If the equilibrium constant $K_c = 0.04$,how many moles/liter of $PCl_5$ are required to obtain $0.1$ mole of $Cl_2$?

For the reactions $X \rightleftharpoons 2Y$ and $Z \rightleftharpoons P + Q$,the equilibrium constants $K_p$ and $K_q$ are in the ratio $1:9$. If the degree of dissociation of $X$ and $Z$ is the same,then the ratio of their total pressures is:

Fill in the blanks:
$a$. If a reaction is in equilibrium,then the rate of the forward reaction and the rate of the backward reaction will be ....... .
$b$. If $\Delta G$ is negative,then thermodynamically the reaction takes place in the ...... direction.
$c$. The equilibrium constant gives ........ information for a reaction.

Consider the following chemical equilibrium of the gas phase reaction at a constant temperature: $A_{(g)} \rightleftharpoons B_{(g)} + C_{(g)}$. If $p$ is the total pressure,$K_p$ is the equilibrium constant,and $\alpha$ is the degree of dissociation,then which of the following is true at equilibrium?

At $550 \ K$,the $K_c$ for the following reaction is $10^4 \ mol^{-1} \ L$: $X_{(g)} + Y_{(g)} \rightleftharpoons Z_{(g)}$. At equilibrium,it was observed that $[X] = \frac{1}{2}[Y] = \frac{1}{2}[Z]$. What is the value of $[Z]$ (in $mol \ L^{-1}$) at equilibrium?

Calculate the equilibrium constant for the reaction $H_{2(g)} + CO_{2(g)} \rightleftharpoons H_2O_{(g)} + CO_{(g)}$ at $1395 \ K$ by using the following data:
$2H_2O_{(g)} \rightleftharpoons 2H_{2(g)} + O_{2(g)}; K_1 = 2.1 \times 10^{-13}$
$2CO_{2(g)} \rightleftharpoons 2CO_{(g)} + O_{2(g)}; K_2 = 1.4 \times 10^{-12}$