When the temperature of a reaction is raised by $10^{\circ}C$,how many times the rate will be enhanced?

Consider the following reversible reaction,
$A_{(g)} + B_{(g)} \rightleftharpoons AB_{(g)}.$
The activation energy of the backward reaction exceeds that of the forward reaction by $2RT$ (in $J \ mol^{-1}$). If the pre-exponential factor of the forward reaction is $4$ times that of the reverse reaction,the absolute value of $\Delta G^{\ominus}$ (in $J \ mol^{-1}$) for the reaction at $300 \ K$ is. . . . . (Given; $\ln(2)=0.7, RT=2500 \ J \ mol^{-1}$ at $300 \ K$ and $G$ is the Gibbs energy)

For a reaction,the activation energy $E_{a} = 0$ and the rate constant at $200 \ K$ is $1.6 \times 10^{6} \ s^{-1}$. The rate constant at $400 \ K$ will be (given $R = 8.314 \ J \ K^{-1} \ mol^{-1}$):

The activation energy for the reaction $2 HI_{(g)} \rightarrow H_{2(g)} + I_{2(g)}$ is $209.5 \ kJ \ mol^{-1}$ at $581 \ K$. Calculate the fraction of molecules of reactants having energy equal to or greater than activation energy?

The differential form of the Arrhenius equation is:

The temperature dependence of the rate constant $(k)$ of a chemical reaction is expressed by the Arrhenius equation,$k = A \cdot e^{-E^*/RT}$. The activation energy $(E^*)$ of the reaction can be calculated by plotting: