Two moles of $NH_3$ when put into a previously evacuated vessel $(1 \ L)$,partially dissociate into $N_2$ and $H_2$. If at equilibrium one mole of $NH_3$ is present,the equilibrium constant is

The equilibrium constants for the reactions $(i)$,$(ii)$,and $(iii)$ are $K_1$,$K_2$,and $K_3$ respectively. Which of the following is the correct relationship?
$(i)$ $N_2 + 2O_2 \rightleftharpoons 2NO_2$
$(ii)$ $2NO_2 \rightleftharpoons N_2 + 2O_2$
$(iii)$ $NO_2 \rightleftharpoons 1/2 N_2 + O_2$

For the gaseous phase reaction $2NO \rightleftharpoons N_2 + O_2$,$\Delta H^\circ = +43.5 \ kcal \ mol^{-1}$. Which statement is correct?

Write the equilibrium constant (equilibrium law) for the following reactions:
$(i)$ $4NH_{3(g)} + 5O_{2(g)} \rightleftharpoons 4NO_{(g)} + 6H_{2}O_{(g)}$
$(ii)$ $H_{2(g)} + I_{2(g)} \rightleftharpoons 2HI_{(g)}$
$(iii)$ $N_{2(g)} + 3H_{2(g)} \rightleftharpoons 2NH_{3(g)}$

Write the expression for the equilibrium constant,$K_{c}$ for each of the following reactions:
$(i)$ $2 NOCl_{(g)} \longleftrightarrow 2 NO_{(g)} + Cl_{2(g)}$
$(ii)$ $2 Cu(NO_{3})_{2(s)} \longleftrightarrow 2 CuO_{(s)} + 4 NO_{2(g)} + O_{2(g)}$
$(iii)$ $CH_{3}COOC_{2}H_{5(aq)} + H_{2}O_{(l)} \longleftrightarrow CH_{3}COOH_{(aq)} + C_{2}H_{5}OH_{(aq)}$
$(iv)$ $Fe^{3+}_{(aq)} + 3 OH^{-}_{(aq)} \longleftrightarrow Fe(OH)_{3(s)}$
$(v)$ $I_{2(s)} + 5 F_{2(g)} \longleftrightarrow 2 IF_{5(g)}$

If the equilibrium constant for the reaction ${N_2}_{(g)} + {O_2}_{(g)} \rightleftharpoons 2NO_{(g)}$ is $K$,then what is the equilibrium constant for the reaction $\frac{1}{2}{N_2}_{(g)} + \frac{1}{2}{O_2}_{(g)} \rightleftharpoons NO_{(g)}$?