The Mole Mystery: Why Chemistry's Most Essential Unit Is Still Misunderstood

The fundamental concept that makes modern chemistry possible remains a puzzle even to many chemists.

By Chemistry Insights | Updated June 2023

Introduction: The Invisible Foundation of Chemistry

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."

What exactly is "amount of substance"?

Definition

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

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 .

The bridge between microscopic and macroscopic worlds

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.

The mathematical foundation

Amount of substance connects various essential chemical relationships through straightforward mathematical equations :

n = N/NA

The amount of substance (n) equals the number of entities (N) divided by the Avogadro constant (NA)

n = m/M

The amount of substance equals the mass of a sample (m) divided by its molar mass (M)

pV = nRT

The ideal gas law, relating pressure (p), volume (V), and temperature (T) to the amount of gas

c = n/V

The relationship between amount of substance concentration (c) and the volume of solution

Molar Mass Calculations

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

Why do we need "amount of substance" at all?

Historical Precedent

Atomic weights and molar masses were known and used reliably long before the Avogadro constant was determined with high accuracy.

Practical Convenience

Working with numbers on the order of 1-1000 moles is far more manageable than handling numbers around 10²³.

Dimensional Clarity

Treating amount of substance as a base quantity with its own dimension enhances the power of dimensional analysis.

The naming controversy

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 .

Alternative Names Proposed
  • Chemical amount
  • Enplethy
  • Stoichiometric amount
  • Numerosity
Current Status

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 problem: A concept without a clear description

Educational challenges

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 .

Textbook Analysis Results (18 first-year university chemistry textbooks)
Concept mentioned in index 3/18
16.7%
Correctly referred to in text 4/18
22.2%
Correct SI definition of mole provided 0/18
0%

The metrological dilemma

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 .

The Seven Base Quantities in the International System of Units (SI)

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

Historical perspective: The evolution of chemical measurement

From alchemy to stoichiometry

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 .

1777

Carl Friedrich Wenzel published "Lessons on Affinity," demonstrating constant proportions in reactions between neutral salts.

1789

Antoine Lavoisier published his "Treatise of Elementary Chemistry," clarifying the law of conservation of mass.

1792

Jeremias Benjamin Richter introduced the first tables of equivalent weights and coined the term "stoichiometry."

1794

Joseph Proust's law of definite proportions generalized equivalent weights to all chemical reactions.

1805

John Dalton published his first paper on atomic theory, including a table of relative weights of particles.

The birth of the mole

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 .

Terminology Evolution
  • 1880s-1890s: "Kilogrammemolekuel", "g-Molekel" (German)
  • 1893: "gramme-molecule" (English)
  • 1898: "Mol" (Walther Nernst)
  • 1902: "mole" (English translation of Ostwald)
  • 1971: Official SI base unit
Key Milestones

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 .

In-depth look: The titration experiment

The practical application of amount of substance

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.

Materials Needed
  • Burette
  • Pipette
  • Conical flask
  • Indicator (e.g., phenolphthalein)
  • Standard solution (known concentration)
  • Analyte solution (unknown concentration)
Safety Precautions
  • Wear safety goggles and lab coat
  • Handle acids and bases with care
  • Dispose of chemicals properly
  • Work in a well-ventilated area

Methodology: Step-by-step procedure

  1. Preparation: Precisely measure a volume of the solution with unknown concentration (the analyte) into a clean flask
  2. Indicator addition: Add a few drops of an appropriate indicator that will change color at the equivalence point
  3. Burette filling: Fill a burette with the solution of known concentration (the titrant)
  4. Titration: Slowly add the titrant to the analyte while continuously swirling the flask
  5. Endpoint detection: Watch for the indicator's color change, signaling the equivalence point
  6. Volume recording: Record the exact volume of titrant used to reach the endpoint
  7. Calculation: Use the simple relationship n₁/n₂ = c₁V₁/c₂V₂ to calculate the unknown concentration

Results and analysis

The power of amount of substance in titration is beautifully expressed by the simple relationship between the reacting species :

nₓ/nᵧ = cₓVₓ/cᵧVᵧ

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.

Titration Data Example for Acid-Base Reaction

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

The scientist's toolkit: Essential resources for understanding amount of substance

IUPAC Green Book

Provides official definitions and conventions for amount of substance and the mole, including discussion of alternative names like "enplethy" .

International Vocabulary of Metrology (VIM)

Contains formal definitions of metrological terms, though its description of amount of substance has been criticized as circular 3 .

ISO 80000-8 (Quantities and units)

The international standard that includes amount of substance as part of the International System of Quantities 3 .

Avogadro constant determination apparatus

Sophisticated equipment used at national metrology institutes to determine the Avogadro constant with ever-increasing precision, currently known to about 5 parts in 10⁸ .

Atomic weight reference materials

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 .

Precision balances

High-precision analytical balances capable of measuring mass to several decimal places, essential for accurate mole calculations in laboratory settings.

Conclusion: The future of amount of substance

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.

Key Takeaways

  • Amount of substance bridges microscopic particles and macroscopic measurements
  • The mole provides a practical counting unit for chemical entities
  • Confusion persists about the definition and naming of this concept
  • Educational materials often fail to properly explain the concept
  • Metrology organizations owe chemists a clearer description
  • Understanding amount of substance remains essential for chemistry

References