Law of Constant Proportions

Fill a glass with river water, melt a block of Antarctic ice, or burn hydrogen in a school lab flask, and in every case the water you get is built the same way: hydrogen and oxygen locked together in exactly the mass ratio 1:8, never 1:7 and never 1:9. That stubborn fixedness is the Law of Constant Proportions — a given chemical compound always contains its elements in the same fixed mass ratio, regardless of where the sample came from or how it was prepared. Discovered by the French chemist Joseph Proust through painstaking mass measurements, the law sits alongside the Law of Conservation of Mass as one of the two pillars on which John Dalton built his atomic theory. This article compresses the statement into a usable rule, derives the scaling method examiners actually test, and works it through numbers you can check by hand.

The core insight

In any pure chemical compound the elements are combined in a fixed mass ratio that never changes with the compound's source or method of preparation.

The core idea

The statement. Also called the Law of Definite Proportions, it says: in a given chemical compound, the elements are always present in a fixed ratio by mass, no matter where the sample comes from or how it was made. Water is the textbook case — river water, glacier ice, and laboratory-synthesised water all give

\text{H} : \text{O} = 1 : 8 \quad \text{by mass}

where: the ratio is a mass comparison, not a count of atoms — of every 9 g of pure water, 1 g is hydrogen and 8 g is oxygen, always in that same 1-to-8 split.

Why it must be true. Proust reached this conclusion by weighing samples of the same compound prepared through completely different routes and finding the element ratio unchanged every time. Dalton then explained why: if a compound always forms from a fixed small whole-number ratio of atoms, and every atom of one element has the same fixed mass as every other atom of that element, the mass ratio of the elements in the compound has no room to wander — it must come out the same however the compound is made. Constant Proportions and Conservation of Mass together are the experimental floor beneath the whole atomic theory.

The general rule for numericals. If the fixed mass ratio $a:b$ between elements $X$ and $Y$ in a compound is known, then given the mass of $X$ in any fresh sample, the mass of $Y$ must scale in that same ratio — this single idea covers almost every question this topic asks.

Figure

Two water samples from different sources both split into the same one part hydrogen to eight parts oxygen by mass

Derivation AScaling an unknown mass using a fixed compound ratio

The goal is to take one known fixed mass ratio between two elements in a compound and turn it into a working formula that predicts the mass of one element the moment you are told the mass of the other, which is the exact skill every board numerical on this law is built to test.

Step 1. Write the known fixed ratio as a fraction. If elements $X$ and $Y$ combine in a compound with established mass ratio $a:b$ , write $\dfrac{\text{mass of } X}{\text{mass of } Y} = \dfrac{a}{b}$ . This fraction is a property of the compound itself and stays the same for every pure sample of it, by the Law of Constant Proportions.

Step 2. Substitute the known mass from the new sample. Suppose a fresh sample of the same compound is found to contain a mass $m_X$ of element $X$ . Since the ratio cannot change, $\dfrac{m_X}{m_Y} = \dfrac{a}{b}$ , where $m_Y$ is the unknown mass of $Y$ we want.

Step 3. Cross-multiply and solve for the unknown mass.

m_Y = \frac{m_X \times b}{a}

where: $m_X$ is the given mass of the known element, $a:b$ is the compound's fixed mass ratio in the order $X:Y$ , and $m_Y$ is the unknown mass produced.

Step 4. Sanity-check the direction. If $Y$ is the heavier partner in the ratio (larger second number), the computed $m_Y$ should come out larger than $m_X$ for a ratio like $1:8$ — that quick size check catches a flipped fraction before it becomes a wrong answer.

Worked example

Problem. Ammonia (NH $_3$ ) always contains nitrogen and hydrogen in the fixed mass ratio N : H = 14 : 3. A chemist decomposes a sample of ammonia and recovers 4.2 g of nitrogen. What mass of hydrogen must have been present in the original sample?

Step 1. Write the known fixed ratio as a proportion.

\frac{\text{mass of N}}{\text{mass of H}} = \frac{14}{3}

Step 2. Substitute the known mass of nitrogen.

\frac{4.2}{m_{\text{H}}} = \frac{14}{3}

Step 3. Solve for the mass of hydrogen using the scaling formula from the derivation, $m_Y = \dfrac{m_X \times b}{a}$ .

m_{\text{H}} = \frac{4.2 \times 3}{14} = \frac{12.6}{14} = 0.9\ \text{g}

Answer: the sample contained 0.9 g of hydrogen, exactly what the fixed 14:3 ratio predicts, however and wherever the ammonia was obtained.

Competitive stretch

A student wants to check whether a natural mineral sample of carbon dioxide obeys the law. The established laboratory ratio is C : O = 3 : 8 by mass. The mineral sample yields 6 g of carbon combined with 16 g of oxygen. Does it obey the law?

Step 1. Simplify the new sample's ratio: $6 : 16 = 3 : 8$ (dividing both terms by 2).

Step 2. Compare with the established ratio, $3:8$ . The two are identical, so the mineral sample does obey the Law of Constant Proportions — the same 3:8 mass ratio appears regardless of the compound's natural or laboratory origin.

Common traps

Confusing "constant proportions" with "conservation of mass." This law is about the ratio of elements within one compound; Conservation of Mass is about total mass before and after a reaction — two different laws entirely.
Mixing mass ratio with atom-count ratio. H:O = 1:8 by mass in water is not the 2:1 ratio of hydrogen atoms to oxygen atoms in H $_2$ O — one compares mass, the other compares particle count.
Applying the law to mixtures. It applies only to pure compounds. A mixture such as air or sugar dissolved in varying water can have any composition, so it simply does not obey this law.
Forgetting to simplify before comparing. Ratios like 6:16 and 3:8 look different until reduced to lowest terms — always simplify first, or you may wrongly conclude the law is violated.

Ask the tutor: Want to check whether a given compound's data obeys the law, or need help simplifying a mass ratio into an unknown-mass calculation — ask the AI tutor for a guided walk-through.

How is the Law of Constant Proportions different from the Law of Conservation of Mass?

Conservation of Mass says the total mass of reactants equals the total mass of products in a chemical reaction — nothing is created or destroyed. Constant Proportions is a different claim about a single compound: whatever its source, the elements inside it always combine in the same fixed mass ratio. One law is about mass before versus after a reaction; the other is about the internal recipe of one substance staying fixed. Both were needed to build Dalton's atomic theory, but they answer different questions.

Does the Law of Constant Proportions apply to mixtures like salt water or air?

No. Mixtures can be made in any proportion you like — a glass of salt water might be barely salty or very salty, and both are still called salt water. The law applies strictly to pure chemical compounds, where the elements are chemically bonded together in a fixed recipe fixed by nature, not by how much of each ingredient you chose to add. That fixed-recipe behaviour is precisely what separates a compound from a mixture in chemistry.

If I get a ratio like 9:24 instead of the expected 3:8, does that mean the law is wrong?

Almost certainly not — check your arithmetic first. Simplify 9:24 by dividing both numbers by their common factor, 3, giving 3:8, which matches the expected ratio exactly. Nearly every "the law seems violated" situation in a textbook numerical is actually an unsimplified ratio in disguise. Genuine violations do not happen for pure compounds; if your simplified ratio still disagrees, suspect impure samples or an arithmetic slip before doubting the law itself.

Law of Constant Proportions

The core idea

Worked example

Competitive stretch

Common traps

Before this

Where this leads