For the reaction $N_2 + 3H_2 \rightleftharpoons 2NH_3$,the equilibrium constant is $k$. What is the equilibrium constant for the reaction $2N_2 + 6H_2 \rightleftharpoons 4NH_3$?

Equilibrium constant,$K_{c}$ for the reaction $N_{2(g)} + 3H_{2(g)} \longleftrightarrow 2NH_{3(g)}$ at $500 \, K$ is $0.061$. At a particular time,the analysis shows that the composition of the reaction mixture is $[N_{2}] = 3.0 \, mol \, L^{-1}$,$[H_{2}] = 2.0 \, mol \, L^{-1}$,and $[NH_{3}] = 0.5 \, mol \, L^{-1}$. Is the reaction at equilibrium? If not,in which direction does the reaction tend to proceed to reach equilibrium?

Consider the following equilibrium reaction in gaseous state at $T(K)$.
$A(g) + 2B(g) \rightleftharpoons 2C(g) + D(g)$
The initial concentration of $B$ is $1.5$ times that of $A$. At equilibrium,the concentrations of $A$ and $B$ are equal. The equilibrium constant for the reaction is

The reaction,$2A_{(g)} + B_{(g)} \rightleftharpoons 3C_{(g)} + D_{(g)}$ is begun with the concentrations of $A$ and $B$ both at an initial value of $1.00 \ M$. When equilibrium is reached,the concentration of $D$ is measured and found to be $0.25 \ M$. The value for the equilibrium constant for this reaction is given by the expression:

$4.5$ moles each of hydrogen and iodine are heated in a sealed $10 \ L$ vessel. At equilibrium,$3$ moles of $HI$ are found. The equilibrium constant for ${H_2}_{(g)} + {I_2}_{(g)} \rightleftharpoons 2HI_{(g)}$ is

For the reaction $2AB \rightleftharpoons A_2 + B_2$,the equilibrium constant is $49$. What will be the equilibrium constant for the reaction $AB \rightleftharpoons 1/2 A_2 + 1/2 B_2$?