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.

Ammonia under a pressure of $15 \ atm$ at $27 \ ^{\circ}C$ is heated to $347 \ ^{\circ}C$ in a closed vessel in the presence of a catalyst. Under these conditions,$NH_3$ is partially decomposed according to the equation,$2NH_3 \rightleftharpoons N_2 + 3H_2$. The vessel is such that the volume remains constant,and the pressure increases to $50 \ atm$. Calculate the percentage of $NH_3$ actually decomposed.

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

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?

One mole of $H_2O$ and one mole of $CO$ are taken in a $10 \ L$ vessel and heated to $725 \ K$. At equilibrium,$40 \%$ of water (by mass) reacts with $CO$ according to the equation:
$H_2O_{(g)} + CO_{(g)} \longleftrightarrow H_{2(g)} + CO_{2(g)}$
Calculate the equilibrium constant $(K_c)$ for the reaction.

Which of the following equations is incorrect?