For the reaction,$N_2O_{4(g)} \rightleftharpoons 2NO_{2(g)}$,if dinitrogen tetroxide is $50\%$ dissociated at $60^\circ C$,the standard free energy change at this temperature and $1 \ atm$ pressure is:

$\Delta _f G^o$ 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 $(R = 2 \, cal \, K^{-1} \, mol^{-1}) \dots \dots \text{atm}$.

In the reaction $2P_{(g)} + Q_{(g)} \rightleftharpoons 3R_{(g)} + S_{(g)}$,if $2 \text{ moles}$ of each $P$ and $Q$ are taken initially in a $1 \text{ L}$ flask,which of the following is true at equilibrium?

For the reaction $P_{(g)} + 3Q_{(g)} \rightleftharpoons 4R_{(g)}$,the initial concentrations of $P$ and $Q$ are equal. If the equilibrium concentrations of $P$ and $R$ are equal,then the equilibrium constant $K_c$ for the reaction will be .....

$N_2O_{4(g)}$ at $300 \ K$ is kept in a closed container under $1 \ atm$. At equilibrium,$20\%$ of $N_2O_{4(g)}$ is converted to $NO_{2(g)}$.
$N_2O_{4(g)} \rightleftharpoons 2NO_{2(g)}$
Hence,the resultant pressure is: (in $atm$)

The equilibrium constant $K_c$ for the following equilibrium:
$2 SO_{2(g)} + O_{2(g)} \rightleftharpoons 2 SO_{3(g)}$
at $563 \ K$ is $100$. At equilibrium,the number of moles of $SO_3$ in the $10 \ L$ flask is twice the number of moles of $SO_2$. Calculate the number of moles of oxygen.