The fundamental concept that makes modern chemistry possible remains a puzzle even to many chemists.
By Chemistry Insights | Updated June 2023
Imagine trying to build a house without a standard unit of measurement for lumber—where a "board" might refer to different lengths depending on the supplier. This is precisely the challenge chemists faced before standardizing how we count molecules, atoms, and ions—the invisible building blocks of matter. At the heart of this challenge lies "amount of substance," a concept so fundamental to chemistry that it forms one of the seven base quantities in the International System of Units (SI), yet remains poorly understood and controversial even within the scientific community.
The unit of amount of substance—the mole—has been part of the SI since 1971, yet a review of first-year university chemistry textbooks reveals that the concept is correctly explained in only 4 out of 18 cases, and a proper SI definition of the mole appears in none 1 . This knowledge gap highlights what one metrology expert describes as "a source of confusion ever since it was used in the International System of Units." In this article, we explore the mystery behind this essential but elusive concept, its critical role in chemistry, and why the world's top measurement authorities still owe chemists a clear description of "amount of substance."
Amount of substance (symbolized as n) is a fundamental physical quantity that measures the size of an ensemble of entities, whether atoms, molecules, ions, or electrons.
The mole (symbol: mol) serves as the SI unit for this quantity. One mole contains exactly 6.02214076×10²³ elementary entities—a value known as the Avogadro constant (NA) 1 .
In simple terms, amount of substance is the quantity that allows chemists to count particles by weighing, bridging the gap between the invisible microscopic world of individual particles and the macroscopic world we can measure and observe 1 .
This number, while seemingly arbitrary, provides a practical scale for chemical measurements, allowing laboratory technicians to work with manageable numbers like 0.1 moles rather than unwieldy values like 6.02214076×10²² particles.
Amount of substance connects various essential chemical relationships through straightforward mathematical equations :
The amount of substance (n) equals the number of entities (N) divided by the Avogadro constant (NA)
The amount of substance equals the mass of a sample (m) divided by its molar mass (M)
The ideal gas law, relating pressure (p), volume (V), and temperature (T) to the amount of gas
The relationship between amount of substance concentration (c) and the volume of solution
| Compound | Formula | Molar Mass Calculation | Molar Mass (g/mol) |
|---|---|---|---|
| Water | H₂O | (2 × 1.0) + 16.0 | 18.0 |
| Carbon dioxide | CO₂ | 12.0 + (16.0 × 2) | 44.0 |
| Magnesium nitrate | Mg(NO₃)₂ | 24.3 + (14.0 × 2) + (16.0 × 6) | 148.3 |
| Sodium chloride | NaCl | 23.0 + 35.5 | 58.5 |
Atomic weights and molar masses were known and used reliably long before the Avogadro constant was determined with high accuracy.
Working with numbers on the order of 1-1000 moles is far more manageable than handling numbers around 10²³.
Treating amount of substance as a base quantity with its own dimension enhances the power of dimensional analysis.
The term "amount of substance" itself has been criticized as unclear and potentially confusing. The phrase sounds similar to everyday English, where "amount" might refer to mass or volume, leading to ambiguity .
Despite these proposals, "amount of substance" remains the official term, though even the International Committee for Weights and Measures has been asked to provide an alternative name without yet delivering a satisfactory solution 3 .
The confusion surrounding amount of substance isn't merely academic—it has real consequences for chemical education. Studies have shown that only 11% of educators identified the mole as the unit of "amount of substance" when surveyed about the concept 3 .
The Consultative Committee on Amount of Substance (CCQM), recently renamed "CC on Amount of Substance—Metrology in Chemistry and Biology," was established in 1993 to advise on matters relating to quantitative measurements in chemistry 3 . Despite its name, the committee's terms of reference include nothing about actually describing the concept of "amount of substance," focusing instead on traceability and measurement uncertainty.
