A mixture of gas and gas is mixed with of gas and ignited with an electric spark. After cooling the — States of Matter and Gaseous State Chemistry Question
Question
A $40\text{ mL}$ mixture of $CO$ gas and $H_2$ gas is mixed with $40\text{ mL}$ of $O_2$ gas and ignited with an electric spark. After cooling the mixture to the original room temperature (condensing the water), the total residual gas volume is measured to be $50\text{ mL}$. Calculate the initial volume of $CO$ present in the original $40\text{ mL}$ mixture (in $\text{mL}$).
💡 Solution & Explanation
Let the initial volume of $CO$ be $a\text{ mL}$ and $H_2$ be $b\text{ mL}$. $a + b = 40$. The combustion reactions are: $CO + 0.5O_2 \rightarrow CO_2$ and $H_2 + 0.5O_2 \rightarrow H_2O(l)$. Total $O_2$ consumed = $0.5a + 0.5b = 0.5(40) = 20\text{ mL}$. Since $40\text{ mL}$ of $O_2$ was added, unreacted $O_2 = 40 - 20 = 20\text{ mL}$. The $CO$ combustion produces $a\text{ mL}$ of $CO_2$. The $H_2$ combustion produces liquid water (negligible volume). Residual gas = $CO_2$ produced + Unreacted $O_2$ = $a + 20$. We are given that residual gas = $50\text{ mL}$. Thus, $a + 20 = 50 \implies a = 30\text{ mL}$.