At $67\,^{\circ}C$ and $1\ bar$ pressure,dinitrogen tetraoxide is $50\%$ dissociated into nitrogen dioxide. $\Delta G^{\circ}$ for the process $N_2O_{4(g)} \rightleftharpoons 2NO_{2(g)}$ is $(R = \frac{25}{3} \ J \ K^{-1} \ mol^{-1}, \ln 2 = 0.7, \ln 3 = 1.1)$.

For the reaction $X_{2(g)} + Y_{2(g)} \rightleftharpoons 2XY_{(g)}$,the reaction is studied at a fixed temperature. Initially,$1 \ mol$ of $X_2$ is taken in a $1 \ L$ flask and $2 \ mol$ of $Y_2$ is taken in a $2 \ L$ flask. If the flasks are connected,what are the equilibrium concentrations of $X_2$ and $Y_2$? (Given: Equilibrium concentration of $XY = 0.6 \ mol/L$)

In a $10 \ L$ vessel,$1 \ mol$ each of $PCl_5$ and $PCl_3$ are present. If the vessel is heated,some $PCl_5$ dissociates. What are the concentrations of $PCl_5$,$PCl_3$,and $Cl_2$ at equilibrium,respectively?

Which of the following statements is correct?

At $600 \ K$,ammonium carbamate decomposes in a closed vessel: $NH_2COONH_{4(s)} \rightleftharpoons 2NH_{3(g)} + CO_{2(g)}$. At equilibrium,the total pressure is $3 \ bar$. Calculate $K_p$. (in $bar^3$)

For the reaction $I_{2(g)} \rightleftharpoons 2I_{(g)}$,the equilibrium constant $K_c$ at $1000 \ K$ is $10^{-6}$. If $1 \ mol$ of $I_2$ is added to a $1 \ L$ container,which of the following statements is true at equilibrium?