$PCl_{5} \rightleftharpoons PCl_{3} + Cl_{2} \quad K_{c} = 1.844$
$3.0 \ \text{moles}$ of $PCl_{5}$ is introduced in a $1 \ \text{L}$ closed reaction vessel at $380 \ \text{K}$. The number of moles of $PCl_{5}$ at equilibrium is $..... \times 10^{-3}$. (Round off to the Nearest Integer)

In the reaction $PCl_{5(g)} \rightleftharpoons PCl_{3(g)} + Cl_{2(g)}$,initially $1 \text{ mole}$ each of $PCl_5$ and $PCl_3$ are present. At equilibrium,$x \text{ moles}$ of $PCl_5$ remain. What is the total number of moles at equilibrium (in $- x$)?

For the ideal gas reaction,$X + Y \rightleftharpoons Z$,a mixture with $n_{X} = 1 \, mol$,$n_{Y} = 3 \, mol$ and $n_{Z} = 2 \, mol$ is at equilibrium at $300 \, K$ and $1 \, bar$. If the pressure is isothermally increased to $2 \, bar$,the number of moles of $X$ in the new equilibrium is closest to $......$

For the reaction $2NO_{2(g)} \rightleftharpoons N_2O_{4(g)}$ at $300 \ K$,the value of $K_p$ is $2 \ atm^{-1}$. The total pressure at equilibrium is $10 \ atm$. If the volume of the container becomes two times its original volume,what will be its equilibrium pressure at $300 \ K$ (in $atm$)?

The number of correct statement$(s)$ involving equilibria in physical processes from the following is:
$A$. Equilibrium is possible only in a closed system at a given temperature.
$B$. Both the opposing processes occur at the same rate.
$C$. When equilibrium is attained at a given temperature,the value of all its parameters becomes constant.
$D$. For dissolution of solids in liquids,the solubility is constant at a given temperature.

For the reaction $NH_2COONH_{4(s)} \rightleftharpoons 2NH_{3(g)} + CO_{2(g)}$. If the equilibrium pressure is $3X \ bar$,then $\Delta G_r^o$ will be: