The energy of activation is

What happens to the most probable kinetic energy and the energy of activation with an increase in temperature?

If the rate constants of a reaction at $500 \ K$ and $700 \ K$ are $0.002 \ s^{-1}$ and $0.06 \ s^{-1}$,respectively,the value of activation energy is $(R=8.314 \ J \ mol^{-1} \ K^{-1}, \log 3=0.477)$.

The equation $k = (6.5 \times 10^{12} \, s^{-1}) e^{-26000 \, K / T}$ is followed for the decomposition of compound $A$. The activation energy for the reaction is $..... \, kJ \, mol^{-1}$. [nearest integer] (Given: $R = 8.314 \, J \, K^{-1} \, mol^{-1}$)

For the reaction $CH_{3}CH_{2}CH_{2}I + OH^{-} \rightarrow CH_{3}CH_{2}CH_{2}OH + I^{-}$,the rate constant is $1.84 \ (mol \ L^{-1})^{-1} \ min^{-1}$ at $27^{\circ}C$ $(300 \ K)$ and $38.84 \ (mol \ L^{-1})^{-1} \ min^{-1}$ at $327 \ K$. Calculate the activation energy $(E_{a})$ in $cal \ mol^{-1}$.

At $298 \text{ K}$ temperature,the activation energy for the reaction $x_2 + y_2 \rightarrow 2xy + 20 \text{ kJ}$ is $15 \text{ kJ}$. What will be the activation energy for the reaction $2xy \rightarrow x_2 + y_2$?