Exactly of an unknown oxide of nitrogen undergoes complete decomposition to produce of gas and of ga — Mole Concept and Some Basic Concepts of Chemistry Chemistry Question
Question
Exactly $10\text{ mL}$ of an unknown oxide of nitrogen undergoes complete decomposition to produce $20\text{ mL}$ of $NO_2$ gas and $5\text{ mL}$ of $O_2$ gas under identical conditions of temperature and pressure. What is the molecular formula of the original nitrogen oxide?
💡 Solution & Explanation
Step 1: Write the general decomposition equation for an oxide of nitrogen $N_xO_y$. $N_xO_y(g) \rightarrow x NO_2(g) + \frac{y-2x}{2} O_2(g)$. Step 2: Apply Gay-Lussac's law of combining volumes. Volume of $NO_2 = 10x\text{ mL} = 20\text{ mL} \implies x = 2$. Volume of $O_2 = 10 \times \left(\frac{y-2x}{2}\right)\text{ mL} = 5\text{ mL}$. Substitute $x=2$: $10 \times \left(\frac{y-4}{2}\right) = 5 \implies 5(y-4) = 5 \implies y-4 = 1 \implies y = 5$. Step 3: The molecular formula is $N_2O_5$.