Question

For the equilibrium, $A(g)\rightleftharpoons B(g),\Delta H=-40kJ/mol$ if the ratio of the activation energies of the forward (${{E}_{f}}$ ) and reverse ( ${{E}_{b}}$ ) reaction is $\dfrac{2}{3}$ then:
(A) ${{E}_{f}}=30kJ/mol;{{E}_{b}}=70kJ/mol$
(B) ${{E}_{f}}=70kJ/mol;{{E}_{b}}=30kJ/mol$
(C) ${{E}_{f}}=80kJ/mol;{{E}_{b}}=120kJ/mol$
(D) ${{E}_{f}}=60kJ/mol;{{E}_{b}}=100kJ/mol$

Answer 1

Hint: If the temperature of the reaction, the rate of reaction increases based on collision theory and Maxwell Boltzmann distribution of molecular energies in a gas. Collisions in a reaction result in the particles colloid with enough energy to get the reaction started, by which the minimum energy required is called activation energy.

Complete step by step solution:
Because of increasing temperature reaction rate increases and a disproportionately large number of high collisions possessing at least the activation energy of the reaction. only these collisions result in a reaction due to their activation energy.
Given equilibrium reaction,
$A(g)\rightleftharpoons B(g),\Delta H=-40kJ/mol$
The above reaction is exothermic because the change in enthalpy shows a negative sign.
The change in enthalpy is equal to the difference between activation energies of forwarding reaction and backward reaction.
$\Delta H={{E}_{f}}-{{E}_{b}}$ --- (1)
Given the ratio of activation energies of forward and backward reaction is,
$\dfrac{{{E}_{f}}}{{{E}_{b}}}=\dfrac{2}{3}$
Then, ${{E}_{f}}=\dfrac{2}{3}{{E}_{b}}$ --- (2)
Substitute the above value in equation (1), and $\Delta H=-40kJ/mol$
$-40={{E}_{b}}-\dfrac{2}{3}{{E}_{b}}$
${{E}_{b}}=-120kJ/mol$
Substitute the value of activation energy of a backward reaction in equation (2),
${{E}_{f}}=\dfrac{2}{3}{{E}_{b}}=\dfrac{2}{3}X(-120)=-80kJ/mol$
Hence, ${{E}_{f}}=80kJ/mol;{{E}_{b}}=120kJ/mol$

The correct answer is option C.

Note: The fraction of molecules present in a gas which have energies equal to or above activation energy at a particular temperature. At an absolute temperature, the fraction of molecules that have kinetic energy than the activation energy. The activation energy of a chemical reaction can be calculated by the Arrhenius equation.