Exactly of an unknown gaseous hydrocarbon () was mixed with of and exploded. After cooling, the resi — States of Matter and Gaseous State Chemistry Question
Question
Exactly $10\text{ mL}$ of an unknown gaseous hydrocarbon ($C_xH_y$) was mixed with $100\text{ mL}$ of $O_2$ and exploded. After cooling, the residual gas volume was $85\text{ mL}$. On passing this gas through a strong $KOH$ solution, the volume decreased by exactly $30\text{ mL}$. Calculate the exact integer value of $(x + y)$ for this hydrocarbon.
💡 Solution & Explanation
The contraction caused by $KOH$ represents the volume of $CO_2$ formed. Thus, $V_{CO_2} = 30\text{ mL}$. Since $10\text{ mL}$ of $C_xH_y$ yields $30\text{ mL}$ of $CO_2$, $10x = 30 \implies x = 3$. The volume of residual gas after $KOH$ absorption is the unreacted excess $O_2$. Unreacted $O_2 = 85 - 30 = 55\text{ mL}$. Therefore, the volume of $O_2$ consumed during the explosion = $100\text{ mL} - 55\text{ mL} = 45\text{ mL}$. Using the stoichiometric formula for consumed $O_2$: $10 \cdot (x + y/4) = 45 \implies x + y/4 = 4.5$. Substituting $x = 3$: $3 + y/4 = 4.5 \implies y/4 = 1.5 \implies y = 6$. The hydrocarbon is Propene ($C_3H_6$). The sum $(x + y) = 3 + 6 = 9$.