For the reaction $A_{(g)} \rightleftharpoons B_{(g)} + C_{(g)}$,$A$ is $33 \%$ dissociated at a total pressure $P$. The correct relation between $P$ and $K_{p}$ is

Given three reactions and their equilibrium constants:
$N_2 + 3H_2 \rightleftharpoons 2NH_3 ; k_1$
$N_2 + O_2 \rightleftharpoons 2NO ; k_2$
$H_2 + \frac{1}{2}O_2 \rightleftharpoons H_2O ; k_3$
The equilibrium constant for the reaction $2NH_3 + \frac{5}{2}O_2 \rightleftharpoons 2NO + 3H_2O$ in terms of $k_1, k_2,$ and $k_3$ is:

For a reaction $2 A \rightleftharpoons B + C$,$K_c$ is $2 \times 10^{-3}$. At a given time,the reaction mixture has $[A] = [B] = [C] = 3 \times 10^{-4} \ M$. Which of the following options is correct?

At $1000 \ K$ in a $0.654 \ L$ vessel,$CaCO_{3(s)}$ is taken. For the reaction $CaCO_{3(s)} \rightleftharpoons CaO_{(s)} + CO_{2(g)}$,the equilibrium constant $K_p$ is $3.9 \times 10^{-2} \ bar$. Find the weight of $CaO$ produced at equilibrium. $(Ca=40, C=12, O=16)$

At a certain temperature,$2HI \rightleftharpoons H_2 + I_2$. If only $50\%$ of $HI$ is dissociated at equilibrium,the equilibrium constant $(K_c)$ is:

At $500 \ K$,for a reversible reaction $A_{2(g)} + B_{2(g)} \rightleftharpoons 2 AB_{(g)}$ in a closed container,$K_C = 2 \times 10^{-5}$. In the presence of a catalyst,the equilibrium is attained $10$ times faster. The equilibrium constant $K_C$ in the presence of a catalyst at the same temperature is: