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:

For a reaction taking place in a container in equilibrium with its surroundings,the effect of temperature on its equilibrium constant $K$ in terms of change in entropy is described by:

Two equilibria,$AB \rightleftharpoons A^{+} + B^{-}$ and $AB + B^{-} \rightleftharpoons AB_2^-$,are simultaneously maintained in a solution with equilibrium constants $K_1$ and $K_2$ respectively. The ratio of $[A^{+}]$ to $[AB_2^-]$ in the solution is

For the reaction,$NO_2 + CO \rightleftharpoons NO + CO_2$,one mole of $NO_2$ and $2$ moles of $CO$ were kept in a vessel. Calculate the equilibrium constant $K_p$,if at equilibrium $25 \%$ of the initial amount of $CO$ is consumed.

At $T \ K$,$K_{c}$ for the reaction $SO_{2(g)} + NO_{2(g)} \rightleftharpoons SO_{3(g)} + NO_{(g)}$ is $16$. If initially one mole each of all the four gases are taken in a $1 \ L$ vessel,the equilibrium concentrations of $SO_{3(g)}$ and $SO_{2(g)}$ in $mol \ L^{-1}$ respectively are:

In a closed vessel at $448^{\circ} C$,$0.5 \ mol$ of $H_2$ and $0.5 \ mol$ of $I_2$ react to form hydrogen iodide.
Reaction: $H_{2(g)} + I_{2(g)} \rightleftharpoons 2HI_{(g)}$,$K_c = 50$.
$(i)$ Calculate the moles of $I_2$ that remain unreacted at equilibrium.
$(ii)$ Calculate $K_p$.