If $8 \, \text{mol}$ of $PCl_5$ is heated in a closed vessel of $10 \, L$ capacity and $25\%$ of it dissociates into $PCl_3$ and $Cl_2$ at equilibrium,then the value of $K_p$ is .....

$2$ moles of $N_2$ are mixed with $6$ moles of $H_2$ in a closed vessel of $1 \ L$ capacity. If $50\%$ of $N_2$ is converted into $NH_3$ at equilibrium,find the value of $K_c$ for the reaction: $N_{2(g)} + 3H_{2(g)} \rightleftharpoons 2NH_{3(g)}$

At $473 \ K$,the equilibrium constant $K_{c}$ for the decomposition of phosphorus pentachloride is $8.3 \times 10^{-3}$. If the decomposition is depicted as:
$PCl_{5(g)} \longleftrightarrow PCl_{3(g)} + Cl_{2(g)} \quad \Delta_{r}H^{\circ} = 124.0 \ kJ \ mol^{-1}$
$(a)$ Write an expression for $K_{c}$ for the reaction.
$(b)$ What is the value of $K_{c}$ for the reverse reaction at the same temperature?
$(c)$ What would be the effect on $K_{c}$ if:
$(i)$ more $PCl_{5}$ is added?
$(ii)$ pressure is increased?
$(iii)$ the temperature is increased?

For the reaction $CH_{4(g)} + 2O_{2(g)} \rightleftharpoons CO_{2(g)} + 2H_{2}O_{(g)}$ with $\Delta H = -170.8 \ kJ \ mol^{-1}$,which of the following statements is incorrect?

In a $20 \ L$ vessel,if $1 \ mol$ each of $CO$,$H_2O$,and $CO_2$ are initially present,then for the equilibrium $CO + H_2O \rightleftharpoons CO_2 + H_2$,which of the following is true?

If the equilibrium constant $K_c = 0.04$,how many moles/liter of $PCl_5$ are required to obtain $0.1$ mole of $Cl_2$?