Consider the following reversible reaction, $\mathrm{A}\left(\mathrm{g}\right)+\mathrm{B}\left(\mathrm{g}\right)\rightleftharpoons \mathrm{AB}\left(\mathrm{g}\right)$ The activation energy of the backward reaction exceeds that of the forward reaction by $2\mathrm{RT}$ (in $\mathrm{J} {\mathrm{mol}}^{-1}$). If the pre-exponential factor of the forward reaction is $4$ times that of the reverse reaction, the absolute value of ${\mathrm{\Delta G}}^{\mathrm{\Theta }}$ (in $\mathrm{J} {\mathrm{mol}}^{-1}$) for the reaction at $300 \mathrm{K}$ is____.

(Given: $\ln \left(2\right)=0.7, \mathrm{RT}=2500 \mathrm{J} {\mathrm{mol}}^{-1}$ at $300 \mathrm{K}$ and $\mathrm{G}$ is the Gibbs energy) 

The rate law from a reaction between the substances $\mathrm{A}$ and $\mathrm{B}$ Is given by:

rate $=\mathrm{k}\left[\mathrm{A}{]}^{\mathrm{n}}\right[\mathrm{B}{]}^{\mathrm{m}}$

On doubling the concentration of $\mathrm{A}$ And halving the concentration of $\mathrm{B}$, the ratio of the new rate to the earlier rate of the reaction will be as:

For the reaction system,

$2\mathrm{NO}\left(\mathrm{g}\right)+{\mathrm{O}}_2\left(\mathrm{g}\right)⟶2{\mathrm{NO}}_2\left(\mathrm{g}\right)$ volume is suddenly reduced to half its value by increasing the pressure on it. If the reaction is of first order with respect to ${\mathrm{O}}_2$ and second order with respect to $\mathrm{NO},$ the rate of reaction will: