The equilibrium constant $(K)$ of a reaction may be written as :

Assertion $(A)$: For every chemical reaction at equilibrium,standard Gibbs energy change of the reaction is zero.
Reason $(R)$: At constant temperature and pressure,chemical reactions are spontaneous in the direction of decreasing Gibbs energy.

For the reaction at $25\,^oC$,${N_2O_4}_{(g)} \rightleftharpoons 2NO_{2_{(g)}}$,if $\Delta G_f^o$ for $N_2O_4$ and $NO_2$ are $23.49 \, KCal$ and $12.39 \, KCal$ respectively,then $K_p$ for the reaction is: (in $, atm$)

Calculate $\Delta_{r} G^{\ominus}$ for the conversion of oxygen to ozone,$\frac{3}{2} O_{2(g)} \rightarrow O_{3(g)}$ at $298 \, K$,if $K_{p}$ for this conversion is $2.47 \times 10^{-29}$.

The value of $\Delta G^{\ominus}$ for the phosphorylation of glucose in glycolysis is $13.8 \, kJ \, mol^{-1}$. Find the value of $K_{c}$ at $298 \, K$.

Hydrolysis of sucrose is given by the following reaction:
$\text{Sucrose} + H_{2}O \rightleftharpoons \text{Glucose} + \text{Fructose}$
If the equilibrium constant $(K_{c})$ is $2 \times 10^{13}$ at $300 \ K$,the value of $\Delta_{r}G^{\Theta}$ at the same temperature will be: