The equilibrium constant for the reaction $N_2 + 3H_2 \rightleftharpoons 2NH_3$ is $K.$ Then,the equilibrium constant for the equilibrium $NH_3 \rightleftharpoons \frac{1}{2}N_2 + \frac{3}{2}H_2$ is

$K_p$ for the following reaction is $3.0$ at $1000 \ K$.
$CO_{2(g)} + C_{(s)} \rightleftharpoons 2CO_{(g)}$
What will be the value of $K_c$ for the reaction at the same temperature?
(Given: $R = 0.083 \ L \ bar \ K^{-1} \ mol^{-1}$)

For the reaction $SO_{2(g)} + 1/2 O_{2(g)} \rightleftharpoons SO_{3(g)}$,the equilibrium constant is $K_1$ at $298 \, K$. For the reaction $2SO_{3(g)} \rightleftharpoons 2SO_{2(g)} + O_{2(g)}$ at the same temperature,the equilibrium constant is $K_2$. Then,which of the following is correct?

For the reaction $P + Q \rightleftharpoons R + C$,the equilibrium constant $K_c$ is $10^{-2}$ and the forward rate constant $K_f$ is $10^{-1}$. The rate constant for the backward reaction $(K_b)$ will be:

At $700 \, K$,the equilibrium constant $K_p$ for the reaction $2SO_{3(g)} \rightleftharpoons 2SO_{2(g)} + O_{2(g)}$ is $1.80 \times 10^{-3}$. The numerical value in $mol \, L^{-1}$ of $K_c$ for this reaction at the same temperature will be $(R = 8.314 \, J \, K^{-1} \, mol^{-1})$.

In a $500 \ mL$ capacity vessel,$CO$ and $Cl_2$ are mixed to form $COCl_2$. At equilibrium,it contains $0.2 \ mol$ of $COCl_2$ and $0.1 \ mol$ of each of $CO$ and $Cl_2$. The equilibrium constant $K_c$ for the reaction $CO + Cl_2 \rightleftharpoons COCl_2$ is: