In the reaction $A + 2B \rightleftharpoons 2C$,if $2$ moles of $A$,$3.0$ moles of $B$ and $2.0$ moles of $C$ are placed in a $2.0 \ L$ flask and the equilibrium concentration of $C$ is $0.5 \ mol/L$. The equilibrium constant $K_c$ for the reaction is:

Reaction between $N_{2}$ and $O_{2}$ takes place as follows:
$2 N_{2(g)} + O_{2(g)} \longleftrightarrow 2 N_{2}O_{(g)}$
If a mixture of $0.482 \ mol$ of $N_{2}$ and $0.933 \ mol$ of $O_{2}$ is placed in a $10 \ L$ reaction vessel and allowed to form $N_{2}O$ at a temperature for which $K_{c} = 2.0 \times 10^{-37}$,determine the composition of the equilibrium mixture.

For a reaction $2 A \rightleftharpoons B + C$,$K_c$ is $2 \times 10^{-3}$. At a given time,the reaction mixture has $[A] = [B] = [C] = 3 \times 10^{-4} \ M$. Which of the following options is correct?

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?

Solid $KClO_3$ is taken in a container maintained at a constant pressure of $1 \ atm$. Upon heating,the following equilibrium is obtained:
$2KClO_{3(s)} \rightleftharpoons 2KCl_{(s)} + 3O_{2(g)}$
If $\Delta H^o = 25 \ kcal/mol$ and $\Delta S^o = 50 \ cal/K$,at what temperature will equilibrium be established in the container? (Ignore variation of $\Delta H^o$ and $\Delta S^o$ with temperature.) $......K$

The following reaction is performed at $298 \, K$.
$2 NO_{(g)} + O_{2(g)} \rightleftharpoons 2 NO_{2(g)}$
The standard free energy of formation of $NO_{(g)}$ is $86.6 \, kJ/mol$ at $298 \, K$. What is the standard free energy of formation of $NO_{2(g)}$ at $298 \, K$? $(K_p = 1.6 \times 10^{12})$