In the Arrhenius equation,the pre-exponential factor represents ...

The decomposition of formic acid on a gold surface follows first-order kinetics. If the rate constant at $300 \ K$ is $1.0 \times 10^{-3} \ s^{-1}$ and the activation energy $E_a = 11.488 \ kJ \ mol^{-1}$,the rate constant at $200 \ K$ is ............ $\times 10^{-5} \ s^{-1}$.
(Round off to the Nearest Integer).
(Given: $R = 8.314 \ J \ mol^{-1} K^{-1}$)

In a first order reaction at $27\,^oC$ and $47\,^oC$,$50\%$ of the reaction is complete in $30\,\min$ and $10\,\min$ respectively. Calculate the energy of activation $(E_a)$.

For an elementary chemical reaction, the Arrhenius plot is given below. If the energy of activation is $6.64 \ kJ \ mol^{-1}$ and $R = 8.3 \ J \ K^{-1} \ mol^{-1}$, the temperature at which the rate constant becomes $e^2 \ min^{-1}$, is (in $K$)

Reactant $A$ shows two reactions:
$A \xrightarrow{K_1} B$,activation energy $= Ea_1$
$A \xrightarrow{K_2} C$,activation energy $= Ea_2$
If $Ea_1 = \frac{Ea_2}{3}$,then the relation between $K_1$ and $K_2$ is:

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 $cal \ mol^{-1}$.