Law of Definite Proportions

The Law of Definite Proportions, also known as Proust's Law, states that a pure chemical compound always contains the same elements combined in the same fixed ratio by mass, regardless of the source of the compound or the method by which it was prepared. For example, water (H₂O) is always composed of hydrogen and oxygen in a mass ratio of approximately 1:8, whether it comes from a river, is synthesized in a laboratory, or is extracted from a mineral. This invariance is one of the most foundational principles in chemistry. This law was first formulated by the French chemist Joseph Louis Proust between 1794 and 1804, based on careful quantitative experiments on metal carbonates and oxides. Proust's work was a direct challenge to the views of his contemporary Claude Louis Berthollet, who believed that compounds could exist in variable proportions. After years of systematic experimentation, the scientific community accepted Proust's position, and the law became a cornerstone of modern chemistry. Understanding the Law of Definite Proportions is essential for grasping how atoms combine to form molecules. Because atoms of a given element have a fixed mass and form bonds in specific integer ratios (as described by atomic theory), any pure sample of a compound will always have the same elemental mass percentages. This law, together with the Law of Conservation of Mass and the Law of Multiple Proportions, forms the foundation of stoichiometry and quantitative chemical analysis.

Key takeaways
  • What 'Definite Proportion' Means
  • Calculating Mass Percentages
  • Verifying the Law Experimentally
  • The Atomic Basis of the Law
  • Distinction from the Law of Multiple Proportions

What 'Definite Proportion' Means

Every molecule of a pure compound is made of the same types and numbers of atoms bonded together. Because each atom has a definite atomic mass, the ratio of the masses of the constituent elements is always constant. For water (\ce{H2O}), each molecule contains 2 hydrogen atoms (each ~1.008 u) and 1 oxygen atom (~16.00 u), giving a mass ratio of H:O = 2.016:16.00 ≈ 1:7.94 by mass.

Calculating Mass Percentages

To find the percentage composition of a compound, divide the total mass of each element in one mole of the compound by the molar mass of the compound, then multiply by 100. For \ce{H2O}: Molar mass = 2(1.008) + 16.00 = 18.016 g/mol. % H = (2.016/18.016) × 100 ≈ 11.19%. % O = (16.00/18.016) × 100 ≈ 88.81%. These percentages are identical for any pure sample of water anywhere in the universe.

Verifying the Law Experimentally

Suppose you decompose two samples of water — one 36.0 g, the other 9.0 g — by electrolysis. The first yields 4.02 g of H and 31.98 g of O; the second yields 1.005 g of H and 7.995 g of O. Check the ratios: 4.02/31.98 ≈ 0.1257 and 1.005/7.995 ≈ 0.1257. Both samples give the same H:O mass ratio, confirming the law.

The Atomic Basis of the Law

Dalton's atomic theory (1808) provided the molecular explanation: if all atoms of an element are identical in mass, and molecules are formed by combining fixed numbers of atoms, the mass ratio must be constant. For \ce{CO2}, carbon and oxygen always combine in the mass ratio 12:32 = 3:8. No matter how large or small the sample, 3 parts by mass of carbon are always paired with 8 parts by mass of oxygen.

Distinction from the Law of Multiple Proportions

It is important not to confuse Proust's law with the Law of Multiple Proportions. Proust's law applies to a single pure compound and states its composition is fixed. The Law of Multiple Proportions applies when two elements form more than one compound (e.g., CO and \ce{CO2}): the masses of one element that combine with a fixed mass of the other are in small whole-number ratios (16:32 = 1:2). Both laws together supported the development of atomic theory.

