At $300 \ K$,for the reaction $PCl_{5(g)} \rightleftharpoons PCl_{3(g)} + Cl_{2(g)}$,the equilibrium constant $K_p = 1.8 \times 10^{-7}$. Calculate its standard Gibbs free energy change $\Delta G^0$.

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 $2000 \ K$?

At $60^{\circ} C$,dinitrogen tetroxide is $50$ per cent dissociated. Calculate the standard free energy change at this temperature and at one atmosphere.

The standard free energy change $(\Delta G^{\circ})$ for $50\%$ dissociation of $N_2O_4$ into $NO_2$ at $27^{\circ}C$ and $1\,atm$ pressure is $-x\,J\,mol^{-1}$. The value of $x$ is $......$ (Nearest Integer)
[Given: $R = 8.31\,J\,K^{-1}\,mol^{-1}$,$\log 1.33 = 0.1239$,$\ln 10 = 2.3$]

Derive the relation between the equilibrium constant $K$,reaction quotient $Q_{c}$,and Gibbs energy change $\Delta G$.

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:
$\Delta G^o_f (NO_2) = 52.0 \ kJ/mol$
$\Delta G^o_f (NO) = 87.0 \ kJ/mol$
$\Delta G^o_f (O_2) = 0 \ kJ/mol$