Exactly of a gaseous hydrocarbon was exploded with of oxygen gas. After cooling to room temperature, — States of Matter and Gaseous State Chemistry Question
Question
Exactly $10\text{ mL}$ of a gaseous hydrocarbon $C_xH_y$ was exploded with $100\text{ mL}$ of oxygen gas. After cooling to room temperature, the residual gas volume was $80\text{ mL}$. On passing this residual gas mixture through strong aqueous $KOH$, the volume was further reduced to exactly $50\text{ mL}$. Determine the number of hydrogen atoms ($y$) in the molecular formula $C_xH_y$.
💡 Solution & Explanation
The contraction caused by $KOH$ represents the volume of $CO_2$ formed. Thus, $V_{CO_2} = 80 - 50 = 30\text{ mL}$. Since $10\text{ mL}$ of $C_xH_y$ yields $30\text{ mL}$ of $CO_2$, $10x = 30 \implies x = 3$. The final $50\text{ mL}$ of gas unabsorbed by $KOH$ is the unreacted excess $O_2$. Therefore, the volume of $O_2$ consumed = $100\text{ mL} - 50\text{ mL} = 50\text{ mL}$. Using the stoichiometric formula for consumed $O_2$: $V \cdot (x + y/4) = 50 \implies 10 \cdot (3 + y/4) = 50 \implies 3 + y/4 = 5 \implies y/4 = 2 \implies y = 8$. The hydrocarbon is $C_3H_8$.