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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 $\log \mathrm{K}$ for the reaction at $500 \mathrm{~K}$ is $6$ , the value of $\left|\log \mathrm{k}_{\mathrm{b}}\right|$ at $250 \mathrm{~K}$ is $\qquad$
$[\mathrm{K}=$ equilibrium constant of the reaction
$\mathrm{k}_{\mathrm{f}}=$ rate constant of forward reaction
$\mathrm{k}_{\mathrm{b}}=$ rate constant of backward reaction]
Statement $II :$ As the size of the elements $\mathrm{F}, \mathrm{Cl}, \mathrm{Br}, \mathrm{I}$ increases down the group, the bond strength of $\mathrm{HF}$, HCl, HBr and HI decreases and so the acid strength increases.
In the light of the above statements, choose the correct answer from the options given below.