Law of Definite Proportions

Introduction

Pure water collected from different sources has the same hydrogen-to-oxygen atom ratio in H₂O and, using ordinary atomic masses, the same characteristic elemental mass ratio. That fixed composition distinguishes a pure compound from a mixture such as salt water, whose amount of dissolved salt can vary.

Core explanation

The law of definite proportions states that a given pure compound has a fixed composition by mass. For H₂O, two hydrogen atoms contribute about 2 mass units and one oxygen atom about 16, giving H:O mass ratio 2:16 = 1:8. A 9.0 g sample of pure water therefore contains about 1.0 g hydrogen and 8.0 g oxygen by elemental mass accounting. A 90 g sample contains ten times each mass but the same ratio.

The law is about a particular compound , not all compounds containing the same elements. Hydrogen peroxide, H₂O₂, has a different H:O ratio. Water and hydrogen peroxide are distinct substances even though both contain H and O. A mixture of water with dissolved salt has variable sodium and chlorine contributions depending on how much salt is added; it is not a new fixed-formula compound.

To test the law with analytical data, compare mass ratios on a common basis. If one sample has 2.0 g H and 16.0 g O, O/H = 8.0. Another has 0.50 g H and 4.0 g O, O/H = 8.0. These are consistent with the same approximate elemental mass ratio. If a purported sample differs, check purity, measurement uncertainty and whether it is actually the same compound before rejecting the chemical principle.

Formula-based ratios rely on relative atomic masses, which are weighted averages for natural isotopic mixtures. Unusual isotope enrichment can make a mass ratio vary slightly even for the same atom-count formula. At this level, the law describes ordinary pure samples with comparable isotopic composition; isotope effects are a refinement, not a reason to treat ordinary compounds as arbitrary mixtures.

The law helped motivate atomic theories because fixed small whole-number atom ratios naturally produce reproducible mass ratios. However, a mass ratio alone may not uniquely identify a compound; two different substances can coincidentally share a ratio or have the same empirical formula. Additional evidence is needed for identity and structure.

Step-by-step reasoning

1. Identify the named pure compound and its formula. 2. Multiply each element's atomic mass by its subscript. 3. Compare those contributions as a mass ratio. 4. Scale the ratio to the measured sample mass. 5. Check whether a sample is pure and whether isotope composition matters.

Visual explanation

Draw several H₂O molecules, each with two small H spheres and one larger O sphere. Under them place equal-size mass bars in a 1:8 H:O proportion. Show a larger sample with more molecules but the same bars' ratio.

Real-world analogy

Every correctly assembled kit contains two bolts and one bracket, so the mass proportion is fixed for that kit type even if the number of kits changes. A mixture of loose parts could have variable proportions.

Real-world example

An analyst may compare elemental percentages of a purified substance with a proposed molecular formula. Agreement supports the formula's composition, though it does not prove molecular structure by itself.

Why?

Why does doubling a pure compound sample not change its elemental ratio? Every added formula unit contributes the same count of each element, so both elemental masses scale together.

Common misconception

“Any two elements always combine in one fixed mass ratio.” The ratio is fixed for one particular compound; the same elements can form several compounds with different formulas.

Worked example

For CO₂, carbon contributes about 12 g per mole of molecules and oxygen contributes 2 × 16 = 32 g. C:O mass ratio is 12:32 = 3:8. In 44 g pure CO₂, 12 g is carbon and 32 g oxygen. A 22 g sample has 6 g carbon and 16 g oxygen, preserving 3:8.

Quick check

1. Does a salt-water mixture obey one fixed salt-to-water mass ratio? Answer: No. Salt amount can vary across mixtures; a fixed elemental ratio applies to a particular pure compound.

Exam focus

Use the compound's exact formula and compare same element order in every ratio. Do not confuse formula composition with a mixture recipe.

Advanced insight

Some nonstoichiometric solids have composition ranges rather than a single ideal ratio. The simple law is most directly applied to well-defined stoichiometric pure compounds in introductory chemistry.

Summary

A given pure compound has a characteristic elemental mass ratio because its formula fixes atom counts. Sample size changes masses but not the ratio. Mixtures and different compounds need not share that composition.

Practice questions

1. Find H:O mass ratio in H₂O using H = 1 and O = 16. Answer: Two H atoms contribute 2 and one O contributes 16, so H:O is 1:8. 2. How much oxygen is in 18 g pure water under this approximation? Answer: Oxygen is 8/9 of water mass, so 18 × 8/9 = 16 g. 3. Why can H₂O₂ have a different elemental ratio from H₂O? Answer: It is a different compound with two oxygen atoms per two hydrogen atoms rather than one oxygen atom per two hydrogen atoms.