Dalton's atomic theory

Before 1808, "atom" was a Greek philosopher's guess, not a scientific idea anyone could test. John Dalton changed that. Working from measured masses of elements combining in chemical reactions, he proposed that matter is made of indivisible atoms, that every atom of a given element is identical, and that atoms combine in fixed small-whole-number ratios to form compounds. The genius of the theory was not the idea of atoms itself — that it explained, in one stroke, every quantitative law of chemical combination chemists had already measured: conservation of mass, definite proportions, and multiple proportions. Dalton's atomic theory is the hinge on which qualitative chemistry became quantitative chemistry. Some of its five postulates were later modified by the discovery of subatomic particles and isotopes, but its central claim — that reactions rearrange a fixed set of atoms in whole-number ratios — remains the working foundation of chemistry today.

The core insight

Dalton's atomic theory explains the laws of chemical combination by proposing that matter consists of indivisible, element-specific atoms that combine and rearrange in fixed small-whole-number ratios, never being created or destroyed.

The core idea

The five postulates. Dalton's theory rests on five statements about matter:

Matter is made of extremely small, indivisible particles called atoms.
Atoms of a given element are identical to each other in mass and properties; atoms of different elements differ in mass and properties.
Atoms combine with each other in simple whole-number ratios to form compounds.
Atoms are neither created nor destroyed in a chemical reaction — a reaction only rearranges existing atoms into new combinations.
The relative number and kind of atoms in a given compound is always the same, fixed ratio.

Why these postulates were needed. By 1800, chemists had already measured three quantitative regularities in how elements combine, purely from laboratory weighing, with no idea why they held. Dalton's postulates are best understood as the minimal particle picture that explains all three at once. The law of conservation of mass says the total mass of reactants equals the total mass of products in a closed chemical reaction:

m_{\text{reactants}} = m_{\text{products}}

where: $m_{\text{reactants}}$ is the total starting mass and $m_{\text{products}}$ is the total mass of everything formed. Postulate 4 explains this directly — if atoms are only rearranged and none is created or lost, the mass they carry cannot change either. The law of definite proportions says a given compound always contains the same elements in the same fixed mass ratio, however it is prepared. Postulates 2 and 5 explain this: a compound is a fixed ratio of atoms, and every atom of an element has the same fixed mass, so the mass ratio is forced to be fixed too. The law of multiple proportions says that when two elements A and B form more than one compound, the different masses of B that combine with a fixed mass of A stand in a ratio of small whole numbers. Postulate 3 explains this: if compounds are built from small-whole-number atom ratios, then for a fixed number of A atoms the possible numbers of B atoms are small whole numbers too, and since every B atom has the same mass, the mass ratios inherit that same small-whole-number pattern.

Figure

Three atoms of element A each paired with either one or two atoms of element B forming two different compounds in a two to one mass ratio

Modifications needed later. The discovery of the electron, proton and neutron showed atoms are not indivisible after all. Isotopes — atoms of the same element with different neutron counts and hence different mass — showed postulate 2 is not strictly true. Nuclear reactions showed atoms can, in fact, be transformed. None of this erases Dalton's achievement: for ordinary chemical reactions, atoms behave exactly as his postulates describe.

Derivation ADeriving the law of multiple proportions from Dalton's postulates

The goal is to show, starting only from postulate 3 (atoms combine in simple whole-number ratios) and postulate 2 (all atoms of one element have identical mass), that when two elements form two different compounds the masses of the second element that combine with a fixed mass of the first must stand in a ratio of small whole numbers — this is exactly the law of multiple proportions that chemists had measured before Dalton had any particle explanation for it.

Step 1. Fix a mass $m_A$ of element A, built from $n_A$ identical atoms of mass $m_a$ each, so $m_A = n_A m_a$ . Since we are comparing two compounds for the same mass of A, $n_A$ and $m_a$ are held constant throughout.

Step 2. In compound 1, postulate 3 says each A atom combines with a small whole number $p$ of B atoms, so the total B atoms present are $n_A p$ , and the mass of B is $m_{B,1} = n_A p\, m_b$ , where $m_b$ is the identical mass of one B atom (postulate 2).

Step 3. In compound 2, the same fixed number of A atoms combines with a different small whole number $q$ of B atoms per A atom, giving $m_{B,2} = n_A q\, m_b$ .

Step 4. Take the ratio of the two masses of B. The common factors $n_A$ and $m_b$ cancel exactly:

\frac{m_{B,2}}{m_{B,1}} = \frac{n_A q\, m_b}{n_A p\, m_b} = \frac{q}{p}

Since $p$ and $q$ are small whole numbers (postulate 3), their ratio $q:p$ is a ratio of small whole numbers — which is precisely the law of multiple proportions. The law that chemists discovered empirically by weighing compounds is thus a direct, unavoidable consequence of Dalton's atomic postulates. Check: with $p = 1$ and $q = 2$ this gives $m_{B,2}/m_{B,1} = 2$ , matching the carbon–oxygen result worked below.

