Question
The activation energy for a simple chemical reaction $$A \to B$$ is $${E_a}$$ in forward direction. The activation energy for reverse reaction
A.
is always double of $${E_a}$$
B.
is negative of $${E_a}$$
C.
is always less than $${E_a}$$
D.
can be less than or more than $${E_a}$$
Answer :
can be less than or more than $${E_a}$$
Solution :
The activation energy of reverse reaction will depend upon whether the forward
reaction is exothermic or endothermic.
As $$\Delta H = {E_a}$$ ( forward reaction ) $$ - {E_a}$$ ( backward reaction )
$$\eqalign{
& {\text{For exothermic reaction}} \cr
& \Delta H = - ve \cr
& \therefore \,\, - \Delta H = {E_a}\left( f \right) - {E_a}\left( b \right) \cr
& {\text{or}}\,\,{E_a}\left( f \right) = {E_a}\left( b \right) - \Delta H \cr
& \therefore \,\,{E_a}\left( f \right) < {E_a}\left( b \right) \cr
& {\text{for endothermic reaction}} \cr
& \Delta H = + ve \cr} $$
$$\therefore \,\,\Delta H = {E_a}\left( f \right) - {E_a}\left( b \right)$$ $${\text{or}}\,\,{E_a}\left( f \right) = \Delta H + {E_a}\left( b \right)$$
$$\therefore \,\,{E_a}\left( f \right) > {E_a}\left( b \right).$$