Question

The activation energy of the reaction $A + B \to C + D + 38kcal$ is $20kcal$. What should be the activation energy of the reaction $C + D \to A + B$ ?
A. $20kcal$
B. $- 20kcal$
C. $18kcal$
D. $58kcal$

Answer 1

In chemistry and physics, activation energy is the energy that must be provided to compounds to result in a chemical reaction. The activation energy (Ea) of a reaction is measured in joules per mole $\left( {J/mol} \right)$ , kilojoules per mole $\left( {kJ/mol} \right)$ or kilocalories per mole $\left( {kcal/mol} \right)$ .

Complete step by step answer:
In the reaction, $A + B \to C + D + 38kcal$, we can see that the reactants A and B react together to yield the products C and D and release $38kcal$ of energy. This means that after attaining the activation energy of $20kcal$, the reaction yields the given products. In other words, the reactants A and B require an energy of $20kcal$ in order to get excited to their transition state and yield the products C and D.
Now, when the reaction is reversed, we find that the reaction is as follows:
$C + D \to A + B$
In this reaction, the reactants are C and D whereas the products are A and B. The activation energy in this case should be the sum of the energy released in the form of heat and the desired activation energy which was earlier required by the reactants to yield the above mentioned products. Thus, in order to rebuild the bonds and for the completion of the reaction, the amount of activation energy for this reversed reaction will be:
${E_a} = (20 + 38)kcal = 58kcal$
Thus, the correct option is D. $58kcal$.

Note:
Activation energy can be thought of as the magnitude of the potential barrier (sometimes 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.