$0.6 \ mol$ of $NH_3$ in a reaction vessel of $2 \ dm^3$ capacity was brought to equilibrium. The vessel was then found to contain $0.15 \ mol$ of $H_2$ formed by the reaction $2NH_{3(g)} \rightleftharpoons N_{2(g)} + 3H_{2(g)}$. Which of the following statements is true?

For the following reaction,the equilibrium constant $K_{c}$ at $298 \ K$ is $1.6 \times 10^{17}$.
$Fe^{2+}_{(aq)} + S^{2-}_{(aq)} \rightleftharpoons FeS_{(s)}$
When equal volumes of $0.06 \ M \ Fe^{2+}_{(aq)}$ and $0.2 \ M \ S^{2-}_{(aq)}$ solutions are mixed,the equilibrium concentration of $Fe^{2+}_{(aq)}$ is found to be $Y \times 10^{-17} \ M$. The value of $Y$ is. . . . .

One mole of $N_2O_4(g)$ is taken in a closed container at $1 \ atm$ and $300 \ K$. When it is heated to $600 \ K$,$20 \%$ of $N_2O_4(g)$ dissociates into $NO_2(g)$. The resulting pressure is .......... $atm$.

If the reaction is started with $NH_4COONH_{2(s)}$ and the equilibrium mixture has a total pressure of $3 \ atm$,then the $K_P$ for the reaction $NH_4COONH_{2(s)} \rightleftharpoons 2NH_{3(g)} + CO_{2(g)}$ is ..... $atm^3$.

Consider a reaction that is first order in both directions: $A \underset{K_b}{\stackrel{K_f}{\rightleftharpoons}} B$. Initially only $A$ is present,and its concentration is $A_{0}$. Assume $A_{t}$ and $A_{\text{eq}}$ are the concentrations of $A$ at time $t$ and at equilibrium,respectively. The time $t$ at which $A_{t} = (A_{0} + A_{\text{eq}})/2$ is $....$

At $473 \ K$, equilibrium constant $K_{c}$ for decomposition of phosphorus pentachloride, $PCl_{5}$, is $8.3 \times 10^{-3}$. If decomposition is depicted as,
$PCl_{5(g)} \rightleftharpoons PCl_{3(g)} + Cl_{2(g)}, \Delta_{r}H^{\Theta} = 124.0 \ kJ \ mol^{-1}$
$(a)$ 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?