Law of conservation of mass
In the 1780s Antoine Lavoisier weighed chemicals very carefully before and after reactions in closed vessels. He found:
Matter can be neither created nor destroyed in a chemical reaction. Total mass of reactants = total mass of products.
Example: 24 g magnesium + 16 g oxygen → 40 g magnesium oxide. If a burning candle seems to lose mass, that is only because gases escape into the air; in a closed jar the mass stays the same.
Law of definite proportions
Joseph Proust found that pure copper carbonate, whether made in the lab or dug from the ground, always had the same percentages of copper, carbon and oxygen.
A given compound always contains exactly the same elements in the same proportion by mass, whatever its source.
Water always has hydrogen : oxygen = 1 : 8 by mass. 9 g of water has 1 g H and 8 g O; 18 g has 2 g H and 16 g O.
Law of multiple proportions
John Dalton noticed that some pairs of elements form more than one compound.
If two elements form two or more compounds, the masses of one element that combine with a fixed mass of the other are in a ratio of small whole numbers.
- CO: 12 g C with 16 g O. CO₂: 12 g C with 32 g O. Ratio 16 : 32 = 1 : 2.
- H₂O: 2 g H with 16 g O. H₂O₂: 2 g H with 32 g O. Ratio 1 : 2.
How to check: fix the mass of one element in both compounds, then compare the other.
Gay-Lussac's law of gaseous volumes
Joseph Gay-Lussac worked with gases (1808).
When gases react or form, their volumes are in a simple whole-number ratio, provided all volumes are measured at the same temperature and pressure.
2 volumes hydrogen + 1 volume oxygen → 2 volumes steam (2 : 1 : 2). 1 volume H₂ + 1 volume Cl₂ → 2 volumes HCl (1 : 1 : 2). This law is about volumes; the law of definite proportions is about masses.
Avogadro's law
Amedeo Avogadro (1811) explained Gay-Lussac's ratios.
Equal volumes of all gases at the same temperature and pressure contain equal numbers of molecules.
So 2 L H₂ has twice as many molecules as 1 L O₂. He also said that gases like hydrogen and oxygen exist as molecules of two atoms (H₂, O₂). Then 2 H₂ + O₂ → 2 H₂O fits the 2 : 1 : 2 volume ratio exactly. He separated the ideas of atom and molecule, which Dalton had mixed up.
Dalton's atomic theory
In 1808 Dalton put forward his theory. Its main points:
- Matter is made of tiny, indivisible particles called atoms.
- All atoms of one element are alike, including in mass. Atoms of different elements differ in mass.
- Compounds form when atoms of different elements join in a fixed ratio of small whole numbers.
- Chemical reactions only rearrange atoms. Atoms are not created or destroyed.
How it explains the laws
Point 4 explains conservation of mass. Point 3 explains definite and multiple proportions.
Limitations
- It could not explain Gay-Lussac's law of gaseous volumes.
- It did not explain why atoms join, or the difference between atoms and molecules.
- We now know atoms can be divided (electrons, protons, neutrons) and that isotopes of one element have different masses.
Try it at home
Seal a little baking soda and vinegar inside a plastic bottle with a balloon over its mouth. Weigh it on a kitchen scale before and after the fizzing. The mass stays the same. Then try the slider in the 3D above.
Key formulas and definitions
- Total mass of reactants = total mass of products
- Mass ratio in a compound is fixed (water H : O = 1 : 8)
- Fixed mass of A → masses of B in a small whole-number ratio
- Gas volumes (same T, P) react in simple whole-number ratios
- Equal volumes (same T, P) ⇒ equal numbers of molecules: V ∝ n
Worked examples
1. 10 g of calcium carbonate is heated. It leaves 5.6 g of calcium oxide. What mass of carbon dioxide escaped?
Line 1: Mass is conserved: mass of CaCO₃ = mass of CaO + mass of CO₂. Line 2: 10 = 5.6 + m(CO₂). Line 3: m(CO₂) = 10 − 5.6 = 4.4 g.
2. 0.24 g of magnesium burns to give 0.40 g of magnesium oxide. A second sample of 1.2 g Mg gives 2.0 g oxide. Show that the data obey the law of definite proportions.
Line 1: Sample 1: O = 0.40 − 0.24 = 0.16 g. Mg : O = 0.24 : 0.16 = 3 : 2. Line 2: Sample 2: O = 2.0 − 1.2 = 0.8 g. Mg : O = 1.2 : 0.8 = 3 : 2. Line 3: Same ratio in both, so the law holds.
3. How much oxygen is needed to make 45 g of water? (H : O = 1 : 8 by mass)
Line 1: 1 + 8 = 9 parts make water. Line 2: Oxygen share = 8/9. Line 3: m(O) = 45 × 8/9 = 40 g (and H = 5 g).
4. Two oxides of nitrogen contain 63.6% N and 46.7% N by mass. Show that they obey the law of multiple proportions.
Line 1: Oxide 1: N 63.6 g, O 36.4 g. O per 1 g N = 36.4/63.6 = 0.572 g. Line 2: Oxide 2: N 46.7 g, O 53.3 g. O per 1 g N = 53.3/46.7 = 1.141 g. Line 3: Ratio 0.572 : 1.141 ≈ 1 : 2, small whole numbers. Law obeyed (these are N₂O and NO).
5. What volume of oxygen reacts with 60 mL of hydrogen to form steam, at the same T and P? What volume of steam forms?
Line 1: 2 H₂ + O₂ → 2 H₂O (volumes 2 : 1 : 2). Line 2: O₂ = 60 × 1/2 = 30 mL. Line 3: steam = 60 × 2/2 = 60 mL.
6. A flask of hydrogen and an equal flask of carbon dioxide are at the same T and P. The hydrogen flask holds 3 × 10²² molecules. How many molecules of CO₂ are in the other, and which flask is heavier?
Line 1: Avogadro: equal volumes, same T and P → equal molecules. Line 2: CO₂ flask also has 3 × 10²² molecules. Line 3: Each CO₂ (44 u) is much heavier than H₂ (2 u), so the CO₂ flask is 22 times heavier.
Common mistakes
- Thinking a burning candle breaks mass conservation. The gases formed escape; weigh in a closed jar.
- Mixing up definite proportions (one compound, fixed ratio) and multiple proportions (two compounds, compare with a fixed mass).
- Using Gay-Lussac's volume ratios for solids or liquids, or with volumes measured at different T and P.
- Saying equal volumes of gases have equal masses. They have equal numbers of molecules, not equal masses.