The Key Equation

Mass Percentage of Element=Mass of Element in 1 mol of CompoundMolar Mass of Compound×100\text{Mass Percentage of Element} = \frac{\text{Mass of Element in 1 mol of Compound}}{\text{Molar Mass of Compound}} \times 100
  • m_{\text{element}} — Mass of element per mole of compound (g/mol): The total mass contributed by all atoms of one element in one formula unit of the compound, calculated as atomic mass × number of atoms of that element.
  • M_{\text{compound}} — Molar mass of compound (g/mol): The sum of the atomic masses of all atoms in one formula unit of the compound; equals the mass of one mole of the substance.
  • \% — Mass percentage (% (dimensionless)): The fraction by mass of the element in the compound, expressed as a percentage. This value is constant for a given pure compound regardless of sample size or origin.

Worked Example

Problem. A student decomposes two separate samples of copper(II) oxide (\ce{CuO}). Sample A (7.96 g) yields 6.36 g of copper and 1.60 g of oxygen. Sample B (3.98 g) yields 3.18 g of copper and 0.80 g of oxygen. (a) Calculate the Cu:O mass ratio for each sample. (b) Calculate the percentage of copper in \ce{CuO} using the molar masses Cu = 63.55 g/mol, O = 16.00 g/mol. (c) Do these results confirm the Law of Definite Proportions?

mCumO=63.5516.00≈3.97⇒% Cu=63.5579.55×100≈79.9%\frac{m_{\text{Cu}}}{m_{\text{O}}} = \frac{63.55}{16.00} \approx 3.97 \quad \Rightarrow \quad \%\,\text{Cu} = \frac{63.55}{79.55} \times 100 \approx 79.9\%

Answer. The Cu:O mass ratio in both samples is approximately 3.97:1, and copper constitutes about 79.9% of CuO by mass. Both samples give identical ratios, confirming the Law of Definite Proportions.

Figure
Diagram
Law of Definite Proportions: Water (H₂O)Two samples, same fixed H:O mass ratioSample A: 18.0 g of H₂OOHHH: 2.016 g → 11.19%O: 16.00 g → 88.81%H:O = 1 : 7.94Sample B: 36.0 g of H₂OOHHH: 4.032 g → 11.19%O: 32.00 g → 88.81%H:O = 1 : 7.94SAMERATIORegardless of sample size or source:Mass % H = 11.19% | Mass % O = 88.81%
Origins · 1 minJoseph Louis Proust and how this was discovered
JL
Joseph Louis Proust
1754–1826 · French

Proust conducted meticulous quantitative experiments on copper carbonate, iron sulfides, and other compounds between 1794 and 1804. He demonstrated that regardless of how a compound was made or where it was obtained, the ratio of its constituent elements by mass was always the same. This became known as the Law of Definite Proportions or Proust's Law, and it was a critical step toward Dalton's atomic theory. Proust spent years in a public scientific debate with Claude Louis Berthollet, who insisted that compounds could have variable compositions. Proust ultimately won the argument through sheer experimental evidence — he repeated and documented hundreds of careful analyses to prove his point, making his work one of the earliest triumphs of evidence-based chemistry.

  • Law of Conservation of Mass — Proust's law and the Law of Conservation of Mass together form the quantitative backbone of chemical reactions; conservation of mass ensures that the total mass of reactants equals products, while definite proportions ensure fixed elemental ratios within each compound.
  • Law of Multiple Proportions — Dalton's Law of Multiple Proportions extends the idea of fixed ratios: when two elements form more than one compound, the masses of one element combining with a fixed mass of the other are in small whole-number ratios, which was evidence for discrete atoms.
  • Dalton's Atomic Theory — Dalton's atomic theory (1808) provided the molecular explanation for the Law of Definite Proportions: because atoms have fixed masses and combine in integer ratios, the mass ratio of elements in a compound must always be constant.
  • Molar Mass and Percentage Composition — Calculating percentage composition by mass is a direct application of the Law of Definite Proportions, using molar masses of elements and compounds to determine fixed elemental percentages.
  • Empirical and Molecular Formulas — The fixed mass ratios guaranteed by the Law of Definite Proportions are used to derive empirical formulas from experimental data — chemists measure elemental percentages and convert them to the simplest whole-number atom ratios.