Which of the following relation is correct for k _f and k_b in an equilibrium process that contains equal moles of reactants and products?

The value of ${\mathrm{K}}_{\mathrm{c}}$ for the reaction, ${\mathrm{N}}_2\left(\mathrm{g}\right)+2{\mathrm{O}}_2\left(\mathrm{g}\right)\rightleftharpoons 2{\mathrm{NO}}_2\left(\mathrm{g}\right)$ at a certain temperature is $400$. calculate the value of equilibrium constant for.

(i) $2{\mathrm{NO}}_2\left(\mathrm{g}\right)\rightleftharpoons {\mathrm{N}}_2\left(\mathrm{g}\right)+2{\mathrm{O}}_2\left(\mathrm{g}\right)$

(ii) $1/2{\mathrm{N}}_2\left(\mathrm{g}\right)+{\mathrm{O}}_2\left(\mathrm{g}\right)\rightleftharpoons {\mathrm{NO}}_2\left(\mathrm{g}\right)$

For the reaction: ${\mathrm{N}}_2{\mathrm{O}}_4\left(\mathrm{g}\right)\rightleftharpoons 2{\mathrm{NO}}_2\left(\mathrm{g}\right)$

Predict the direction in which the reaction will shift, in order to attain equilibrium [Given at $\mathrm{T}=298\mathrm{K}, 2.303\mathrm{RT}=5.7\mathrm{kJ}/\mathrm{mol}.]$ $[\mathrm{JEE} 2004, 2/60]$

Given : ${\mathrm{Hg}}_2^{2+}+2\mathrm{e}⟶2\mathrm{Hg}, {\mathrm{E}}^{\circ }=0.789 \mathrm{V} \& {\mathrm{Hg}}^{2+}+2\mathrm{e}⟶\mathrm{Hg}, {\mathrm{E}}^{\circ }=0.854 \mathrm{V}$

Calculate the equilibrium constant for ${\mathrm{Hg}}_2^{2+}⟶\mathrm{Hg}+{\mathrm{Hg}}^{2+}$.