A mixture of hydrogen and oxygen has volume 500 cm³, temperature 300 K, pressure 400 kPa and mass 0.76 g. The ratio of masses of oxygen to hydrogen will be :-

Solution

Physics sir · 4 steps

Get the total moles from PV = nRT, then split the 0.76 g between H₂ and O₂ to match.

1. Total moles. Use SI units: V = 500 cm³ = 5 × 10⁻⁴ m³ and P = 4 × 10⁵ Pa. Then n = PV/RT = 200/(8.314 × 300) ≈ 0.08 mol.
2. Two equations. Let the hydrogen mass be m grams, so the oxygen mass is 0.76 - m. Hydrogen is H₂ (2 g/mol) and oxygen is O₂ (32 g/mol), and their moles must add up to 0.08.

   m/2 + (0.76 - m)/32 = 0.08

3. Solve. Multiply through by 32: 16m + 0.76 - m = 2.56, so 15m = 1.8 and m = 0.12 g. The oxygen mass is 0.76 - 0.12 = 0.64 g.
4. So. Oxygen to hydrogen by mass is 0.64 : 0.12 = 16 : 3, which is option (c).

The idea to keep. For a gas mixture, PV = nRT gives only the total moles. Pair it with the total mass and use molecular masses (H₂ = 2, O₂ = 32) to split it.

Answer from the NTA final answer key. Solution by PrepWiser.