Avogadro's Law: volume counts molecules
Avogadro's Law states that at constant temperature and pressure, the volume of a gas is directly proportional to the number of moles. In equation form: V₁/n₁ = V₂/n₂. Add more gas to a container and the volume increases; remove gas and the volume shrinks — provided temperature and pressure stay the same.
Amedeo Avogadro proposed this in 1811 in a paper titled "Essay on a Manner of Determining the Relative Masses of the Elementary Molecules of Bodies." His key insight was that equal volumes of different gases at the same temperature and pressure contain equal numbers of particles, regardless of the identity of the gas. This was revolutionary because it distinguished atoms from molecules and allowed chemists to determine relative atomic masses.
Avogadro's hypothesis was largely ignored for 50 years. John Dalton, the leading chemist of the era, rejected it because it implied that some elemental gases, like hydrogen and oxygen, existed as diatomic molecules (H₂ and O₂) rather than as single atoms. Stanislao Cannizzaro revived Avogadro's ideas at the Karlsruhe Congress of 1860, and they became the foundation of modern molecular chemistry.
The mole and molar volume
Avogadro's number, 6.02214076 × 10²³ mol⁻¹, was fixed by international agreement in 2019 as part of the redefinition of the SI base units. One mole of any substance contains exactly this many elementary entities. For an ideal gas at STP (0 °C, 1 atm), one mole occupies 22.414 L. This value is a direct consequence of the Ideal Gas Law: V = nRT/P = (1 × 0.08205746 × 273.15) / 1 = 22.414 L.
Worked examples
Example 1: Adding gas to a balloon. A balloon contains 0.50 mol He at 1.5 L. If 1.00 mol more He is added at constant T and P, what volume? V₂ = V₁ × n₂/n₁ = 1.5 × 1.50/0.50 = 4.5 L.
Example 2: Finding moles from volume. A gas occupies 11.2 L at STP. How many moles? n = V/22.414 = 11.2/22.414 = 0.500 mol. This is a classic stoichiometry step in chemistry problems.
Example 3: Comparing two gases. 2.0 L of oxygen at STP and 2.0 L of nitrogen at STP contain the same number of molecules, even though O₂ (32.0 g/mol) is heavier than N₂ (28.0 g/mol). The masses differ, but the counts are equal — exactly what Avogadro's Law predicts.
Avogadro's number: from hypothesis to defined constant
Avogadro never calculated the number that bears his name. He proposed the hypothesis in 1811 but had no way to determine the actual count of particles in a mole. The first estimate came from Johann Josef Loschmidt in 1865, who used the kinetic theory of gases to calculate that 1 cm³ of gas at STP contains about 2.7 × 10¹⁹ molecules. This gave roughly 6 × 10²³ per mole, within a factor of order of magnitude of the correct value.
Later determinations used Brownian motion (Jean Perrin, 1909), oil drop experiments (Robert Millikan, 1910s), and X-ray crystallography. Each method produced a slightly different value, converging on 6.022 × 10²³. In 2019, the General Conference on Weights and Measures redefined the mole by fixing Avogadro's number at exactly 6.02214076 × 10²³ mol⁻¹. This was part of the broader redefinition of SI base units that also fixed Planck's constant, the elementary charge, Boltzmann's constant, and the speed of light.
Why Avogadro's Law matters for chemical reactions
Avogadro's Law is the foundation of stoichiometry with gases. The balanced equation 2 H₂ + O₂ → 2 H₂O says that two molecules of hydrogen react with one molecule of oxygen to produce two molecules of water. Because Avogadro's Law establishes that equal volumes contain equal numbers of molecules (at the same T and P), the volume ratios are identical to the mole ratios: 2 volumes of H₂ react with 1 volume of O₂ to produce 2 volumes of H₂O (as steam). This relationship holds regardless of which gas is involved.
This is a remarkable shortcut: you can predict the volumes of gaseous reactants and products directly from the balanced equation, without converting to moles or masses. If you react 10.0 L of hydrogen with excess oxygen, you consume 5.0 L of oxygen and produce 10.0 L of steam — all at the same temperature and pressure. The mass ratios differ, but the volume ratios are fixed by the stoichiometric coefficients.
The historic rejection and its resolution
Avogadro's hypothesis was rejected for half a century primarily because of John Dalton's influence. Dalton's atomic theory, published in 1808, assumed that atoms of the same element repelled each other, so they could not form diatomic molecules. When Avogadro proposed that hydrogen gas consists of H₂ molecules rather than individual H atoms, Dalton saw it as a direct challenge to his theory. The scientific community sided with Dalton.
Stanislao Cannizzaro revived Avogadro's ideas at the 1860 Karlsruhe Congress, the first international chemistry conference. Cannizzaro distributed a pamphlet arguing that Avogadro's hypothesis resolved the confusion over atomic weights that had plagued chemistry for decades. By distinguishing atoms (H, O) from molecules (H₂, O₂, H₂O), Avogadro's system produced a consistent set of atomic weights. The congress was a turning point; within a few years, Avogadro's hypothesis became the accepted foundation of molecular chemistry.
More applications
Gas collection. When a gas is produced in a chemical reaction, its volume at known T and P tells you the number of moles produced. If 44.8 L of CO₂ is collected at STP, the amount is 44.8/22.414 = 2.00 mol. From the balanced equation, you can then determine how much reactant was consumed.
Breathing mixtures. Scuba divers and mountaineers use Avogadro's Law implicitly when blending gas mixtures. If a cylinder is filled with 80% nitrogen and 20% oxygen at 200 atm, the partial pressures and mole fractions are identical: P_O₂ = 0.20 × 200 = 40 atm. The volume of each component gas follows directly from its mole fraction.
Frequently asked questions
Avogadro never calculated the number that bears his name. He proposed the hypothesis in 1811 but had no way to determine the actual count of particles in a mole. The first estimate came from Johann Josef Loschmidt in 1865, who used the kinetic theory of gases to calculate that 1 cm³ of gas at STP contains about 2.7 × 10¹⁹ molecules. This gave roughly 6 × 10²³ per mole, within a factor of order of magnitude of the correct value.
Later determinations used Brownian motion (Jean Perrin, 1909), oil drop experiments (Robert Millikan, 1910s), and X-ray crystallography. Each method produced a slightly different value, converging on 6.022 × 10²³. In 2019, the General Conference on Weights and Measures redefined the mole by fixing Avogadro's number at exactly 6.02214076 × 10²³ mol⁻¹. This was part of the broader redefinition of SI base units that also fixed Planck's constant, the elementary charge, Boltzmann's constant, and the speed of light.
Avogadro's Law is the foundation of stoichiometry with gases. The balanced equation 2 H₂ + O₂ → 2 H₂O says that two molecules of hydrogen react with one molecule of oxygen to produce two molecules of water. Because Avogadro's Law establishes that equal volumes contain equal numbers of molecules (at the same T and P), the volume ratios are identical to the mole ratios: 2 volumes of H₂ react with 1 volume of O₂ to produce 2 volumes of H₂O (as steam). This relationship holds regardless of which gas is involved.
This is a remarkable shortcut: you can predict the volumes of gaseous reactants and products directly from the balanced equation, without converting to moles or masses. If you react 10.0 L of hydrogen with excess oxygen, you consume 5.0 L of oxygen and produce 10.0 L of steam — all at the same temperature and pressure. The mass ratios differ, but the volume ratios are fixed by the stoichiometric coefficients.
Avogadro's hypothesis was rejected for half a century primarily because of John Dalton's influence. Dalton's atomic theory, published in 1808, assumed that atoms of the same element repelled each other, so they could not form diatomic molecules. When Avogadro proposed that hydrogen gas consists of H₂ molecules rather than individual H atoms, Dalton saw it as a direct challenge to his theory. The scientific community sided with Dalton.
Stanislao Cannizzaro revived Avogadro's ideas at the 1860 Karlsruhe Congress, the first international chemistry conference. Cannizzaro distributed a pamphlet arguing that Avogadro's hypothesis resolved the confusion over atomic weights that had plagued chemistry for decades. By distinguishing atoms (H, O) from molecules (H₂, O₂, H₂O), Avogadro's system produced a consistent set of atomic weights. The congress was a turning point; within a few years, Avogadro's hypothesis became the accepted foundation of molecular chemistry.
Gas collection. When a gas is produced in a chemical reaction, its volume at known T and P tells you the number of moles produced. If 44.8 L of CO₂ is collected at STP, the amount is 44.8/22.414 = 2.00 mol. From the balanced equation, you can then determine how much reactant was consumed.
Breathing mixtures. Scuba divers and mountaineers use Avogadro's Law implicitly when blending gas mixtures. If a cylinder is filled with 80% nitrogen and 20% oxygen at 200 atm, the partial pressures and mole fractions are identical: P_O₂ = 0.20 × 200 = 40 atm. The volume of each component gas follows directly from its mole fraction.
What is Avogadro's Law? V₁/n₁ = V₂/n₂. At constant T and P, the volume of a gas is proportional to the number of moles.
What is Avogadro's number? 6.02214076 × 10²³ particles per mole, fixed by the 2019 SI redefinition.
What is molar volume at STP? 22.414 L for one mole of any ideal gas at 0 °C and 1 atm.