$5 \, \text{moles}$ of $PCl_5$ are heated in a closed vessel of $5 \, \text{L}$ capacity. At equilibrium,$40\%$ of $PCl_5$ is found to be dissociated. What is the value of $K_c$ (in $, \text{M}$)?

Consider the following reaction equilibrium:
$N_{2(g)} + 3H_{2(g)} \rightleftharpoons 2NH_{3(g)}$
Initially,$1 \ mol$ of $N_2$ and $3 \ mol$ of $H_2$ are taken in a $2 \ L$ flask. At equilibrium,if the number of moles of $N_2$ is $0.6$,what is the total number of moles of all gases present in the flask?

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:

For the reaction $3A + B \rightleftharpoons 2C + D$,if the equilibrium concentrations of $A, B,$ and $C$ are $0.03 \ M, 0.01 \ M,$ and $0.008 \ M$ respectively,what is the initial concentration of $A$ (in $M$)?

For the reaction $X_{(g)} + Y_{(g)} \rightleftharpoons Z_{(g)}$ at $550 \ K$,the value of $K_c$ is $10^{-4} \ mol^{-1} \ L$. If at equilibrium $[X] = \frac{1}{2}[Y] = \frac{1}{2}[Z]$,then the value of $[Z]$ at equilibrium will be:

The equilibrium constant $K_c$ for the following equilibrium:
$2 SO_{2(g)} + O_{2(g)} \rightleftharpoons 2 SO_{3(g)}$
at $563 \ K$ is $100$. At equilibrium,the number of moles of $SO_3$ in the $10 \ L$ flask is twice the number of moles of $SO_2$. Calculate the number of moles of oxygen.