If the equilibrium constant for $2 SO_2 + O_2 \rightleftharpoons 2 SO_3$ is $K$,then the equilibrium constant for $SO_3 \rightleftharpoons SO_2 + \frac{1}{2} O_2$ will be :

For ammonia formation from constituent elements,the expression for $K_{C}$ is

For the given hypothetical reactions,the equilibrium constants are as follows:
$X \rightleftharpoons Y ; K_1=1.0$
$Y \rightleftharpoons Z ; K_2=2.0$
$Z \rightleftharpoons W ; K_3=4.0$
The equilibrium constant for the reaction $X \rightleftharpoons W$ is (in $.0$)

At equilibrium,the concentrations of $N_{2} = 3.0 \times 10^{-3} \, M$,$O_{2} = 4.2 \times 10^{-3} \, M$ and $NO = 2.8 \times 10^{-3} \, M$ in a sealed vessel at $800 \, K$. What will be $K_{c}$ for the reaction
$N_{2(g)} + O_{2(g)} \rightleftharpoons 2NO_{(g)}$

Consider the following gaseous equilibria with equilibrium constants $K_{1}$ and $K_{2}$ respectively:
$SO_{2(g)} + \frac{1}{2} O_{2(g)} \rightleftharpoons SO_{3(g)}$
$2 SO_{3(g)} \rightleftharpoons 2 SO_{2(g)} + O_{2(g)}$
The equilibrium constants are related as:

At $490\,^{\circ}C$,the equilibrium constant for the synthesis of $HI$ is $50$. The value of $K$ for the dissociation of $HI$ will be: