Why was the Avogadro constant redefined?

Because the Avogadro constant is, in essence, a human-defined number; it should therefore be defined directly as a pure number—not as a quantity tied to experimental measurements. Moreover, according to the underlying principle of the Avogadro constant, it could theoretically take any numerical value. The reason its value is conventionally taken today as 6.02 × 10²³ is simply that its original definition was anchored to the metric unit ‘gram’. Had the imperial unit ‘pound’ been used instead, the Avogadro ‘constant’ would become 2.73 × 10²⁶. Originally conceived as a dimensionless number, its numerical value nevertheless depends on the chosen unit system—making it clearly distinct from truly fundamental, dimensionless natural constants like the fine-structure constant. This is precisely why the International System of Units (SI) later designated ‘mole’ as a base unit and reclassified the ‘Avogadro constant’ as the ‘Avogadro constant’ (with explicit units of per mole, /mol). Moreover, unlike fundamental natural constants such as the speed of light (associated with relativity) or Planck’s constant (associated with energy quantization), the Avogadro constant does not correspond to any fundamental law of nature. If anything, the quantity it reflects is not itself—but rather the ‘relative atomic mass’ tabulated in the periodic table. Initially, scientists discovered the ‘law of definite proportions’ while studying chemical reactions—for instance, hydrogen and oxygen react completely only when their masses stand in an exact 1:8 ratio. It thus occurred naturally to scientists to define the atomic mass of one element as a reference unit, then determine other elements’ relative atomic masses by measuring their reaction mass ratios with that reference element. Because oxygen was easiest to handle experimentally in early chemistry, it became the reference standard, yielding the first tables of relative atomic masses. During the early 19th century, chemical calculations resembled those taught in junior high school today: write the balanced equation (e.g., 2H₂ + O₂ → 2H₂O), consult the atomic mass table (where oxygen was originally assigned 100, and hydrogen 6.25), and solve proportionally—for example, if 1 g of H₂ is given, solve 2×6.25×2/1 = 2×100/x to find x, the required mass of O₂. By the late 19th century, French scientist Jean Perrin proposed: since repeatedly setting up stoichiometric equations is cumbersome, why not directly link the reference atom count to a macroscopic mass unit? His idea was: define a specific number—call it a ‘quasi-constant’—such that exactly that many oxygen atoms weigh precisely 1 gram. According to contemporary atomic mass tables, hydrogen’s relative atomic mass was 1/16 that of oxygen; thus, if that same number of oxygen atoms weighs 1 g, then that same number of hydrogen atoms must weigh exactly 1/16 g—thereby perfectly bridging atomic-scale masses and macroscopic mass measurements. Perrin named this number the ‘Avogadro constant’, honoring Amedeo Avogadro, whose eponymous law laid the scientific foundation for determining relative atomic masses (note: Avogadro himself did not define this number). However, saying ‘an Avogadro constant number of…’ proved unwieldy. Perrin initially termed it the ‘gram-molecule’; later, the scientific community extracted the prefix ‘mol-’ from ‘molecule’ and coined the new term ‘mole’, meaning precisely ‘an Avogadro constant number of entities’.

Strictly speaking, isolated systems do not exist; however, like many other idealized models, we can approximate certain systems as isolated. A state in which the macroscopic properties of a system remain unchanged over time under conditions free from external influence is called a thermodynamic equilibrium state. An equilibrium state differs from a steady state—a state reached under constant external influence. Derivation of the ideal gas equation of state: Microscopic features of the ideal gas model: ・Molecular size is neglected. ・Intermolecular forces—and forces between molecules and container walls—are neglected, except during instantaneous collisions. ・All collisions—between molecules and between molecules and walls—are perfectly elastic. In short: ideal gas molecules are freely moving, perfectly elastic point particles. Three empirical gas laws obeyed by ideal gases: ・Boyle’s law: At constant temperature, pressure p and volume V are inversely proportional. ・Gay-Lussac’s law: At constant pressure, volume V and absolute temperature T are directly proportional. ・Charles’s law: At constant volume, pressure p and absolute temperature T are directly proportional. Thus: pV = C₁, p/T = C₂, V/T = C₃. Combining yields p²V²/T² = C₁C₂C₃ ⇒ pV = CT. At standard conditions: p₀ = 1 atm = 1.013 × 10⁵ Pa, T₀ = 273.15 K, C = (p₀/T₀)(M/μ)V₀ = (M/μ)R = νR, leading to the familiar form: \boxed{pV = \nu RT} where \boxed{R \approx 8.31~\mathrm{J \cdot mol^{-1} \cdot K^{-1}}} is the universal gas constant. Using the Avogadro constant N_A, let N denote the total number of molecules; then N = N_A ν, giving: \boxed{pV = N(R/N_A)T = NkT}, where \boxed{k = R/N_A \approx 1.38 \times 10^{-23}~\mathrm{J/K}} is the Boltzmann constant. Defining molecular number density as n = N/V yields: \boxed{p = nkT}. If gas mass density ρ (in g/m³) is known, another useful relation is: \boxed{p\mu = \rho RT}. A common conversion formula is mR = μk. Statistical assumptions for ideal gases in equilibrium: ・The number of molecules per unit volume is uniform throughout the container—no spatial location is statistically favored. ・Molecular motion is isotropic: motion along any direction is no more probable than along any other. Hence, velocity components are uniformly distributed across directions, and all directional averages are equal: \overline{v_x} = \overline{v_y} = \overline{v_z} = 0. Let n_i denote the number of molecules with speed v_i, and N the total number of molecules. Then: \overline{v^2} = \frac{\sum_i n_i v_i^2}{N}.

How Avogadro’s Number Became Constant

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C&EN commemorates the centennial of the proof of atomic existence, detailing how Avogadro's number was standardized despite early 20th-century scientific skepticism.

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2026-11-11

How Avogadro’s Number Became Constant

How Avogadro’s Number Became Constant

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