For a chemical reaction, the standard Gibbs energy change, $\Delta G^{\circ}$ is $-7.64 \times 10^4 \ J \ mol^{-1}$. What is the value of equilibrium constant $(K)$?

For a certain reaction at $300 \ K$,$K=10$,then $\Delta G^{\circ}$ for the same reaction is . . . . . . $\times 10^{-1} \ kJ \ mol^{-1}$. (Given $R=8.314 \ J \ K^{-1} \ mol^{-1}$)

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.)

$K_p$ for the conversion of oxygen to ozone at $400 \ K$ is $1.0 \times 10^{-30}$,its standard Gibbs energy change in $kJ \ mol^{-1}$ is approximately

Calculate $\Delta G^{\circ} \ (kJ/mol)$ at $127 \ ^{\circ}C$ for a reaction with $K_{equilibrium} = 10^5$.

For the reaction taking place at a certain temperature $NH_2COONH_{4(s)} \rightleftharpoons 2NH_{3(g)} + CO_{2(g)}$,if the equilibrium pressure is $X \ bar$,then $\Delta_r G^o$ would be :-