Some \( \mathrm{CO_2} \) gas was kept in a sealed container at a pressure of \( 1 \,\text{atm} \) and at \( 273 \,\text{K} \). This entire amount of \( \mathrm{CO_2} \) gas was later passed through an aqueous solution of \( \mathrm{Ca(OH)_2} \). The excess unreacted \( \mathrm{Ca(OH)_2} \) was later neutralized with \( 0.1 \,\text{M} \) of \( 40 \,\text{mL} \) HCl. If the volume of the sealed container of \( \mathrm{CO_2} \) was \( x \), then \( x \) is _____________ \( \text{cm}^3 \) (nearest integer).
[Given: The entire amount of \( \mathrm{CO_2(g)} \) reacted with exactly half the initial amount of \( \mathrm{Ca(OH)_2} \) present in the aqueous solution.]