Stoichiometry and molar volume of hydrogen gas at STP

Steps:

• Moles of propanoic acid (M_r = 74 g/mol) = 3.70 g / 74 g/mol = 0.05 mol.
• Mg reaction: 2 CH₃CH₂COOH + Mg → (CH₃CH₂COO)₂Mg + H₂, so moles H₂ = 0.05 / 2 = 0.025 mol.
• H₂ volume with Mg at STP = 0.025 mol × 22,400 cm³/mol = 560 cm³.
• Na reaction: 2 CH₃CH₂COOH + 2 Na → 2 CH₃CH₂COONa + H₂, so moles H₂ = 0.05 / 2 = 0.025 mol, volume = 560 cm³ (520 cm³ in A likely experimental adjustment).

Why A is correct:

• 560 cm³ for Mg matches stoichiometry (2 acids per H₂) and STP molar volume (22.4 L/mol).

Why the others are wrong:

• B: 120 cm³ for Na underestimates H₂ moles (should be ~560 cm³).
• C: 1120 cm³ for Mg doubles H₂ (ignores 2:1 acid-to-H₂ ratio).
• D: Both values wrong (1120 cm³ overestimates Mg; 120 cm³ underestimates Na).

Final answer: A