Some $\mathrm{CO}_{2}$ gas was kept in a sealed container at a pressure of 1 atm and at 273 K . This

Question

Some $\mathrm{CO}_{2}$ gas was kept in a sealed container at a pressure of 1 atm and at 273 K . This entire amount of $\mathrm{CO}_{2}$ gas was later passed through an aqueous solution of $\mathrm{Ca}(\mathrm{OH})_{2}$. The excess unreacted $\mathrm{Ca}(\mathrm{OH})_{2}$ was later neutralized with 0.1 M of 40 mL HCl . If the volume of the sealed container of $\mathrm{CO}_{2}$ was $x$, then $x$ is $\_\_\_\_$ $\mathrm{cm}^{3}$ (nearest integer).\ [Given : The entire amount of $\mathrm{CO}_{2(g)}$ reacted with exactly half the initial amount of $\mathrm{Ca}(\mathrm{OH})_{2}$ present in the aqueous solution.]\

Professor PC Thomas Classes · Answer

(45) : $\mathrm{Ca}(\mathrm{OH})_{2}+\mathrm{CO}_{2} \longrightarrow$\ $\mathrm{CaCO}_{3}+\mathrm{H}_{2} \mathrm{O}$\ Amount of unreacted $\mathrm{Ca}(\mathrm{OH})_{2}$\ $=0.1 	imes 40 	imes \frac{1}{2}$ millimol=2 millimol\ It is given that $\mathrm{CO}_{2}$ reacts with exactly half of the initial amount of $\mathrm{Ca}(\mathrm{OH})_{2}$.\ Thus, initial amount of $\mathrm{Ca}(\mathrm{OH})_{2}$\ = 4 millimoles\ Amount of $\mathrm{CO}_{2}=2$ millimoles $$ \begin{aligned} & =\left(2 	imes 10^{-3} 	imes 22400ight) \mathrm{cm}^{3} \ & =44.8 \mathrm{~cm}^{3} \approx 45 \mathrm{~cm}^{3} \end{aligned} $$