The plot of ${\mathrm{logk}}_{\mathrm{f}}$ versus $\frac{1}{\mathrm{T}}$ for a reversible reaction $\mathrm{A}\left(\mathrm{g}\right)\rightleftharpoons \mathrm{P}\left(\mathrm{g}\right)$ is shown.

Pre-exponential factors for the forward and backward reactions are ${10}^{15} {\mathrm{s}}^{-1}$ and ${10}^{11} {\mathrm{s}}^{-1}$, respectively. If the value of $\mathrm{logK}$ for the reaction at $500 \mathrm{K}$ is $6$, the value of $\left|{\mathrm{logk}}_{\mathrm{b}}\right|$ at $250 \mathrm{K}$ is
$\left[\mathrm{K}=\right.$equilibrium constant of the reaction, ${\mathrm{k}}_{\mathrm{f}}=$rate constant of forward reaction, ${\mathrm{K}}_{\mathrm{b}}=$rate constant of backward reaction]

Consider the given plots for a reaction obeying Arrhenius equation $(0°C<T<300°C):$ ($K$and $E_a$ are rate constant and activation energy, respectively )

(I) 

(II) 

The Arrhenius plots of two reactions, I and II are shown graphically-



The graph suggests that-

A sample of milk splits after $60\mathrm{}\mathrm{m}\mathrm{i}\mathrm{n}$ at $300\mathrm{}\mathrm{K}$ and after $40\mathrm{}\mathrm{m}\mathrm{i}\mathrm{n}$ at $400\mathrm{}\mathrm{K}$ when the population of Iactobacillus acidophilus in it doubles. The activation energy (in $\mathrm{kJ}/\mathrm{mol}$) for this process is closest to ______________.

$\left(\mathrm{Given}: \mathrm{R} =8.3 \mathrm{J} {\mathrm{mol}}^{-1}{\mathrm{K}}^{-1} , \ln \left(\frac{3}{2}\right)=0.4\right)$

For a reaction, consider the plot of $lnk$ versus $1/T$ given in the figure. If the rate constant of this reaction at $400K$ is ${10}^{-5}{s}^{-1}$ , then the rate constant at $500K$ is: