Law of Definite Proportions

Take a sample of pure water made in a laboratory by burning hydrogen in oxygen, and a sample of water drawn from a natural spring on the other side of the world. Analyse both, and something remarkable happens: the mass of oxygen combined with every gram of hydrogen is exactly the same in both samples. Different origin, different method, different total mass — identical ratio. This is the law of definite proportions (also called the law of constant composition), proposed by Joseph Proust from his careful analysis of compounds such as copper carbonate. It is the second of the classical laws of chemical combination in Unit I, "Some Basic Concepts of Chemistry," and it says something deep about matter well before atoms were understood: a compound is not a loose mixture with room for variation, it is a fixed recipe. This article states the law precisely, shows why it becomes the basis of percentage composition, walks through two fully worked numeric checks, and connects it to the mole-ratio language you will use once atomic masses enter the picture — the conceptual bridge to Dalton's atomic theory.

The core insight

A given chemical compound always contains its constituent elements combined in the same fixed ratio by mass, regardless of the source or method of preparation of the sample.

The core idea

The statement. For a compound made of elements X and Y, every pure sample — however it was made, wherever it came from — gives the same mass ratio between X and Y. This is what "constant composition" means: the ratio is a fixed property of the compound, not of any particular sample.

\frac{\text{mass of X}}{\text{mass of Y}} = \text{constant}

where: mass of X and mass of Y are the masses of the two elements found in any pure sample of the compound, and the constant is a fixed number characteristic of that compound alone — it does not depend on how much of the compound you have or where it came from.

Why "definite," not "equal." A common first misreading is to think the law means equal masses of each element are present. It does not — it means a fixed ratio, which is very often far from 1:1 (water's ratio of oxygen to hydrogen by mass is 8:1, not 1:1). What is fixed is the ratio itself, sample after sample.

Where it comes from historically. Proust reached this law by analysing copper carbonate obtained both from natural mineral deposits and from laboratory synthesis. In every sample, copper, carbon, and oxygen appeared in the same fixed mass ratio. This was a striking result at the time: it suggested that when elements combine to form a compound, nature is not sloppy — it follows a strict, reproducible recipe.

The bridge to percentage composition. Because the mass ratio between elements in a compound is fixed, the percentage of each element by mass is also fixed for that compound. This is exactly what lets a chemist take one sample's composition data and predict the composition of any other sample of the same substance — the calculation you will practice below.

Figure

Two samples of water from different sources both showing the same eight to one mass ratio of oxygen to hydrogen

Derivation AFinding an unknown mass from a known compound's fixed ratio

The goal is to show, with nothing beyond ratio and proportion, how the law of definite proportions turns one sample's measured composition into a predictive tool: given the fixed mass ratio of a compound from one analysed sample, the mass of one element in any other pure sample of that same compound can be calculated the instant the mass of the other element is known, because the ratio itself never changes.

Step 1. Fix the ratio from a known, fully analysed sample. Suppose a first sample of a compound made of elements X and Y is found to contain $m_{X,1}$ grams of X combined with $m_{Y,1}$ grams of Y. By the law of definite proportions, the ratio $r = m_{Y,1}/m_{X,1}$ is a fixed number for this compound — true of every pure sample, not just this one.

Step 2. Write the same ratio for a second, only partly known sample. A second pure sample of the identical compound contains a known mass $m_{X,2}$ of element X, but the mass of Y, call it $m_{Y,2}$ , has not been measured directly. Because the ratio is fixed by the law, this second sample must obey $m_{Y,2}/m_{X,2} = r$ as well.

Step 3. Solve for the unknown mass. Rearranging, $m_{Y,2} = r \times m_{X,2} = \dfrac{m_{Y,1}}{m_{X,1}} \times m_{X,2}$ . This is the general rule: multiply the known mass in the new sample by the fixed ratio carried over from the first sample.

Step 4. Read the result. This single algebraic step is exactly the tool used below to find an unknown mass of oxygen in carbon dioxide, and it is the same reasoning that defines percentage composition — once the ratio is fixed, everything about the compound's makeup follows from it, for a sample of any size.

Worked example

Problem. A first sample of carbon dioxide is analysed and found to contain $3.0\ \text{g}$ of carbon combined with $8.0\ \text{g}$ of oxygen. A second sample, confirmed by other tests to be pure $\text{CO}_2$ , contains $6.0\ \text{g}$ of carbon combined with an unmeasured mass $x$ of oxygen. Find $x$ using the law of definite proportions, then calculate the percentage of carbon by mass in $\text{CO}_2$ , and state what that percentage predicts for a third sample containing $9.0\ \text{g}$ of carbon.

Step 1. Fix the mass ratio from Sample 1. $\dfrac{\text{mass O}}{\text{mass C}} = \dfrac{8.0}{3.0}$ . This ratio is a property of $\text{CO}_2$ itself, so it must hold in every pure sample.

Step 2. Apply the same ratio to Sample 2. $\dfrac{x}{6.0} = \dfrac{8.0}{3.0}$ , so $x = 6.0 \times \dfrac{8.0}{3.0} = 16.0\ \text{g}$ of oxygen.

Step 3. Find the percentage composition. Total mass of Sample 2 is $6.0 + 16.0 = 22.0\ \text{g}$ , so $\%\text{C} = \dfrac{6.0}{22.0} \times 100 = 27.3\%$ .

Step 4. Extend to a third sample. Because $27.3\%$ carbon by mass is fixed for every pure sample of $\text{CO}_2$ , a third sample containing $9.0\ \text{g}$ of carbon must have a total mass of $9.0 / 0.273 = 33.0\ \text{g}$ , meaning $33.0 - 9.0 = 24.0\ \text{g}$ of oxygen — consistent with the same $8.0:3.0$ ratio, since $9.0 \times (8.0/3.0) = 24.0\ \text{g}$ . The unknown mass is $x = 16.0\ \text{g}$ of oxygen, carbon is $27.3\%$ by mass in $\text{CO}_2$ , and this percentage correctly predicts $24.0\ \text{g}$ of oxygen for the third sample.

Common traps

Confusing definite proportions with multiple proportions — this law concerns one compound always showing the same ratio; multiple proportions concerns two different compounds formed from the same two elements in different ratios.
Reading "same proportion" as "equal masses" — the fixed ratio is rarely 1:1 (water's O:H ratio is 8.0, not 1.0).
Applying the law to mixtures rather than compounds — mixtures such as alloys or solutions can have variable composition; only true compounds obey definite proportions.
Forgetting the law is stated in terms of mass ratios, even though it also implies a fixed mole ratio once atomic masses are brought in.

Ask the tutor: if you are unsure whether a mixed-up ratio problem is testing definite proportions or multiple proportions, ask the AI tutor to work both interpretations side by side with fresh numbers.

How is the law of definite proportions different from the law of conservation of mass?

They answer different questions. Conservation of mass says that in a chemical reaction, the total mass of reactants equals the total mass of products — nothing is created or destroyed. Definite proportions says something about the composition of one specific compound: whatever sample of it you analyse, the elements inside are combined in the same fixed mass ratio. One is about mass through a reaction; the other is about the fixed recipe of a substance.

Does the law of definite proportions apply to solutions like salt water?

No. Solutions and mixtures such as salt water, air, or alloys can have variable composition — you can dissolve a little salt or a lot in the same volume of water, and both are still "salt water." The law of definite proportions applies only to true chemical compounds, where the elements are chemically combined in a fixed way, not physically mixed in whatever amount you choose.

Why does the law of definite proportions matter for Dalton's atomic theory later in this unit?

Once atomic masses and the mole concept are available, a fixed mass ratio between elements translates directly into a fixed mole ratio of atoms, because mass and moles are linked by fixed atomic masses. A constant mole ratio is exactly what Dalton's atomic theory predicts if atoms combine in small whole-number ratios. So the law of definite proportions, discovered purely from mass measurements before atoms were understood, became one of the key pieces of evidence supporting the atomic theory that explained it.

Law of Definite Proportions

The core idea

Worked example

Common traps

Before this

Where this leads