A Story Spanning More Than 200 Years: Where the Mole and Atomic Weight Converged

How Atomic Weight Began with a Debate over Proportions

Those formulas that once made you suffer may be the result of years of work by many people.

In the late eighteenth century, the French chemist Joseph Louis Proust (1754–1826) proposed what would later be called the law of definite proportions. He argued that the elements in a compound always occur in a fixed mass ratio, regardless of where the compound comes from or how it is prepared._[1]

Proust’s claim immediately met opposition from another French chemist, Claude Louis Berthollet (1748–1822).

In Essai de statique chimique, Berthollet proposed a “law of indefinite proportions” (loi des proportions indéfinies). Unlike Proust, he believed that the proportions in a compound could vary with the conditions._[3]

The debate between Proust and Berthollet continued for nearly ten years. During that time, Proust used a large number of careful experiments to support the idea of fixed proportions.

After the debate, the Swedish chemist Jöns Jacob Berzelius (1779–1848) carried out more precise chemical analyses and atomic-weight measurements in the early nineteenth century. His work further supported the idea that compounds have fixed compositions and helped Proust’s position gain wider acceptance._[5]

This debate also led scientists to ask a deeper question: if proportions could be measured reliably, might there be a more basic unit behind the composition of matter?

In the early nineteenth century, the English chemist John Dalton (1766–1844) answered that question with the atomic theory presented in A New System of Chemical Philosophy.

Dalton’s atomic theory included several central ideas: elements are made of indivisible atoms; atoms of the same element have the same mass; compounds are formed from atoms in whole-number ratios; and chemical reactions rearrange atoms._[7]

His theory also used the term “atomic weight” to describe atomic mass. This was the term’s first appearance in the history of science.

Dalton’s “atomic weight” was not an atom’s mass expressed in an absolute unit. It was the ratio between the mass of an atom of an element and the mass of an atom of hydrogen, the lightest element.

Scientists used a ratio because the technology of the time could not measure the absolute mass of a single atom. They could only infer atomic masses from the proportions found in compounds.

Dalton’s atomic-weight proposal relied on experimental results then interpreted as water containing 12.5% hydrogen and 87.5% oxygen, giving a hydrogen-to-oxygen mass ratio of 1:7. That is clearly different from our modern understanding._[9]

Later experiments also showed that several parts of Dalton’s atomic theory needed correction. Even so, his reasoning drove the development of atomic-weight tables and gave later scientists a foundation to revise._[10] It allowed chemists to compare the masses of different elements with numbers.

Meanwhile, the Italian scientist Amedeo Avogadro (1776–1856) proposed Avogadro’s law in 1811: equal volumes of gases at the same temperature and pressure contain equal numbers of molecules._[11]

This hypothesis laid a foundation for molecular theory and the gas laws. It also opened the way to thinking about how many particles are contained in one mole—the quantity later described by Avogadro’s number.

About ninety years later, the German chemist Wilhelm Friedrich Ostwald (1853–1932) introduced the mole concept near the end of the nineteenth century, defining it as the number of grams corresponding to an atomic or molecular weight._[13]

The number of particles in a mole was not yet known, but the concept formed an important bridge. It gave chemists a macroscopic starting point for connecting measurable grams with atomic weight.

The Search for Avogadro’s Number—and Greater Precision

By the twentieth century, scientists were still asking two questions: how should the mass of an atom be determined, and exactly how many particles are in one mole?

In 1909, the American physicist Robert Andrews Millikan (1868–1953) performed his famous oil-drop experiment.

He suspended tiny oil drops in an electric field and observed their motion to measure the electron’s charge precisely. Combining that value with the Faraday constant made it possible to calculate the number of electrons per mole indirectly—an important step toward determining Avogadro’s constant._[15]

At about the same time, the French physicist Jean Baptiste Perrin (1870–1942) used Brownian motion, sedimentation equilibrium, and other methods to measure Avogadro’s constant directly.

Brownian motion is the irregular movement of tiny particles suspended in a liquid. Perrin studied the statistical distribution of that motion to estimate the number of molecules.

In the sedimentation-equilibrium method, he observed the height distribution at which colloidal particles balance the effects of gravity and thermal motion, then used it to estimate particle number.

