1. Gay-Lussac's law of combining volumes
Statement: when gases react, they do so in volumes that bear a simple whole-number ratio to one another and to the volumes of the gaseous products, all volumes being measured at the same temperature and pressure.
- The volume ratio equals the ratio of the coefficients of the gases in the balanced equation: N₂ + 3H₂ → 2NH₃ gives 1 : 3 : 2.
- Count gases only. Water formed at room temperature is a liquid; solids are ignored.
- If one gas is in excess, find the gas that is used up first; the unused excess is part of the gas left.
Method: balanced equation → volume ratio of the gases → multiply → add up the gases left (excess + gaseous products).
| Reaction | Volume ratio of gases |
|---|---|
| N₂ + 3H₂ → 2NH₃ | 1 : 3 : 2 |
| 2CO + O₂ → 2CO₂ | 2 : 1 : 2 |
| CH₄ + 2O₂ → CO₂ + 2H₂O (room temperature) | 1 : 2 : 1 (water not counted) |
Key terms
- Gay-Lussac's law
Reacting gases and gaseous products are in a simple whole-number ratio by volume, at the same temperature and pressure.
- Excess reactant
A reactant present in more than the amount needed; part of it remains after the reaction.
2. Avogadro's law and atomicity
Avogadro's law: equal volumes of all gases, at the same temperature and pressure, contain equal numbers of molecules.
- At fixed temperature and pressure: ratio of volumes = ratio of molecules = ratio of coefficients.
- Equal volumes of different gases have different masses, because their molecules have different masses.
Atomicity is the number of atoms in one molecule of an element. Hydrogen, oxygen, nitrogen and chlorine are diatomic (H₂, O₂, N₂, Cl₂). This follows from volume results. 1 volume of hydrogen + 1 volume of chlorine gives 2 volumes of hydrogen chloride, so each hydrogen molecule must split into two atoms. Similarly 1 volume of nitrogen + 1 volume of oxygen gives 2 volumes of nitrogen monoxide. (The formal proof is not examined.)
| Atomicity | Examples |
|---|---|
| 1 (monatomic) | He, Ne, Ar |
| 2 (diatomic) | H₂, O₂, N₂, Cl₂ |
| 3 (triatomic) | O₃ (ozone) |
| 4 (tetratomic) | P₄ |
Key terms
- Avogadro's law
Equal volumes of all gases at the same temperature and pressure contain equal numbers of molecules.
- Atomicity
The number of atoms in one molecule of an element.
3. The mole and Avogadro's number
Mole: the amount of a substance that contains as many particles (atoms, molecules or ions) as there are atoms in exactly 12 g of carbon-12.
Avogadro's number (use when the question says so).
- Number of particles = moles × .
- Number of atoms = number of molecules × atoms in one molecule (atomicity, or atoms in the formula).
| Sample | Moles | Particles |
|---|---|---|
| 12 g of carbon | 1 | 6.022 × 10²³ atoms |
| 36 g of water | 2 | 1.2044 × 10²⁴ molecules |
| 0.5 mol of oxygen gas | 0.5 | 3.011 × 10²³ molecules (6.022 × 10²³ atoms) |
Formulas
- Moles from number of particles
- Avogadro's number
Key terms
- Mole
The amount of substance containing as many particles as there are atoms in exactly 12 g of carbon-12.
- Avogadro's number
The number of particles in one mole, 6.022 × 10²³.
4. Gram atomic mass and gram molecular mass
| Term | Meaning | Example |
|---|---|---|
| Atomic mass | Mass of one atom relative to one-twelfth of a carbon-12 atom | Na = 23 u |
| Gram atomic mass | Atomic mass in grams; the mass of 1 mol of atoms | 23 g of sodium |
| Molecular mass | Sum of the atomic masses in one molecule | H₂O = 18 u |
| Gram molecular mass (molar mass) | Molecular mass in grams; the mass of 1 mol of molecules | 18 g of water |
Moles = mass ÷ molar mass. Always show the molar mass working, for example CaCO₃: 40 + 12 + 3 × 16 = 100 g.
| Compound | Working | Molar mass / g |
|---|---|---|
| H₂SO₄ | 2 × 1 + 32 + 4 × 16 | 98 |
| CaCO₃ | 40 + 12 + 3 × 16 | 100 |
| (NH₄)₂SO₄ | 2 × 14 + 8 × 1 + 32 + 4 × 16 | 132 |
Formulas
- Moles from mass (m in g, M in g mol⁻¹)
Key terms
- Gram atomic mass
The atomic mass of an element expressed in grams; the mass of one mole of its atoms.
- Gram molecular mass
The molecular mass of a substance expressed in grams; the mass of one mole of its molecules.
5. Molar volume at STP
Molar volume: one mole of any gas occupies 22.4 dm³ (22 400 cm³) at STP (273 K and 1 atm, that is 760 mm of mercury).
- 22.4 dm³ of a gas at STP weighs its gram molecular mass.
- Moles of gas = volume at STP in dm³ ÷ 22.4. Convert cm³ to dm³ first (divide by 1000).
- Molar volume applies to gases only. (Its derivation is not examined.)
| Gas | Mass | Moles | Volume at STP |
|---|---|---|---|
| Oxygen | 3.2 g | 0.1 | 2.24 dm³ |
| Carbon dioxide | 8.8 g | 0.2 | 4.48 dm³ |
| Ammonia | 1.7 g | 0.1 | 2.24 dm³ |
Formulas
- Moles of a gas from its volume at STP
Key terms
- Molar volume
The volume occupied by one mole of a gas: 22.4 dm³ at STP.
- STP
Standard temperature and pressure: 273 K (0 °C) and 1 atm (760 mm of mercury).
6. Vapour density
Vapour density (VD): the ratio of the mass of a certain volume of a gas to the mass of the same volume of hydrogen, at the same temperature and pressure.
- Relative molecular mass = 2 × vapour density (use the relation; its proof is not examined).
- Vapour density has no unit (a ratio of two masses).
- A gas with VD greater than about 14.4 (air) is heavier than air.
Typical chain: VD → M = 2 × VD → moles = mass ÷ M → volume = moles × 22.4 dm³.
| Gas | M | VD |
|---|---|---|
| Ammonia | 17 | 8.5 |
| Oxygen | 32 | 16 |
| Sulphur dioxide | 64 | 32 |
| Chlorine | 71 | 35.5 |
Formulas
- Relative molecular mass from vapour density
Key terms
- Vapour density
Mass of a volume of a gas divided by the mass of the same volume of hydrogen at the same temperature and pressure.
Exam tips
Common mistakes
- Counting liquid water as a gas volume in Gay-Lussac problems at room temperature.
- Forgetting to add the excess gas to the gas left at the end.
- Writing "equal numbers of atoms" in Avogadro's law; it is molecules.
- Dividing a volume in cm³ by 22.4 instead of 22 400.
- Giving the number of molecules when the question asks for atoms.
- Writing a unit for vapour density.
How marks are usually awarded
- Calculations: the molar mass working, the number of moles, then the final answer with its unit (one mark each in a 3-mark item).
- Laws (1 mark each): include "same temperature and pressure".
- Volume problems: the volume ratio from the balanced equation earns the first mark.