The $\Delta G^o$ for the reaction $X + Y \rightleftharpoons Z$ is $-4.606 \ kcal$. The value of the equilibrium constant of the reaction at $227 \ ^oC$ is $(R = 2.0 \ cal \ mol^{-1} K^{-1})$.

The equilibrium concentrations of the species in the reaction $A + B \rightleftharpoons C + D$ are $2, 3, 10$ and $6 \, mol \, L^{-1}$,respectively at $300 \, K$. $\Delta G^{\circ}$ for the reaction is $(R = 2 \, cal \, mol^{-1} \, K^{-1})$ (in $, cal$)

Which of the following relations is incorrect?

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.

The correct relationship between the standard Gibbs free energy change $(\Delta G^o)$ and the equilibrium constant $(K_c)$ for a reaction is .......

Calculate $\Delta G^\circ$ for the conversion of oxygen to ozone $\frac{3}{2} O_{2(g)} \to O_{3(g)}$ at $298 \ K$,if $K_p$ for this conversion is $2.47 \times 10^{-29}$.