In 1909, Perrin used Brownian motion and sedimentation equilibrium to determine Avogadro’s number. In his 1913 book Les Atomes, he later gathered and compared many independent measurement methods._[17][18][19] Most produced values of roughly 6 × 10²³, close to one another. A representative value Perrin later summarized in his Nobel lecture was about 6.2 × 10²³—not the exact value used in today’s definition.

Together, Perrin’s many experiments formed a powerful “this cannot all be coincidence” argument. They persuaded the scientific community to accept atomic and molecular theory, and Perrin received the 1926 Nobel Prize for this work._[19]

Avogadro’s number was making major progress, but atomic mass was not nearly as cooperative.

After Dalton proposed that matter consisted of indivisible atoms, scientists expected an element’s atomic weight—the mass ratio relative to hydrogen—to be a whole number.

As more elements were measured, however, scientists found that atomic-weight tables contained many non-integers. That conflicted with the intuition that atoms were the smallest units and compounds formed in whole-number ratios. The puzzle troubled scientists throughout the nineteenth century.

A quick side note: even before Dalton proposed atomic theory, the French chemist Antoine-Laurent de Lavoisier (1743–1794) had already described ways to define and distinguish “elements” and “compounds” in his 1789 Traité élémentaire de chimie._[21]

Isotopes × Atomic Weight × Mass Number

To understand the differences among isotopes, atomic weight, and mass number, we first need to look at how atomic structure was discovered.

In 1911, the New Zealand physicist Ernest Rutherford (1871–1937) used alpha-particle scattering from gold foil to reveal atomic structure. He found that most of an atom is empty space and that its mass is concentrated in a tiny, positively charged nucleus. This was the first real picture of how atomic mass is distributed._[23]

The British physicist J. J. Thomson (1856–1940) later studied positive rays and found particles of neon with different masses in 1913, laying groundwork for isotope measurement._[25] In the same year, the British chemist Frederick Soddy (1877–1956) introduced the concept of “isotopes” for atoms with the same chemical properties but different atomic masses._[26] In 1919, the British physicist Francis William Aston (1877–1945) developed the mass spectrograph, which separated many isotopes and measured their masses more precisely._[27]

Aston also proposed the Whole Number Rule: the mass of an isotope is approximately a whole-number multiple of the mass of a hydrogen atom._[28]

This was an important early discovery in mass spectrometry. It helped scientists understand atomic structure and isotopes, explained why atomic-weight tables looked irregular, and made more precise atomic weights possible.

The discovery of isotopes also established the idea of average atomic weight: the weighted average of the masses of an element’s naturally occurring isotopes, calculated from their natural abundances.

It is an average for the element, not the mass of one particular atom, so it is often not a whole number.

One detail matters here: by the time Aston was studying isotopes, scientists were already using integer “mass numbers” to distinguish atoms. They simply did not yet know what those numbers represented inside the nucleus.

Only after James Chadwick (1891–1974) discovered the neutron in 1932 did scientists understand that the nucleus contains protons and neutrons._[31][32] The physical meaning of mass number then became clear: it is the total number of protons and neutrons in the nucleus._[33] In other words, the neutron’s discovery did not invent mass number from nothing—it explained why that number exists.

This history leaves us with several different concepts:

Mass number: the total number of protons and neutrons, so it is always an integer.

Relative isotopic mass: the mass of a particular atom relative to a chosen standard. Because measuring an atom’s absolute mass directly was difficult, scientists compared other atoms with standards such as hydrogen. Aston’s Whole Number Rule suggested that isotope masses should lie close to integers on the early scale.

Average atomic weight: the abundance-weighted average of naturally occurring isotopes, so it usually contains decimals.

Unifying the Standard—and the Scientific System

When Dalton first proposed atomic theory and atomic weight, hydrogen seemed the best comparison standard because it was the lightest atom._[35]

As chemical analysis improved, however, scientists found hydrogen difficult to measure consistently and especially sensitive to experimental error. They began searching for another element to serve as the atomic-weight standard.

By the early twentieth century, oxygen was widely present in compounds and convenient to analyze, so scientists selected it as the new mass standard for atomic weights.

The discovery of isotopes then created a serious split: physicists and chemists did not mean the same “oxygen” when they defined the standard.

Chemists used natural oxygen, a mixture of oxygen-16, oxygen-17, and oxygen-18. Physicists used the pure isotope oxygen-16.

