At a definite temperature and $3 \ atm$ pressure,$75\%$ of $PCl_5$ decomposes into $PCl_3$ and $Cl_2$. Find $K_p$ for the reaction: $PCl_{5(g)} \rightleftharpoons PCl_{3(g)} + Cl_{2(g)}$ (in $atm$)

For the reaction $N_2O_{4_{(g)}} \rightleftharpoons 2NO_{2_{(g)}}$ at $298 \ K$,the equilibrium constant $K_p$ is $0.14 \ atm$. Calculate the value of $K_c$. $(R = 0.082 \ L \ atm \ K^{-1} \ mol^{-1})$

For the reactions:
$2NO + O_2 \rightleftharpoons 2NO_2$; $K_1$
$4NO + 2Cl_2 \rightleftharpoons 4NOCl$; $K_2$
$NO_2 + \frac{1}{2}Cl_2 \rightleftharpoons NOCl + \frac{1}{2}O_2$; $K_3$
Where $K_1, K_2, K_3$ are equilibrium constants,then $K_3^2$ is equal to:

At $1000 \, K$,for the reaction $A_{(g)} + 2B_{(g)} \rightleftharpoons 3C_{(g)} + D_{(g)}$,the value of $K_p$ is $0.05 \, atm$. What will be the value of $K_c$ in terms of $R$?

At $T(K)$,the following gaseous equilibrium is established: $W + X \rightleftharpoons Y + Z$. The initial concentration of $W$ is two times the initial concentration of $X$. The system is heated to $T(K)$ to establish equilibrium. At equilibrium,the concentration of $Y$ is four times the concentration of $X$. What is the value of $K_c$?

For the reaction $2NO_{2(g)} \rightleftharpoons 2NO_{(g)} + O_{2(g)}$,the value of $K_c$ is $1.8 \times 10^{-6}$ at $184^{\circ}C$. Given $R = 0.083 \ L \cdot bar \cdot K^{-1} \cdot mol^{-1}$,compare $K_p$ and $K_c$ at $184^{\circ}C$.