Exactly of a gaseous hydrocarbon is completely burnt in an excess of gas. The reaction yields of gas — Mole Concept and Some Basic Concepts of Chemistry Chemistry Question
Question
Exactly $500\text{ mL}$ of a gaseous hydrocarbon is completely burnt in an excess of $O_2$ gas. The reaction yields $2.5\text{ L}$ of $CO_2$ gas and $3.0\text{ L}$ of water vapour, with all volumes measured under identical high-temperature conditions. Which of the following statements correctly describe the hydrocarbon and the reaction?
💡 Solution & Explanation
Since all are gases under same conditions, Gay-Lussac's law allows direct volume ratios instead of moles. Equation: $C_xH_y + (x + y/4)O_2 \rightarrow xCO_2 + (y/2)H_2O(g)$. $1\text{ vol} \rightarrow x\text{ vol } CO_2$ and $(y/2)\text{ vol } H_2O$. $500\text{ mL} \rightarrow 2500\text{ mL } CO_2 \implies 500x = 2500 \implies x = 5$. $500\text{ mL} \rightarrow 3000\text{ mL } H_2O \implies 500(y/2) = 3000 \implies 250y = 3000 \implies y = 12$. Formula: $C_5H_{12}$ (Pentane, a saturated alkane). Statements A, B, and D are true ($C_5H_{12}$ cannot be reduced further). Volume of $O_2$ consumed = $500 \times (x + y/4) = 500 \times (5 + 3) = 500 \times 8 = 4000\text{ mL} = 4.0\text{ L}$. Statement C is true.