward)
Step 2: In this step, we will use the correct formula to find the ${E_a}$ for the backward reaction will be $(per\,\,mol)$ :
The activation energy for the backward reaction is equal to the sum of the activation energy of the forward reaction and the enthalpy change of the reaction.
$\Delta H\,\, = \,\,{E_{a(forward)\,}}\, - \,\,{E_{a(backward)}}$
$\Rightarrow \,\,\,{E_{a(backward)}}\, = \,\,{E_{a(forward)\,}}\, - \,\Delta H\,$
$\therefore {E_{a(backward)}}\, = \,\,77 - 72\,\, = \,\,$ $+ 5kJ$ and this is the value of ${E_a}$ for the backward reaction $(per\,\,mol)$.
Hence we got our required answer, ${E_{a(backward)}}\,$ = $+ 5kJ$

Clearly, the correct answer is Option (D).

Note: In chemistry and physics, activation energy is the energy that must be provided to compounds to result in a chemical reaction. Activation energy can be thought of as the magnitude of the potential barrier (also called the energy barrier) separating minima of the potential energy surface pertaining to the initial and final thermodynamic state. For a chemical reaction to proceed at a reasonable rate, the temperature of the system should be high enough such that there exists an appreciable number of molecules with translational energy equal to or greater than the activation energy.