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:

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 $K_1, K_2, K_3$ are equilibrium constants for the formation of $AD, AD_2, AD_3$ respectively as follows: $A + D \rightleftharpoons AD$,$AD + D \rightleftharpoons AD_2$,$AD_2 + D \rightleftharpoons AD_3$. Then the equilibrium constant '$K$' for $A + 3D \rightleftharpoons AD_3$ is related as:

For the reaction $cis-C_2H_2Cl_2 \rightleftharpoons trans-C_2H_2Cl_2$,the equilibrium constant at $500 \ K$ is $0.6$. The equilibrium constant for the reaction $trans-C_2H_2Cl_2 \rightleftharpoons cis-C_2H_2Cl_2$ at the same temperature will be ...............

In the reaction $A + 2B \rightleftharpoons 2C + D$,the initial concentration of $B$ was $1.5$ times that of $[A]$. At equilibrium,the concentrations of $A$ and $B$ became equal. The equilibrium constant for the reaction is:

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: