The partial pressures of an equilibrium mixture of $H_2$,$N_2$,and $NH_3$ are $2 \, atm$,$1 \, atm$,and $3 \, atm$ respectively. If the value of $K_P$ for the reaction $N_2 + 3H_2 \rightleftharpoons 2NH_3$ at $725 \, K$ is $4.28 \times 10^{-5} \, atm^{-2}$,in which direction will the reaction proceed?

For the reaction $A + 2B \rightleftharpoons 2C + D$,the initial concentration of $A$ is $a$ and the initial concentration of $B$ is $1.5$ times that of $A$. If the concentrations of $A$ and $D$ are equal at equilibrium,what will be the concentration of $B$ at equilibrium?

$10 \%$ of $PCl_5$ decomposes at a definite temperature and $4 \ atm$ pressure. At the same temperature,if $20 \%$ of $PCl_5$ decomposes,find the pressure. (Temperature remains constant.) (in $atm$)

For the reaction $Br_2 \rightleftharpoons 2Br$,the equilibrium constants at $327\,^oC$ and $527\,^oC$ are $6.1 \times 10^{-12}$ and $1.0 \times 10^{-7}$ respectively. The reaction is ...........

$2 \ mol$ of $N_2O_{4(g)}$ is kept in a closed container at $298 \ K$ and under $1 \ atm$ pressure. It is heated to $596 \ K$ when $20 \%$ by mass of $N_2O_{4(g)}$ decomposes to $NO_2$. The resulting pressure is (in $atm$)

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?