If the equilibrium constants for the given reactions are $K_1$ and $K_2$ respectively,find the relationship between $K_2$ and $K_1$.
$2SO_{2(g)} + O_{2(g)} \rightleftharpoons 2SO_{3(g)}$
$SO_{2(g)} + \frac{1}{2} O_{2(g)} \rightleftharpoons SO_{3(g)}$

The equilibrium constant $(K_c)$ for the reaction $N_{2(g)} + O_{2(g)} \rightleftharpoons 2 NO_{(g)}$ at temperature $T$ is $4 \times 10^{-4}$. The value of $K_c$ for the reaction $NO_{(g)} \rightleftharpoons \frac{1}{2} N_{2(g)} + \frac{1}{2} O_{2(g)}$ at the same temperature is:

At $298 \ K$,for the reaction $Ag^{+} + 2NH_3 \rightleftharpoons Ag(NH_3)_2^{+}$,the concentrations of $Ag^{+}$,$Ag(NH_3)_2^{+}$,and $NH_3$ are $10^{-1} \ M$,$10^{-1} \ M$,and $10^3 \ M$ respectively. The value of $K_c$ at $298 \ K$ for this equilibrium is ...... .

The equilibrium constants for the following reactions are given at $25^{\circ} C$:
$2 A \rightleftharpoons B + C, K_{1} = 1.0$
$2 B \rightleftharpoons C + D, K_{2} = 16$
$2 C + D \rightleftharpoons 2 P, K_{3} = 25$
The equilibrium constant for the reaction $P \rightleftharpoons A + \frac{1}{2} B$ at $25^{\circ} C$ is

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
$N_{2(g)} + O_{2(g)} \rightleftharpoons 2NO_{(g)}$

In a closed vessel,$PCl_{5(g)}$ is obtained by the chemical reaction between $PCl_{3(g)}$ and $Cl_{2(g)}$. If the equilibrium concentrations in this vessel of $PCl_3$,$Cl_2$,and $PCl_5$ at $500 \ K$ are $1.59 \ M$,$1.59 \ M$,and $1.41 \ M$ respectively,then find the equilibrium constant $K_c$ for the reaction: $PCl_{3(g)} + Cl_{2(g)} \rightleftharpoons PCl_{5(g)}$