One mole of $PCl_{5(g)}$ was heated in a $1 \ L$ closed flask at $500 \ K$. At equilibrium,$0.1 \ mole$ of $Cl_{2(g)}$ was formed. What is its $K_{p}$ (in $atm$)? (Given $R=0.082 \ L \ atm \ mol^{-1} \ K^{-1}$)

In the reaction,$A_{(s)} + B_{(g)} \rightleftharpoons 2C_{(s)} + 2D_{(g)}$,equilibrium is established. If the pressure of $B$ is doubled,then to reestablish the equilibrium,how many times does the pressure of $D$ become as compared to its initial pressure?

For the reaction $C_{(s)} + CO_{2_{(g)}} \rightleftharpoons 2CO_{(g)}$,the partial pressure of $CO_2$ and $CO$ at equilibrium are $4 \ atm$ and $8 \ atm$ respectively. $K_p$ for the reaction is

At $1127 \, K$ and $1 \, atm$ pressure,a gaseous mixture of $CO$ and $CO_2$ in equilibrium with solid carbon has $90.55 \%$ $CO$ by mass.
$C_{(s)} + CO_{2(g)} \longleftrightarrow 2CO_{(g)}$
Calculate $K_c$ for this reaction at the above temperature.

$K_{p} = 0.04 \ atm$ at $899 \ K$ for the equilibrium shown below. What is the equilibrium pressure of $C_{2}H_{6}$ when it is placed in a flask at $4.0 \ atm$ pressure and allowed to come to equilibrium?
$C_{2}H_{6(g)} \longleftrightarrow C_{2}H_{4(g)} + H_{2(g)}$

For the reaction $A_{(g)} \rightleftharpoons 2 B_{(g)}$,the backward reaction rate constant is higher than the forward reaction rate constant by a factor of $2500$,at $1000 \ K$. [Given : $R = 0.0831 \ L \ atm \ mol^{-1} \ K^{-1}$] $K_p$ for the reaction at $1000 \ K$ is