A mixture of hydrogen and oxygen has volume 2000 cm³, temperature 300 K, pressure 100 kPa and mass 0.76 g. The ratio of number of moles of hydrogen to number of moles of oxygen in the mixture will be:
[Take gas constant R = 8.3 JK⁻¹mol⁻¹]

Solution

Physics sir · 4 steps

The gas law gives the total moles, the mass gives a second equation, and two equations give both gases.

1. Total moles. Use PV = nRT in SI units: V = 2000 cm³ = 2 × 10⁻³ m³ and P = 10⁵ Pa, so PV = 200 J.

   nₜₒₜₐₗ = PV/RT = 200/(8.3 × 300) = 200/2490 ≈ 0.0803 mol

2. Mass equation. Let x be the moles of H₂ (molar mass 2 g) and y the moles of O₂ (molar mass 32 g). Then x + y = 0.0803 and 2x + 32y = 0.76.
3. Solve. Put y = 0.0803 - x into the mass equation: 2x + 2.570 - 32x = 0.76, so 30x = 1.81. This gives x ≈ 0.0603 mol and y ≈ 0.0200 mol.
4. So. x/y = 0.0603/0.0200 ≈ 3. Hydrogen to oxygen is 3 : 1, option (b).

The idea to keep. For a two-gas mixture, PV = nRT gives the total moles and the total mass gives a weighted sum. Solve the two together. Always convert cm³ to m³ first.

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