Question

Relation between activation energies of the below reaction is:

(E= activation energy)
A. ${{\text{E}}_{\text{2}}}{\text{ > }}{{\text{E}}_{\text{1}}}{\text{ > }}{{\text{E}}_{\text{3}}}$
B. ${{\text{E}}_3}{\text{ > }}{{\text{E}}_{\text{1}}}{\text{ > }}{{\text{E}}_2}$
C. ${{\text{E}}_3}{\text{ > }}{{\text{E}}_2}{\text{ > }}{{\text{E}}_1}$
D. ${{\text{E}}_1}{\text{ > }}{{\text{E}}_2}{\text{ > }}{{\text{E}}_{\text{3}}}$

Answer 1

Activation energy is the minimum amount of energy required to start any chemical reaction. Generally, stable compounds have higher activation energy than unstable compounds because of high bond dissociation energy which is energy needed to break a bond.

Complete step by step answer: For a reaction to start, and occur, first of all, existing bonds are broken and then new bonds are formed. If the compound is more stable then it will need more energy to break its existing bonds, and hence, will have higher activation energy.
In the given figure, the first compound is benzene, which is an aromatic conjugated compound. Aromaticity can be seen by Huckle’s rule, which states, in an aromatic compound there are $\left( {4n + 2} \right)\pi$ electrons where n is any natural number that satisfies the rule.
First compound is converted to the second compound by hydrogenation, which is an addition of ${H_2}$ to double bond. That’s why, the second structure has one less double bond than the first structure. Then, again hydrogenation is done to convert it to a third compound. In doing so, conjugation of dienes is decreasing with every compound. Conjugated dienes are comparatively more stable than non-conjugated dienes due to the factor of delocalization of charge through resonance, and hybridization energy in conjugated dienes. So, activation energy of conjugated dienes is greater than non-conjugated. Therefore, ${{\text{E}}_1}{\text{ > }}{{\text{E}}_2}{\text{ > }}{{\text{E}}_{\text{3}}}$.
Hence, option (d) is the right answer.

Note: Activation energy of compounds can be calculated through an equation which relates the rate constant of a reaction with the temperature of the system in which reaction is occurring. This equation is called Arrhenius equation, it is given by: $K = Z{e^{\frac{{ - {E_a}}}{{RT}}}}$
where, ${\text{K}}$ is the rate constant,
${E_a}$ is the activation energy,
${\text{R}}$ is the gas constant,
${\text{T}}$ is the temperature,
and, ${\text{Z}}$ is the Arrhenius constant.