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Two volumes of hydrogen and one volume of oxygen give two volumes of water vapour, not three, as Fig. 1.9 of the NCERT Class 11 chemistry chapter shows. That simple fact puzzles many students, and it puzzled chemists too until Joseph Louis Gay-Lussac collected enough examples to see a law behind it. This post explains what he found, how to use it, and where students slip.
Who was Gay-Lussac?
The Science History Institute profile gives his dates as 1778 to 1850. He studied at the École Polytechnique in Paris, where his mentors included Laplace and Berthollet, and later taught physics and chemistry there. In 1804 he made balloon ascents of over 7,000 metres to measure magnetism, pressure, temperature and humidity and to collect air samples. With Louis Jacques Thénard he also helped discover boron.
What did he find about gases?
In 1808 he announced the result he is most remembered for, published in 1809 as the Memoir on the Combination of Gaseous Substances with Each Other. He began from a ratio he and Humboldt had measured: 100 volumes of oxygen to 200 of hydrogen in forming water. Suspecting other gases might also combine in simple ratios, he tested them. Hydrogen chloride (then "muriatic gas") combined with exactly its own volume of ammonia. He also collected results from others: ammonia from 100 volumes of nitrogen and 300 of hydrogen, and three oxides of nitrogen with nitrogen to oxygen ratios of 100 : 50, 100 : 100 and 100 : 200.
His conclusion, in the translated text, was that gases combine "in very simple ratios, so that representing one of the terms by unity, the other is 1, or 2, or at most 3." He added that such ratios are not observed "when we consider weights".
He also found that the shrinkage on combining follows a rule. For ammonia, he wrote, the contraction is "precisely half the total volume": four volumes of reactants become two of product.
How does this fit with atoms and molecules?
Gay-Lussac did not explain why volumes behave so neatly. The NCERT Class 11 chapter Some Basic Concepts of Chemistry presents his law, dated 1808, and then Avogadro's proposal that equal volumes of gases at the same temperature and pressure contain equal numbers of molecules. Read our post on Avogadro's hypothesis for how that idea turned volume ratios into molecule ratios.
Worked example: nitrogen and hydrogen
A vessel holds 10 mL of nitrogen and 24 mL of hydrogen at the same temperature and pressure. They react completely to make ammonia, N2 + 3H2 → 2NH3. What volume is left, and what is in it?
Find the limiting gas. 10 mL of N2 would need 30 mL of H2. Only 24 mL is present, so hydrogen runs out first.
Use the volume ratio. 24 mL of H2 reacts with 24 / 3 = 8 mL of N2 and makes 24 × 2/3 = 16 mL of NH3.
Add what is left. Leftover N2 = 10 − 8 = 2 mL. Final volume = 16 + 2 = 18 mL, down from 34 mL.
Check against Gay-Lussac's rule. The 32 mL that reacted (8 + 24) became 16 mL, a contraction of half, exactly as he described.
Which mistakes does this help you avoid?
Assuming volumes add up. Gas volumes are not conserved in a reaction. Mass is.
Using volume ratios for liquids or solids. The law is for gases only. If water is formed as a liquid at room temperature, its volume does not follow the 2 : 1 : 2 pattern.
Mixing conditions. If one gas is measured hot and another cold, convert first using the gas laws. Our post on Jacques Charles and gas volume shows how.
The JEE (Main) 2026 syllabus lists "Laws of chemical combination" in its first chemistry unit. Check the current year's syllabus for your exam.
What can a student take from Gay-Lussac's way of working?
Look at the data another way. Weights showed no clear pattern. Volumes did. Changing what you measure can reveal a law.
Gather other people's results. Much of his memoir reworks data from Davy, Berthollet and others, converted to volumes.
Allow for small errors. Davy's nitric oxide figures gave 100 : 108.9, not 100 : 100. Gay-Lussac checked it by experiment and found the simple ratio held.
If the jump from volumes to moles still feels shaky, the Fermi Concept Library covers every concept in chemistry with its own lesson, so you can revise the mole and the gas laws one at a time.
Try it now: 20 mL of carbon monoxide burns in 15 mL of oxygen to give carbon dioxide. Work out the final volume and what it contains.