Worked example

Carbon and oxygen form two compounds: carbon monoxide ( $\text{CO}$ ) and carbon dioxide ( $\text{CO}_2$ ). In $\text{CO}$ , $12\ \text{g}$ of carbon combines with $16\ \text{g}$ of oxygen. In $\text{CO}_2$ , the same $12\ \text{g}$ of carbon combines with $32\ \text{g}$ of oxygen. Verify the law of multiple proportions and explain the result using Dalton's postulates.

Step 1. Fix the mass of carbon at $12\ \text{g}$ in both compounds, so any difference in oxygen mass is due purely to how many oxygen atoms combine per carbon atom.

Step 2. Read off the oxygen masses: in $\text{CO}$ , oxygen $= 16\ \text{g}$ ; in $\text{CO}_2$ , oxygen $= 32\ \text{g}$ .

Step 3. Form the ratio of oxygen masses:

\frac{\text{mass of O in CO}_2}{\text{mass of O in CO}} = \frac{32}{16} = 2 : 1

This is a simple whole-number ratio, confirming the law of multiple proportions experimentally.

Step 4. Explain with the derivation above. In $\text{CO}$ , one carbon atom combines with one oxygen atom ( $p = 1$ ); in $\text{CO}_2$ , one carbon atom combines with two oxygen atoms ( $q = 2$ ). By the derivation, the mass ratio must equal $q/p = 2/1 = 2$ — exactly the $2:1$ ratio measured. The measured 2:1 mass ratio of oxygen matches the 1:2 atom ratio predicted by Dalton's postulates.

Competitive stretch

Nitrogen and oxygen form $\text{N}_2\text{O}$ , $\text{NO}$ and $\text{NO}_2$ . For a fixed mass of nitrogen, the oxygen masses are in the ratio $1 : 2 : 4$ across the three compounds. Using the same reasoning, this corresponds to $p : q : r = 1 : 2 : 4$ oxygen atoms per two nitrogen atoms (i.e. $\text{N}_2\text{O}$ , $\text{N}_2\text{O}_2 \equiv 2\times\text{NO}$ , $\text{N}_2\text{O}_4 \equiv 2\times\text{NO}_2$ ) — a direct extension of the same whole-number logic to three compounds instead of two.

Common traps

Saying atoms are "indivisible" without noting this was later revised by the discovery of subatomic particles — a frequent exam deduction.
Confusing "atoms of the same element are identical" with the existence of isotopes, which showed this postulate needs modification.
Mixing up which postulate explains which law: conservation of mass comes from postulate 4 (atoms conserved), definite proportions from postulates 2 and 5 (fixed atomic ratio, identical atomic mass), and multiple proportions from postulate 3 (whole-number combining ratios).
Forgetting Dalton's theory applies only to chemical reactions — it cannot explain nuclear reactions, where one element transforms into another.

Ask the tutor: want to work through why isotopes specifically challenge postulate 2, or see the multiple-proportions derivation applied to a three-compound example step by step?

If atoms are not actually indivisible, is Dalton's theory wrong

Not wrong so much as incomplete for a scale Dalton had no way to probe. For every ordinary chemical reaction — the scope Dalton's theory was built to explain — atoms genuinely do behave as the smallest unchanged unit, only rearranging into new bonds. The discovery of electrons, protons and neutrons revised postulate 1 but did not undo the reasoning that explains conservation of mass, definite proportions, or multiple proportions; those explanations still hold using atoms as the relevant unit for chemistry.

How exactly does the theory explain the law of definite proportions

A compound like water always has the same fixed ratio of hydrogen atoms to oxygen atoms, however it is made — that is postulate 5. Postulate 2 adds that every hydrogen atom has the same mass and every oxygen atom has the same mass. Multiply a fixed atom ratio by fixed atomic masses and you get a fixed mass ratio, no matter how much water you make or how you make it. That is the law of definite proportions, derived rather than assumed.

Why does the law of multiple proportions need two different compounds to test it

Because the whole-number pattern only shows up in a comparison. A single compound just has one fixed mass ratio, which by itself proves nothing about whole numbers. It is only when you fix the mass of one element and look at how the mass of the other element changes across two or more compounds of the same pair of elements that the small-whole-number ratio appears — exactly as carbon monoxide and carbon dioxide show a 1:2 ratio of oxygen atoms turning into a 1:2 ratio of oxygen masses.

Dalton's atomic theory

The core idea

Worked example

Competitive stretch

Common traps

Before this

Where this leads