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 following equilibrium constants are given: $N_2 + 3 H_2 \rightleftharpoons 2 NH_3$ $(k_1)$,$N_2 + O_2 \rightleftharpoons 2 NO$ $(k_2)$,$H_2 + 1/2 O_2 \rightleftharpoons H_2 O$ $(k_3)$. The equilibrium constant for the oxidation of $1 \text{ mole } NH_3$ by oxygen to give $NO$ according to the reaction $NH_3 + 5/4 O_2 \rightleftharpoons NO + 3/2 H_2 O$ is:

For the equilibrium $N_2 + 3H_2 \rightleftharpoons 2NH_3$,$K_c$ at $1000 \ K$ is $2.37 \times 10^{-3}$. If at equilibrium $[N_2] = 2 \ M$ and $[H_2] = 3 \ M$,the concentration of $NH_3$ is: (in $M$)

For the reaction ${N_2}_{(g)} + 2{O_2}_{(g)} \rightleftharpoons 2{NO_2}_{(g)}$,the equilibrium constant is $100$. Find the equilibrium constant for the following reactions:
$(1)$ $2{NO_2}_{(g)} \rightleftharpoons {N_2}_{(g)} + 2{O_2}_{(g)}$
$(2)$ ${NO_2}_{(g)} \rightleftharpoons \frac{1}{2}{N_2}_{(g)} + {O_2}_{(g)}$

From equations $1$ and $2$,
$CO_2 \rightleftharpoons CO + \frac{1}{2} O_2 \, [K_{C_1} = 9.1 \times 10^{-12} \, \text{at} \, 1000^{\circ} C] \, \text{(Eq. } i\text{)}$
$H_2O \rightleftharpoons H_2 + \frac{1}{2} O_2 \, [K_{C_2} = 7.1 \times 10^{-12} \, \text{at} \, 1000^{\circ} C] \, \text{(Eq. } ii\text{)}$
The equilibrium constant for the reaction,$CO_2 + H_2 \rightleftharpoons CO + H_2O$ at the same temperature,is

At constant temperature,the equilibrium constant $(K_p)$ for the decomposition reaction $N_2O_4 \rightleftharpoons 2NO_2$ is expressed by $K_p = \frac{4x^2P}{1 - x^2}$,where $P = \text{pressure}$,$x = \text{extent of decomposition}$. Which one of the following statements is true?