For the chemical reaction $X \rightleftharpoons Y$,the standard reaction Gibbs energy depends on temperature $T$ (in $K$) as
${\Delta_r}{G^o}$ (in $kJ \ mol^{-1}$) $= 120 - \frac{3}{8} \ T$
The major component of the reaction mixture at $T$ is

Solid $KClO_4$ is taken in a container maintained at a constant pressure of $1 \, atm$. Upon heating,the following equilibrium is obtained:
$2KClO_{4(s)} \rightleftharpoons 2KCl_{(s)} + 3O_{2(g)}$
If $\Delta H^o = 25 \, kcal/mol$ and $\Delta S^o = 50 \, cal/K \cdot mol$,at what temperature will equilibrium be established in the container (in $, K$)? (Ignore variation of $\Delta H^o$ and $\Delta S^o$ with temperature.)

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:

Describe the relationship between Gibbs energy change and chemical equilibrium.

For the reaction $CH_{4(g)} + H_{2(g)} \longrightarrow C_2H_{6(g)}$,$K_p = 3.356 \times 10^{17}$,calculate $\Delta G^{\circ}$ for the reaction at $298 \ K$.

The value of $\log _{10} K$ for a reaction $A \rightleftharpoons B$ is
(Given : $\Delta _{r} H_{298 K}^{\circ} = -54.07 \ kJ \ mol^{-1}$,$\Delta _{r} S_{298 K}^{\circ} = 10 \ J \ K^{-1} \ mol^{-1}$ and $R = 8.314 \ J \ K^{-1} \ mol^{-1}$; $2.303 \times 8.314 \times 298 = 5705$)