The correct relationship between standard free energy change $(\Delta G^o)$ and equilibrium constant $(K)$ is:

Find out $\ln K_{eq}$ for the formation of $NO_2$ from $NO$ and $O_2$ at $298 \ K$.
$NO_{(g)} + \frac{1}{2} O_{2(g)} \rightleftharpoons NO_{2(g)}$
Given:
$\Delta G^o_f (NO_2) = 52.0 \ kJ/mol$
$\Delta G^o_f (NO) = 87.0 \ kJ/mol$
$\Delta G^o_f (O_2) = 0 \ kJ/mol$

For the reaction $A_{(g)} \rightarrow B_{(g)},$ the value of the equilibrium constant at $300 \ K$ and $1 \ atm$ is equal to $100.0.$ The value of $\Delta_{r}G^{\circ}$ for the reaction at $300 \ K$ and $1 \ atm$ in $J \ mol^{-1}$ is $-xR,$ where $x$ is ........... (Rounded off to the nearest integer) ($R = 8.31 \ J \ mol^{-1} K^{-1}$ and $\ln 10 = 2.3$)

Find out the value of the equilibrium constant for the following reaction at $298 \, K$.
$2 NH_{3(g)} + CO_{2(g)} \leftrightharpoons NH_{2}CONH_{2(aq)} + H_{2}O_{(l)}$
Standard Gibbs energy change,$\Delta_{r} G^{\ominus}$ at the given temperature is $-13.6 \, kJ \, mol^{-1}$.

For a homogeneous gaseous reaction,the equilibrium constant $K_p$ is $10^{-8}$. The standard Gibbs free energy change for the reaction is ........... $kcal$. $(R = 2.0 \, cal \, K^{-1} \, mol^{-1}, T = 298 \, K)$

Describe the relationship between Gibbs energy change and chemical equilibrium.