Which one of the following statements is NOT correct?

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NDA-I (GAT) Official Paper (Held On: 13 Apr, 2025)
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  1. Half mole of nitrogen gas is measured 11·2 litre at STP
  2. 17 gram of ammonia gas contains 6·022 × 10²³ molecules at STP
  3. 22·4 litre of CO₂ gas at STP contains 44 gram of molecules
  4. 4 gram of hydrogen gas contains 6·022 × 10²³ molecules

Answer (Detailed Solution Below)

Option 4 : 4 gram of hydrogen gas contains 6·022 × 10²³ molecules
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Detailed Solution

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CONCEPT:

Avogadro's Law and Molar Relationships at STP

  • Avogadro's Law: At Standard Temperature and Pressure (STP), 1 mole of any ideal gas occupies 22.4 liters of volume.
  • Molecular Relationships:
    • 1 mole of a substance contains Avogadro's number of molecules, which is 6.022 × 1023.
    • 1 mole of a compound is equivalent to its molar mass in grams.

EXPLANATION:

  • Half mole of nitrogen gas is measured 11.2 liters at STP.
    • At STP, 1 mole of nitrogen gas occupies 22.4 liters.
    • Thus, half a mole of nitrogen gas will occupy 22.4 ÷ 2 = 11.2 liters.
    • This statement is correct.
  • 17 grams of ammonia gas contains 6.022 × 1023 molecules at STP.
    • The molar mass of ammonia (NH3) is 14 (N) + 1×3 (H) = 17 g/mol.
    • 17 grams of ammonia corresponds to 1 mole, which contains 6.022 × 1023 molecules.
    • This statement is correct.
  • 22.4 liters of CO2 gas at STP contains 44 grams of molecules.
    • The molar mass of CO2 is 12 (C) + 16×2 (O) = 44 g/mol.
    • At STP, 22.4 liters of CO2 corresponds to 1 mole, which weighs 44 grams.
    • This statement is correct.
  • 4 grams of hydrogen gas contains 6.022 × 1023 molecules.
    • The molar mass of H2 is 1×2 = 2 g/mol.
    • 4 grams of H2 corresponds to 4 ÷ 2 = 2 moles.
    • Since 1 mole contains 6.022 × 1023 molecules, 2 moles would contain 2 × 6.022 × 1023 = 1.2044 × 1024 molecules.

The given statement is incorrect because 4 grams of H2 does not contain 6.022 × 1023 molecules, but rather twice that amount.

Therefore, the incorrect statement is Option 4.

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