Equilibrium constants $K_1$ and $K_2$ for the following equilibria:
$(a)$ $NO_{(g)} + \frac{1}{2}O_{2(g)} \rightleftharpoons NO_{2(g)}$
$(b)$ $2NO_{2(g)} \rightleftharpoons 2NO_{(g)} + O_{2(g)}$
are related as:

The rate constant for forward and backward reactions of hydrolysis of ester are $1.1 \times 10^{-2} \text{ min}^{-1}$ and $1.5 \times 10^{-3} \text{ min}^{-1}$ respectively. The equilibrium constant for the reaction $CH_3COOC_2H_5 + H_2O \rightleftharpoons CH_3COOH + C_2H_5OH$ is: (in $.33$)

$x A_{(s)} \rightleftharpoons y B_{(g)} + z C_{(g)}$. If $\frac{K_c}{K_p} = (RT)^{-2}$,then which is correct?

In which one of the following gaseous equilibria is $K_p$ less than $K_c$?

At $1000 \ K$,if the equilibrium constant $K_p$ for the reaction $2 \ NOCl_{(g)} \rightleftharpoons 2 \ NO_{(g)} + Cl_{2(g)}$ is $4.157 \times 10^{-4} \ bar$,the $K_c$ (in $mol \ L^{-1}$) is $(R = 0.083 \ L \ bar \ K^{-1} \ mol^{-1})$

For the reaction $PCl_{5(g)} \rightleftharpoons PCl_{3(g)} + Cl_{2(g)}$,$1 mol$ of $PCl_5$ is taken at $5 atm$ pressure. If $50\%$ of $PCl_5$ dissociates at equilibrium,calculate $K_p$.