$\Delta _f G^o$ at $500 \, K$ for substance '$S$' in liquid state and gaseous state are $+100.7 \, kcal \, mol^{-1}$ and $+103 \, kcal \, mol^{-1}$,respectively. The vapour pressure of liquid '$S$' at $500 \, K$ is approximately equal to $(R = 2 \, cal \, K^{-1} \, mol^{-1}) \dots \dots \text{atm}$.

For the reaction,$H_{2(g)} + I_{2(g)} \rightleftharpoons 2 HI_{(g)}$,the attainment of equilibrium is predicted correctly by:

Consider the following reaction approaching equilibrium at $27^{\circ} C$ and $1 \ atm$ pressure. Given the rate constants for the forward and backward reactions are $K_{f} = 10^{3} \ s^{-1}$ and $K_{b} = 10^{2} \ s^{-1}$ respectively,calculate the standard Gibb's energy change $(\Delta_{r} G^{\circ})$ at $27^{\circ} C$ in $kJ \ mol^{-1}$ (Nearest integer). (Given: $R = 8.3 \ J \ K^{-1} \ mol^{-1}$ and $\ln 10 = 2.3$)

For the equilibrium reaction $A + B \rightleftharpoons C + D$,if we start with equal concentrations of $A$ and $B$,at equilibrium,the concentration of $C$ is $2$ times that of $A$. Find the value of $K_c$.

For the following reactions,equilibrium constants are given:
$S_{(s)} + O_{2(g)} \rightleftharpoons SO_{2(g)}; K_1 = 10^{52}$
$2S_{(s)} + 3O_{2(g)} \rightleftharpoons 2SO_{3(g)}; K_2 = 10^{129}$
The equilibrium constant for the reaction $2SO_{2(g)} + O_{2(g)} \rightleftharpoons 2SO_{3(g)}$ is:

For the reaction $2A_{(g)} + B_{(g)} \rightleftharpoons 3C_{(g)} + D_{(g)}$,$2 \ mol$ each of $A$ and $B$ are taken in a flask. Which of the following will always be true when the system reaches equilibrium?