JEE Main · 2025 · 22 Jan 2025 · Shift 1 · Some Basic Concepts of Chemistry

Some

CO_{2}

gas was kept in a sealed container at a pressure of 1 atm and at 273 K . This entire amount of

CO_{2}

gas was later passed through an aqueous solution of

Ca (OH)_{2}

. The excess unreacted

Ca (OH)_{2}

was later neutralized with 0.1 M of 40 mL HCl . If the volume of the sealed container of

CO_{2}

was x , then x is ____

cm^{3}

(nearest integer).
[Given : The entire amount of

CO_{2} (g)

reacted with exactly half the initial amount of

Ca (OH)_{2}

present in the aqueous solution.]

Answer: 45

Solution

Let the moles of

C O_{2}

n

. The entire amount of

C O_{2}

reacts with exactly half of the total

C a (O H)_{2}

initially present, via

C O_{2} + C a (O H)_{2} \to C a C O_{3} + H_{2} O

so if

n

mol

C O_{2}

reacts with

n

mol

C a (O H)_{2}

, the total initial

C a (O H)_{2}

2 n

, leaving

n

mol unreacted.

This excess

C a (O H)_{2}

is neutralised by HCl:

C a (O H)_{2} + 2 H C l \to C a C l_{2} + 2 H_{2} O

Equating equivalents:

n \times 2 = 0.1 \times \frac{40}{1000}

, giving

n = 2 \times 1 0^{- 3}

mol.

At 1 atm and 273 K, the volume of

C O_{2}

is:

V = n \times 22400 = 2 \times 1 0^{- 3} \times 22400 = 44.8 c m^{3} \approx 45 c m^{3}

JEE Main · 2025 · 22 Jan 2025 · Shift 1 · Integer answer