The Avogadro constant, commonly referred to as Avogadro’s Number (\(N_A\)), represents the number of constituent particles—atoms, molecules, or ions—contained within one mole of a substance. This quantity, approximately \(6.022 \times 10^{23}\), bridges the macroscopic world of laboratory measurements and the microscopic world of individual particles. Although the constant bears his name, the Italian scientist Amedeo Avogadro never calculated its numerical value. His contribution, a foundational hypothesis about gas behavior, set the theoretical stage almost a century before the number was experimentally determined.
Avogadro’s 1811 Hypothesis
Amedeo Avogadro published his seminal hypothesis in 1811, seeking to reconcile two conflicting ideas of the time: John Dalton’s indivisible atomic theory and Joseph Louis Gay-Lussac’s observations on combining gas volumes. Gay-Lussac had shown that gases reacted in simple, whole-number volume ratios, a finding that seemed incompatible with Dalton’s idea that atoms combined one-by-one. Avogadro resolved this paradox by proposing a crucial distinction between atoms and molecules. He suggested that elemental gases did not consist of solitary atoms but were instead made up of multi-atom molecules, such as oxygen existing as \(\text{O}_2\).
This insight led to Avogadro’s Law, which states that equal volumes of any two gases, when held at the same temperature and pressure, contain an equal number of molecules. This meant that the density of a gas was directly proportional to the relative mass of its molecules. For example, if a volume of hydrogen gas weighed less than the same volume of oxygen, the hydrogen molecules were lighter than the oxygen molecules. Avogadro’s work provided a systematic method for determining the relative molecular weights of gases, but it did not offer a way to count the absolute number of particles in any given volume. His hypothesis remained largely unrecognized for nearly five decades after its initial publication.
Defining the Mole and Molar Mass
The theoretical framework established by Avogadro was finally adopted and standardized through the efforts of Italian chemist Stanislao Cannizzaro. At the first international chemistry congress in Karlsruhe in 1860, Cannizzaro presented a case for using Avogadro’s hypothesis to establish a uniform system of atomic and molecular weights. This presentation clarified the existing confusion among chemists regarding the difference between atomic and molecular mass. His work allowed for the consistent determination of the smallest relative mass of an element present in the molecular mass of its gaseous compounds.
The formal concept of the mole was later established to represent a specific, fixed quantity of a substance. Before a 2019 redefinition, the mole was defined as the amount of substance that contains as many elementary entities as there are atoms in exactly 12 grams of carbon-12 (\(\text{^{12}C}\)). This definition fixed the molar mass of carbon-12 at 12 grams per mole, which provided a reference point for all other molar masses. Once the mole was defined, Avogadro’s constant became the absolute count of atoms in 12 grams of carbon-12. The task was then to measure this precise number.
Experimental Methods Used to Determine the Constant
The numerical value of Avogadro’s constant was obtained through experiments that calculated properties of individual particles.
Loschmidt’s Estimate (1865)
The first significant estimate came in 1865 from Austrian physicist Josef Loschmidt, who used the kinetic theory of gases. By measuring the mean free path of molecules in a gas (the average distance a molecule travels before colliding) and combining this with the condensation volume of the gas, Loschmidt estimated the density of molecules in a unit volume. This value, known as the Loschmidt constant, provided the first rough estimation of the number that would later be named after Avogadro.
Perrin and Brownian Motion (1900s)
A major breakthrough in precision measurement occurred with the work of French physicist Jean Perrin in the early 1900s, who utilized Albert Einstein’s theory of Brownian motion. Perrin observed the random, jiggling motion of tiny particles suspended in a liquid, caused by collisions with the fluid’s invisible molecules. By analyzing the sedimentation equilibrium (how particle concentration varied with height under gravity), Perrin treated the suspended particles like a heavy gas. His measurements allowed him to calculate Avogadro’s constant with a much higher degree of accuracy, providing evidence for the reality of atoms and molecules.
Electrochemistry and Millikan’s Experiment
Another highly accurate method relied on the relationship between two fundamental constants: the Faraday constant (\(F\)) and the elementary charge (\(e\)). The Faraday constant represents the total electric charge carried by one mole of electrons, and its value had been determined accurately through electrolysis experiments. Robert Millikan’s famous oil drop experiment, performed around 1910, successfully measured the charge of a single electron, \(e\). Since the total charge on a mole of electrons is the charge of one electron multiplied by the number of electrons in a mole, Avogadro’s constant could be calculated by dividing the Faraday constant by the elementary charge (\(N_A = F/e\)). The convergence of values obtained from these vastly different experimental approaches—gas theory, random particle motion, and electrochemistry—provided definitive confirmation of the constant’s true value.