As one critic noted, "The problem of not understanding 'amount of substance' was exacerbated in 2009 when the IUPAC asked CCQM for an alternative/better name for 'amount of substance.' CCQM still owes a reply to that question" 3 .
| Base Quantity | Symbol | Base Unit | Unit Symbol |
|---|---|---|---|
| Length | l | metre | m |
| Mass | m | kilogram | kg |
| Time | t | second | s |
| Electric current | I, i | ampere | A |
| Thermodynamic temperature | T | kelvin | K |
| Amount of substance | n | mole | mol |
| Luminous intensity | Iv | candela | cd |
The concept of amount of substance developed alongside the birth of modern chemistry. While alchemists and early metallurgists had some intuitive notion of quantity in matter, no generalized concept existed beyond specific recipes 1 .
Carl Friedrich Wenzel published "Lessons on Affinity," demonstrating constant proportions in reactions between neutral salts.
Antoine Lavoisier published his "Treatise of Elementary Chemistry," clarifying the law of conservation of mass.
Jeremias Benjamin Richter introduced the first tables of equivalent weights and coined the term "stoichiometry."
Joseph Proust's law of definite proportions generalized equivalent weights to all chemical reactions.
John Dalton published his first paper on atomic theory, including a table of relative weights of particles.
The term "mole" has a complex history. German scientists used terms like "Kilogrammemolekuel" and "g-Molekel" in the 1880s-1890s, referring to a mass equal to the molecular weight in grams. The term "gramme-molecule" appeared in English in 1893 in the Encyclopedia Britannica .
These awkward terms were shortened to "Mol" by Walther Nernst in 1898, with the English "mole" first appearing in the 1902 translation of Wilhelm Ostwald's "Principles of Inorganic Chemistry" .
The concept continued to evolve with discoveries in isotope chemistry, eventually leading to the adoption of the carbon-12 standard in 1961 and the official inclusion of the mole as a base SI unit in 1971 .
Titration represents one of the most important practical applications of amount of substance in analytical chemistry. This technique allows chemists to determine the unknown concentration of a solution by reacting it with a solution of known concentration .
In a typical acid-base titration, the point at which the acid exactly neutralizes the base (the equivalence point) is determined using an indicator or pH meter. The fundamental principle is that molecules, ions, or other entities react in simple, fixed ratios—the core concept that amount of substance helps to quantify.
The power of amount of substance in titration is beautifully expressed by the simple relationship between the reacting species :
Where the ratio (nₓ/nᵧ) is a simple rational fraction (1:1, 1:2, 2:1, etc.). This mathematical expression represents the law of multiple proportions in action—the very principle that makes the concept of amount of substance indispensable to chemistry.
| Solution | Volume (mL) | Concentration (mol/L) | Amount of Substance (mol) |
|---|---|---|---|
| NaOH (unknown) | 25.0 | ? | ? |
| HCl (standard) | 18.5 | 0.100 | 0.00185 |
| Calculation | Ratio 1:1 | c = n/V = 0.00185/0.0250 | 0.0740 |
Provides official definitions and conventions for amount of substance and the mole, including discussion of alternative names like "enplethy" .
Contains formal definitions of metrological terms, though its description of amount of substance has been criticized as circular 3 .
The international standard that includes amount of substance as part of the International System of Quantities 3 .
Sophisticated equipment used at national metrology institutes to determine the Avogadro constant with ever-increasing precision, currently known to about 5 parts in 10⁸ .
Critical resources that allow accurate determination of molar masses, with many known to about 1 part in 10⁹—more precise than the Avogadro constant itself .
High-precision analytical balances capable of measuring mass to several decimal places, essential for accurate mole calculations in laboratory settings.
The concept of amount of substance and its unit, the mole, sits at the very foundation of chemistry, enabling the quantitative relationships that define chemical reactions. Yet, decades after its official adoption into the SI, it remains poorly understood and controversially defined.
The ongoing revision of the SI presents an opportunity to clarify the description of this fundamental quantity. As one metrologist aptly stated, "The present revision of the SI offers an excellent opportunity for CCQM to provide its own simple clarification of the concept 'amount of substance' and improve its understanding and usefulness by a clear and handsome description that meets the chemist's needs" 3 .
Until then, amount of substance remains both essential and enigmatic—a testament to the complex relationship between our human-scale measurements and the particulate nature of matter. For students and practitioners of chemistry, understanding this concept—despite its ambiguities—remains crucial to navigating the quantitative aspects of the molecular world.