The correct relation is:

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

At $300 \ K$,$\Delta_{r} G^{\circ}$ for the reaction $A_{2(g)} \rightleftharpoons B_{2(g)}$ is $-11.5 \ kJ \ mol^{-1}$. The equilibrium constant at $300 \ K$ is approximately $(R=8.314 \ J \ mol^{-1} \ K^{-1})$.

The equilibrium concentrations of the species in the reaction $A + B \rightleftharpoons C + D$ are $3, 5, 10$ and $15 \ mol \ L^{-1}$ respectively at $300 \ K$. The $\Delta G$ for the reaction is (in $cal$)

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 $298 \ K$.

Consider the reaction $A \rightleftharpoons B$ at $1000 \ K$. At time $t^{\prime}$,the temperature of the system was increased to $2000 \ K$ and the system was allowed to reach equilibrium. Throughout this experiment,the partial pressure of $A$ was maintained at $1 \ bar$. Given below is the plot of the partial pressure of $B$ with time. What is the ratio of the standard Gibbs energy of the reaction at $1000 \ K$ to that at $2000 \ K$?