Question

An endothermic reaction, $A \to {\text{ }}B$ has an activation energy 15 kcal/mol and energy of the reaction is 5 kcal/mol. The activation energy of the reaction, $B{\text{ }} \to {\text{ }}A$ is:
(A) 20 kcal/mol
(B) 15 kcal/mol
(C) 10 kcal/mol
(D) 5 kcal/mol

Answer 1

Hint : In this question, we have to find out the activation energy of the reverse reaction. To do so we need to apply the concept that the total energy of the reaction is the difference of the forward and the reverse reaction of any given chemical reaction. Thus we can substitute the values given and find out the required quantity.

Complete Step By Step Answer:
We are given that the reaction is endothermic meaning that heat is being released from the reacting system as the reaction proceeds.
Thus the energy of the reaction will be a positive quantity and the value is given as 5 kcal/mol.
We are also given that the activation energy of the forward reaction is 15 kcal/mol
We can use the below formula to find out the required quantity which is the activation energy for the reverse or backward reaction:
$\Rightarrow \Delta H = {({E_a})_{forward}} - {({E_a})_{Backward}}$
Thus we can substitute the values and say that:
$\Rightarrow 5 = 15 - {({E_a})_{Backward}}$
Rearranging the terms we get,
$\Rightarrow {({E_a})_{Backward}} = 15 - 5 = 10{\text{ }}kcal/mol$
Thus we can say that the correct answer for this question will be option (C).

Note :
The change in enthalpy for the forward reaction is negative of that value in a reverse reaction. Let’s say that the value of enthalpy in the forward direction is positive, then that means that the reaction is endothermic. If we want the reverse reaction, then the change in enthalpy must be negative because the opposite of endothermic is exothermic. So the forward reaction absorbs heat from the surroundings while the reverse reaction releases heat to the surroundings.