Amount-of-substance concentration—often simply “concentration” and denoted c—quantifies the amount of a
specified component per unit volume of mixture. In the ISO/ISQ framework, its coherent SI unit is mol·m⁻³
(not “M” or mol·L⁻¹, which are convenient but non-coherent). Amount-of-substance concentration underpins quantitative
physical chemistry, analytical chemistry, process control, environmental monitoring, and biochemistry. ISO 80000-9
standardizes the quantity symbol, unit usage, and naming to ensure unambiguous communication across disciplines. Pair
this explainer with the
molality guide
and the
pH activity overview
to connect concentration, mass-based composition, and logarithmic acidity within a single workflow.
Definition and SI Coherence
For component B in a mixture,
c_B = n_B / V
where nB is amount of substance (mol) and V is the total volume of the mixture (m³). The unit
mol·m⁻³ is coherent with SI base units and maintains algebraic consistency across thermodynamic and
transport equations. Practical laboratory work often uses mol·L⁻¹ (equivalently mol·dm⁻³) for convenience;
the exact relation is
1 mol·L⁻¹ = 10³ mol·m⁻³
Historical Notes and Terminology
Historically, molarity (capital “M”) denoted mol·dm⁻³ and dominated chemical practice because volumetric glassware was
easy to calibrate. Modern standards nonetheless favor coherent units for computation and metrology. ISO 80000-9 and
IUPAC nomenclature distinguish amount-of-substance concentration (mol·m⁻³) from related quantities such as mass
concentration (kg·m⁻³), number concentration (m⁻³), and
molality (mol·kg⁻¹).
Conceptual Foundations
Concentration vs. activity
Many equilibrium and rate laws are thermodynamically written in terms of activities ai. For solutes,
a_i = γ_i · (c_i / c°)
with c° a chosen standard concentration (commonly 1 mol·dm⁻³) and γi the activity coefficient capturing
non-ideality (ionic strength, specific interactions). Using ai ensures generality, while ci remains
the measurable operational quantity.
Temperature dependence and density
Because V changes with temperature and pressure, c is not strictly invariant under thermal/pressure changes. This
motivates the complementary use of
molality
(mol·kg⁻¹), which is mass-based and comparatively temperature-insensitive. Conversion between c and molality b requires
solution density ρ and composition (see below), a relationship explored in the
pH activity primer
when relating hydrogen-ion activities to measured concentrations.
Relationships with Other Composition Quantities
Let wB denote mass fraction of B, MB its molar mass, and ρ the mixture density.
From mass fraction to concentration:
c_B = (ρ · w_B) / M_B
From concentration to molality: If wB is small (dilute solutions),
b_B ≈ c_B / ρ_solvent
whereas in general,
b_B = w_B / [M_B · (1 - w_B)]
From concentration to mole fraction xB:
x_B = c_B / Σ c_i
For liquids, care is needed when summing components due to partial molar volumes and compressibility.
Measurement and Traceability
Primary and classical methods
Gravimetry and coulometry can realize substance amounts with low uncertainty.
Titrimetry using primary standards (e.g., potassium hydrogen phthalate, silver nitrate) assigns c to
standard solutions; traceability flows from mass calibrations, purity assessments, and stoichiometry.
Volumetric calibration (flasks, pipettes, burettes) must include temperature, buoyancy, and meniscus corrections.
Instrumental methods
UV–Vis spectrophotometry via Beer–Lambert law A = ε · ℓ · c for species with known molar absorptivity.
ICP-OES/ICP-MS for elemental concentrations across many orders of magnitude.
Ion chromatography, HPLC, GC with external calibration, internal standards, or standard addition to handle matrix effects.
Electroanalytical techniques (potentiometry, voltammetry) for ionic species, often relating potential/current to c.
Uncertainty sources
Dominant contributions include volumetric calibration, balances, standard purity, temperature control (thermal expansion), detector linearity, and matrix interferences. Best practice reports expanded uncertainty, the calibration hierarchy, and measurement conditions (T, p, ionic strength). Use the
pH from concentration calculator
alongside these guidelines to keep hydrogen-ion measurements aligned with activity models.
Applications
Environmental and clinical chemistry
Nutrient ions (nitrate, phosphate), heavy metals, and organics in water are regulated as amount-of-substance concentrations. Clinical analytes (electrolytes, metabolites) are routinely reported in mmol·L⁻¹, convertible to mol·m⁻³ for SI coherence.
Process and energy industries
Electrolyte concentrations govern conductivity, corrosion, and battery performance; in polymerization and catalysis, c drives rates and selectivity. Cross-check these profiles with the
ideal gas pressure tool
when gas handling couples with solution-phase reactions.
Fundamental and applied research
Kinetics experiments (initial-rate methods, stopped-flow) and equilibrium studies (binding, complex formation) require accurate c with activity corrections. Relate these outcomes to
pH control strategies
whenever protonation equilibria anchor the interpretation.
Good Practice
Specify the component, matrix, temperature, and unit (e.g., “chloride in seawater, 25 °C, 0.54 mol·L⁻¹”).
When using non-coherent units (mol·L⁻¹), provide conversion to mol·m⁻³.
For ionic systems, report ionic strength and, where relevant, the activity model used.
Use certified reference materials and recovery checks for traceability.
Why It Matters
Amount-of-substance concentration is the operational backbone of quantitative chemistry. ISO 80000-9’s disciplined symbols and units prevent ambiguity, support equation coherence, and facilitate comparison across laboratories, industries, and regulatory regimes.
Related resources on CalcSimpler
Explore these guides to expand your measurement toolkit and connect theory to hands-on calculations.
ISO 80000-9: Quantities and Units of Physical Chemistry
Review the standard that formalises concentration symbols, naming, and their coherence with other composition quantities.