Those different definitions produced slightly different atomic-mass units in physics and chemistry. The chemical scale was about 0.028% larger than the physical scale._[35]

The number sounds tiny, but it could cause confusion in interdisciplinary research and precision calculations, particularly when scientists tried to align molecular weights and the definition of the mole._[36]

To remove the inconsistency, the International Union of Pure and Applied Chemistry (IUPAC) and the International Union of Pure and Applied Physics (IUPAP) agreed in 1959–1960 to use carbon-12 as the new standard._[37]

Carbon-12 is stable and can be measured precisely. Under this system, 12 grams of carbon-12 contained one mole of atoms. In 1961, the atomic weight of carbon-12 was formally set to exactly 12, and the relative atomic weights of all other elements were expressed from that standard._[38]

At the same time, the unified atomic mass unit (u or Da) was introduced and defined as one-twelfth of the mass of a carbon-12 atom._[35][39]

The new unit replaced the older “chemical amu” and “physical amu,” giving different fields one consistent standard.

The decision resolved the hydrogen-versus-oxygen standard debate and let scientists compare atomic and molecular masses on one scale, supporting later work in nuclear physics and chemistry._[40]

In 1971, the mole became one of the seven base units of the International System of Units (SI). It was then defined as the amount of substance containing as many particles as there are atoms in 12 grams of carbon-12._[41]

Readers who first met physics and chemistry in school may remember that definition. But because it still depended on the mass of carbon-12, improving measurement precision led scientists to seek a more stable natural constant as the foundation.

At its 26th meeting in 2018, the General Conference on Weights and Measures (CGPM) approved a new definition of the mole by fixing Avogadro’s constant at exactly 6.02214076 × 10²³ mol⁻¹. The new definition took effect on May 20, 2019._[41][42]

The mole therefore no longer depends on measuring the mass of carbon-12. It is based directly on a natural constant, supporting long-term stability and consistent measurement worldwide.

Where the Microscopic and Macroscopic Worlds Meet

Once the carbon-12 atomic-weight standard had been established and Avogadro’s constant had been fixed, microscopic atomic masses and macroscopic masses measured in grams could be connected within one system.

In junior- and senior-high calculations, we can still treat 12 grams of carbon-12 as containing approximately 6.02214076 × 10²³ atoms. At very high precision, however, what has been fixed exactly since 2019 is Avogadro’s constant. The relationship between 12 grams of carbon-12 and that number of atoms is extremely close, but it is no longer an exact equality by definition._[41][42]

That is why school-level conversions can use Avogadro’s constant to estimate how many grams correspond to one unified atomic mass unit (1 u, also commonly written 1 amu). The exact definition of 1 u remains one-twelfth of the mass of one carbon-12 atom; the calculation shown below is the approximation commonly used in school problems:

This value forms a bridge between the microscopic and macroscopic worlds.

Modern physics and chemistry also revealed that even the atomic mass of a single isotope is not an integer.

The total mass of a nucleus is smaller than the combined masses of its separate protons and neutrons. The difference is called the mass defect.

The mass defect corresponds to nuclear binding energy. According to Einstein’s mass–energy relation, E = mc², that energy is released when the nucleus forms, so an isotope’s actual mass is not an integer.

The electrons also contribute to the atom’s total mass, shifting the precise value still farther away from an integer.

So in the end, even the mass of one real atom is not a whole number.

Conclusion

After roughly two centuries of development, scientists finally distinguished mass number from atomic weight. By determining Avogadro’s number and agreeing on an atomic-weight standard, they connected microscopic atomic masses with macroscopic masses.

This history also shows us that knowledge often advances through debate and error.

From Proust and Berthollet’s dispute over compound composition to Dalton’s atomic theory, no one could know from the beginning that an argument was correct. Later experiments had to test it.

Right or wrong, the person willing to speak the first sentence can still have an enormous influence on everyone who comes later.

The many experiments used to investigate Avogadro’s number also show scientists refusing to stop at the achievements of their own time. They keep improving their methods and moving closer to the real answer—to truth.

It is as if scientists are always looking toward a distant horizon, then walking toward it with the most careful steps they can take.

Even a single short formula or conclusion in a textbook may represent years, decades, or even centuries of work by many scientists.

The next time a textbook topic feels dull, look for the story behind it. You may find a very human history filled with real lives.

Make the most of what you are learning now. Perhaps one day, you too will become a scientist remembered by future generations!

I’m Wakame, your world-weary physics teacher. That is all for today’s story—see you in the next article!

References

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