The half-life periods of a first order reaction at $300 \ K$ and $400 \ K$ are $50 \ s$ and $10 \ s$ respectively. The activation energy of the reaction in $kJ \ mol^{-1}$ is $(\log 5 = 0.70)$

Write the Arrhenius equation to calculate the activation energy $(E_a)$ at two different temperatures.

Consider a complex reaction taking place in three steps with rate constants $k_1$,$k_2$,and $k_3$ respectively. The overall rate constant $k$ is given by the expression $k = \sqrt{\frac{k_1 k_3}{k_2}}$. If the activation energies of the three steps are $60$,$30$,and $10 \ kJ \ mol^{-1}$ respectively,then the overall energy of activation in $kJ \ mol^{-1}$ is $..........$ $(Nearest \ integer)$

Write the Arrhenius equation representing the relationship between the rate constants $k_1$ and $k_2$ at two different temperatures $T_1$ and $T_2$.

The $\Delta H$ value of the reaction $H_2 + Cl_2 \rightleftharpoons 2HCl$ is $-44.12 \ kcal$. If $E_1$ is the activation energy of the backward reaction and $E_2$ is the activation energy of the forward reaction,then for the above reaction:

The rate of a reaction: