Some $\mathrm{CO}_2$ gas was kept in a sealed container at a pressure of 1 atm and at 273 K. This entire…
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 $\mathrm{HCl}$. 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 $\mathrm{CO}_2(\mathrm{g})$ reacted with exactly half the initial amount of $\mathrm{Ca}(\mathrm{OH})_2$ present in the aqueous solution.]
Solution
Let moles of $\mathrm{CO}_2=\mathrm{n}$ moles of $\mathrm{Ca}(\mathrm{OH})_2$ total initially $=2 \mathrm{n}$ excess $\mathrm{Ca}(\mathrm{OH})_2=\mathrm{n}$ gm equivalent of $\mathrm{Ca}(\mathrm{OH})_2=\mathrm{gm}$ equivalent of HCl $\begin{aligned} & \mathrm{n} \times 2=0.1 \times \frac{40}{1000} \times 1 \\ & \mathrm{n}=2 \times 10^{-3} \end{aligned}$ Volume of $\mathrm{CO}_2=2 \times 10^{-3} \times 22400=44.8 \mathrm{~cm}^3$