The Arrhenius plots of two reactions,$I$ and $II$ are shown graphically. The graph suggests that

The activation energy of a first-order reaction at $25\,^{\circ}C$ is $30\,kJ/mol$. In the presence of a catalyst,the activation energy of the same reaction at $25\,^{\circ}C$ becomes $24\,kJ/mol$. The rate of the reaction in the presence of the catalyst will be how many times the original rate?

The influence of temperature on the rate of reaction can be found out by

The energy of activation is

For a reaction,$A \rightarrow B$,the average energies of $A$ and $B$ are $30 \ kcal/mol$ and $60 \ kcal/mol$ respectively. The energy of activation for the backward reaction is $93 \ kcal/mol$. The energy of activation for the forward reaction is:

For the reaction,$A \rightleftharpoons B$,$E_a = 50 \ kJ \ mol^{-1}$ and $\Delta H = -20 \ kJ \ mol^{-1}$. When a catalyst is added,$E_a$ decreases by $10 \ kJ \ mol^{-1}$. What is the $E_a$ for the backward reaction in the presence of the catalyst?