In a hypothetical reaction X$\to$Y , the activation energy for the forward and backward reactions is 15 and 9 kJ mol^–1, respectively. The potential energy of X is 10 kJ mol^–1. Then Plot of t_1/2 vs. concentration

For reaction X$\to$Y , of concentration

${\mathrm{E}}_{\mathrm{a}\left(\mathrm{i}\right)}=15\mathrm{kJ}{\mathrm{mol}}^{-1},{\mathrm{E}}_{\mathrm{a}\left(\mathrm{b}\right)}=9\mathrm{kJ}{\mathrm{mol}}^{-1}$
$\text{ Heat of reaction }{\mathrm{E}}_{\mathrm{a}\left(\mathrm{f}\right)}-{\mathrm{E}}_{\mathrm{a}\left(\mathrm{b}\right)}=15-9=6\mathrm{kJ}{\mathrm{mol}}^{-1}$
$\text{ Potential energy of }\mathrm{Y}\text{ is }=10+6=16\mathrm{kJ}$
Threshold energy of the reaction = $\mathrm{PE}\text{ of }\mathrm{X}+{\mathrm{E}}_{\mathrm{a}\left(\mathrm{f}\right)}=10\mathrm{kJ}+15\mathrm{kJ}=25\mathrm{kJ}$
The reaction is endothermic because ${\mathrm{E}}_{\mathrm{a}\left(\mathrm{f}\right)}>{\mathrm{E}}_{\mathrm{a}\left(\mathrm{b}\right)}$