State Avogadro's hypothesis. Derive the relationship between relative molecular mass and vapour density, and give two other applications of the hypothesis.

1. 1 · State the hypothesis. Equal volumes of all gases under the same conditions of temperature and pressure contain equal numbers of molecules.
2. 2 · Define vapour density. VD = mass of a volume of gas ÷ mass of the same volume of hydrogen, at the same temperature and pressure.
3. 3 · Derive the relation.
   • Let the volume hold n molecules; the same volume of hydrogen also holds n molecules.
   • VD = mass of 1 molecule of gas ÷ mass of 1 molecule of H₂
   • Mass of 1 molecule of H₂ = 2 × mass of 1 H atom
   • VD = RMM ÷ 2, so RMM = 2 × VD
4. 4 · Draw the volume diagram. [Boxes: 1 vol H₂ + 1 vol Cl₂ → 2 vol HCl, with n, n and 2n molecules written inside]
5. 5 · Two more applications.
   • It shows hydrogen and chlorine are diatomic (atomicity).
   • It gives the molar volume: 1 mole of any gas = 22.4 L at STP.
6. 6 · Real-life link. A balloon grows as you add air, because more molecules need more volume at the same temperature and pressure.
7. 7 · Close in one line. Hence relative molecular mass is twice the vapour density.

Scoring tip: Write each line of the derivation as a separate step and box the final relation RMM = 2 × VD.