$A$ catalyst increases the rate of a chemical reaction by

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: $R = 8.314 \ J \ mol^{-1} K^{-1}$)

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

In a laboratory,a biochemical reaction performed outside the human body in the absence of an enzyme proceeds at a rate $10^{-6}$ times slower. If this reaction is performed in the presence of an enzyme,what will be the activation energy of the reaction?

$A$ given sample of milk turns sour at room temperature $(27^{\circ} C)$ in $5 \ h$. In a refrigerator at $-3^{\circ} C$,it can be stored $10$ times longer. The energy of activation for the souring of milk is

$A \rightarrow B$
The rate constants of the above reaction at $200 \, K$ and $300 \, K$ are $0.03 \, min^{-1}$ and $0.05 \, min^{-1}$ respectively. The activation energy for the reaction is $.... \, J$ (Nearest integer).
(Given: $\ln 10 = 2.3$,$R = 8.3 \, J \, K^{-1} \, mol^{-1}$,$\log 5 = 0.70$,$\log 3 = 0.48$,$\log 2 = 0.30$)