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Avogadro's law is easy to state: equal volumes of gases, at the same temperature and pressure, contain equal numbers of molecules. Yet when Amedeo Avogadro published it in 1811, almost nobody used it for half a century. The reasons say a lot about how science works, and his own paper contains a calculation you can redo in five minutes. This post covers both.
What problem was Avogadro trying to solve?
In 1808 Joseph Louis Gay-Lussac showed that reacting gases combine in simple whole-number ratios by volume. Two volumes of hydrogen and one of oxygen give two volumes of water vapour. The Science History Institute biography of Avogadro explains why this bothered John Dalton, who rejected Gay-Lussac's work. If oxygen were made of single atoms, one volume of oxygen could not make two volumes of water vapour without the atoms splitting.
What did the 1811 paper say?
Avogadro's paper appeared in the Journal de Physique in 1811. In the Alembic Club English translation, his central claim reads: "the number of integral molecules in any gases is always the same for equal volumes, or always proportional to the volumes."
His second move solved Dalton's puzzle. He argued that a gas such as oxygen is made of molecules that can divide. Looking at water, ammonia and the oxides of nitrogen, he concluded that "there must be a division of the molecule into two". In modern terms, hydrogen and oxygen are diatomic: 2H₂ + O₂ → 2H₂O, so two volumes plus one volume give two volumes.
He did not use the word atom the way we do. As the Science History Institute notes, he spoke of several kinds of "molecules", including an "elementary molecule", which we would call an atom.
Worked example: Avogadro's own calculation
If equal volumes hold equal numbers of molecules, the ratio of gas densities equals the ratio of molecular masses. Avogadro used densities measured relative to air: oxygen 1.10359 and hydrogen 0.07321.
Oxygen : hydrogen = 1.10359 / 0.07321 = 15.074.
His paper gives exactly this: the oxygen molecule is "about 15 times that of the molecule of hydrogen, or, more exactly as 15.074 to 1".
For nitrogen he used 0.96913 / 0.07321 = 13.238.
Today, O₂ : H₂ = 32.00 / 2.016 = 15.87 and N₂ : H₂ = 28.01 / 2.016 = 13.89. His method was correct; the density measurements of 1811 were off by about 5%.
The modern version. One mole of any ideal gas occupies the same volume at the same temperature and pressure. NCERT Class 11 Chemistry uses 22.7 L per mole at 273.15 K and 1 bar. So 11.35 L of any gas at those conditions holds half a mole, which is 0.5 × 6.022 × 10²³ = 3.01 × 10²³ molecules.
Common mistakes:
Using 22.4 L with 1 bar. 22.4 L is the molar volume at 1 atm; at 1 bar it is 22.7 L. Use the value your textbook and question define.
Counting atoms instead of molecules. 1 mol of O₂ has 6.022 × 10²³ molecules but twice as many atoms.
Applying it to liquids or solids. The law is about gases, and only approximately for real gases.
Why was it ignored for about 50 years?
The Science History Institute points to two main reasons. First, the leading chemist Jöns Jakob Berzelius held that compounds were held together by attraction between positive and negative charges. On that view, two identical oxygen atoms could not bond, so an O₂ molecule seemed impossible. Second, Avogadro worked in Turin, far from the centres of chemistry in France, Germany, England and Sweden.
The turning point came at the first international chemistry congress, held at Karlsruhe in 1860. As NCERT Unit 1 describes, Stanislao Cannizzaro presented a course of chemical philosophy that stressed the importance of Avogadro's work. Avogadro had died in 1856.
Where does Avogadro's number come from?
Jean Perrin, who won the 1926 Nobel Prize in Physics for work on "the discontinuous structure of matter", set out the idea in his Nobel lecture: "The number N of the molecules constituting any gram-molecule is Avogadro's number." He noted that early estimates from the kinetic theory of gases ranged from 40 × 10²² to 120 × 10²². Today the value is fixed exactly at 6.02214076 × 10²³ per mole. The JEE (Main) 2026 syllabus lists Avogadro's number under kinetic theory of gases; check the current bulletin.
What can a student take from Avogadro's way of working?
Take the data at face value. Gay-Lussac's simple ratios were telling him something, and he found the hypothesis that explained them.
Clear words matter. Confusion between atoms and molecules kept his idea hidden for decades.
Being right is not enough. An idea also has to reach the right people, which Cannizzaro did for him.
If mole and gas-volume problems trip you up, the Fermi Problem Library has a step-by-step solver that explains the reasoning behind each conversion. For more practice, try our guide to ideal gas problems.
Try this now: how many molecules are in 4.54 L of carbon dioxide at 273.15 K and 1 bar, and how many oxygen atoms do they contain?
