The Law of Constant Composition

Introduction

Water collected from a glacier, water produced in a car engine and water made by burning hydrogen in a laboratory all look and behave the same. Careful analysis shows something even more remarkable: in every sample, the mass of oxygen is always about eight times the mass of hydrogen. This regularity is called the law of constant composition , also known as the law of definite proportions. It was one of the first great clues that matter is made of atoms.

Core explanation

Statement of the law. A given compound always contains the same elements combined in the same proportions by mass, no matter where it comes from or how it was made.

History. Around 1799, the French chemist Joseph Proust analysed samples of copper carbonate, some made in the laboratory and some found in nature. He found that every sample had the same percentage of copper, carbon and oxygen. Another chemist, Claude-Louis Berthollet, argued that compositions could vary, but Proust's careful measurements won the debate.

Examples of fixed mass ratios.

Compound Formula Mass ratio of elements --- --- --- Water H₂O hydrogen : oxygen = 1 : 8 Carbon dioxide CO₂ carbon : oxygen = 3 : 8 Magnesium oxide MgO magnesium : oxygen = 3 : 2 Iron(II) sulfide FeS iron : sulfur = 7 : 4

Using the ratio. Because the ratio is fixed, you can predict the mass of each element in any sample. In water, every 9 g contains 1 g of hydrogen and 8 g of oxygen. So 18 g of water contains 2 g of hydrogen and 16 g of oxygen, and 90 g of water contains 10 g of hydrogen and 80 g of oxygen.

Excess reactants. If you try to make a compound using the "wrong" proportions, the extra amount of one element is simply left over. For example, if 10 g of iron is heated with 4 g of sulfur, only 7 g of iron can react with the 4 g of sulfur; 3 g of iron remains unreacted.

Contrast with mixtures. This law is a key difference between compounds and mixtures. A mixture of iron and sulfur can have any proportions, but iron(II) sulfide always has the 7 : 4 ratio.

Explanation using atoms. In a compound, atoms combine in fixed whole-number ratios: in water, always two hydrogen atoms to one oxygen atom. Each kind of atom has its own fixed mass, so a fixed number ratio of atoms must give a fixed mass ratio.

Formulae

Mass of element in a sample = (mass of sample) × (parts of that element ÷ total parts in the ratio). Percentage by mass = (mass of element ÷ mass of compound) × 100.

Step-by-step reasoning

To find the mass of an element in a sample of a compound:

1. Write down the mass ratio of the elements. 2. Add the parts together to find the total number of parts. 3. Divide the mass of the sample by the total parts to find the mass of one part. 4. Multiply by the number of parts for the element you want.

Visual explanation

Picture a pile of water molecules, each drawn as one large red oxygen circle with two small white hydrogen circles attached. However large or small the pile, every molecule is identical, so the fraction of the mass that is oxygen stays the same. Doubling the pile doubles both the hydrogen and the oxygen.

Real-world analogy

A bicycle always has two wheels and one frame. A factory making 100 bicycles needs exactly 200 wheels and 100 frames. If it receives 250 wheels, 50 are left over. Compounds work the same way: the "recipe" at the level of atoms is fixed, so the proportions by mass are fixed too.

Real-world example

Pharmaceutical companies test every batch of a medicine to check that it has exactly the expected percentage of each element. A batch with a different composition must contain an impurity or a different compound, so the law of constant composition is used every day as a quality check.

Why?

Why was this law so important historically? It suggested that elements combine in definite units rather than in any amount, like a continuous fluid. John Dalton used this idea to support his atomic theory in the early 1800s: if matter is made of atoms that combine in whole numbers, a fixed composition is exactly what you would expect.

Common misconception

"A mass ratio of 1 : 8 in water means there is one hydrogen atom for every eight oxygen atoms." The ratio is by mass, not by number of atoms. Water has two hydrogen atoms for every oxygen atom, but an oxygen atom is about sixteen times heavier than a hydrogen atom, giving a mass ratio of 2 : 16, or 1 : 8.

Worked example

Question: Carbon dioxide contains carbon and oxygen in the mass ratio 3 : 8. What mass of carbon is present in 44 g of carbon dioxide, and what is the percentage by mass of carbon?

Reasoning: Total parts = 3 + 8 = 11. One part = 44 ÷ 11 = 4 g. Carbon = 3 × 4 = 12 g. Percentage of carbon = (12 ÷ 44) × 100 = 27.3%.

Answer: 12 g of carbon; 27.3% carbon by mass.

Quick check

1. What mass of oxygen is present in 27 g of water, given that hydrogen : oxygen = 1 : 8 by mass? Answer: 27 ÷ 9 = 3 g per part, so oxygen = 8 × 3 = 24 g.

Exam focus

State the law precisely, including the words "same elements" and "same proportions by mass". In calculations, always add the parts of the ratio first. You may be given data from two samples and asked to show they are the same compound: calculate the ratio or percentage for each and show they match.

Advanced insight

A few solid compounds do not quite obey the law. Iron(II) oxide, for example, usually has slightly fewer iron atoms than oxygen atoms because some positions in its crystal are empty, so its formula is closer to Fe₀.₉₅O. Such substances are called non-stoichiometric compounds. They are exceptions that arise from defects in crystal structures, and for molecular compounds such as water the law holds exactly.

Summary

The law of constant composition states that a compound always contains the same elements in the same proportions by mass, however it is made. Water is always 1 : 8 hydrogen to oxygen by mass, and carbon dioxide 3 : 8 carbon to oxygen. The law arises because atoms combine in fixed whole-number ratios and each atom has a fixed mass. It lets us calculate the mass of each element in any sample.

Practice questions

1. State the law of constant composition. Answer: A given compound always contains the same elements combined in the same proportions by mass, however it is made. 2. Magnesium oxide contains magnesium and oxygen in the mass ratio 3 : 2. What mass of magnesium is in 20 g of magnesium oxide? Answer: Total parts 5; one part = 4 g; magnesium = 3 × 4 = 12 g. 3. Sample A of a compound contains 2.0 g of copper and 0.5 g of oxygen. Sample B contains 4.0 g of copper and 1.0 g of oxygen. Could they be the same compound? Explain. Answer: Yes; both have a copper : oxygen mass ratio of 4 : 1, so their composition is the same. 4. 14 g of iron is heated with 4 g of sulfur. Using the ratio iron : sulfur = 7 : 4, what mass of iron is left unreacted? Answer: 4 g of sulfur reacts with 7 g of iron, so 14 − 7 = 7 g of iron is left over.