For a reaction,the rate constant is expressed as,$K = A \cdot e^{-40000/T}$. The energy of activation is ....... $cal$.

The reaction: $Cr_{2}O_{3} + 2 Al \rightarrow Al_{2}O_{3} + 2 Cr$ $\quad (\Delta_{r}G^{\Theta} = -421 \ kJ)$ is thermodynamically feasible as is apparent from the Gibbs energy value. Why does it not take place at room temperature?

For an exothermic reaction $A \rightarrow B$,the activation energy is $15 \, K \, cal/mol$ and the heat of reaction is $5 \, K \, cal/mol$. The activation energy for the reverse reaction $B \rightarrow A$ will be ......... $K \, cal/mol$.

For the decomposition of $N_2O_5,$ the reaction is $2N_2O_{5(g)} \rightarrow 4NO_{2(g)} + O_{2(g)}$ with activation energy $E_a.$ If the reaction is written as $N_2O_{5(g)} \rightarrow 2NO_{2(g)} + 1/2 O_{2(g)}$ with activation energy $E_a',$ what is the relationship between $E_a$ and $E_a'$?

For the forward reaction $X \rightarrow Y$,the activation energy is $60 \ kJ \ mol^{-1}$ and $\Delta H = -20 \ kJ \ mol^{-1}$. What is the activation energy for the reverse reaction $Y \rightarrow X$ in $kJ \ mol^{-1}$?

The activation energy is ..........