# Concentration
**Concentration** is the amount of a constituent divided by the volume of the mixture containing it, the quantity chemists use to state how much of a substance is present in a solution or gas mixture. In formal terms the quantity is the amount concentration (also called amount-of-substance concentration, or substance concentration in clinical chemistry), defined as \( c_{\mathrm{B}} = n_{\mathrm{B}}/V \), where \( n_{\mathrm{B}} \) is the amount of substance of constituent B and \( V \) is the volume of the mixture[1](https://goldbook.iupac.org/terms/view/A00295) • [2](https://www.nist.gov/pml/special-publication-811/nist-guide-si-chapter-8). The word is also used more broadly: IUPAC defines "concentration" as a group of four quantities characterizing the composition of a mixture with respect to its volume, namely mass, amount, volume, and number concentration[3](https://goldbook.iupac.org/terms/view/C01222).
| Key fact | Detail |
|---|---|
| Definition | Amount of a constituent divided by the volume of the mixture, \( c_{\mathrm{B}} = n_{\mathrm{B}}/V \)[1](https://goldbook.iupac.org/terms/view/A00295) • [2](https://www.nist.gov/pml/special-publication-811/nist-guide-si-chapter-8) |
| SI unit | Mole per cubic meter (mol/m3); in practice mol/dm3 or mol/L, sometimes denoted M[1](https://goldbook.iupac.org/terms/view/A00295) • [2](https://www.nist.gov/pml/special-publication-811/nist-guide-si-chapter-8) |
| Symbol | \( c_{\mathrm{B}} \), or the formula of the entity in square brackets, as in [B][1](https://goldbook.iupac.org/terms/view/A00295) • [2](https://www.nist.gov/pml/special-publication-811/nist-guide-si-chapter-8) |
| Temperature dependence | Volume-based concentrations change with temperature; molality and mole fraction do not[4](https://openstax.org/books/chemistry-2e/pages/11-4-colligative-properties) |
| Dilution | Adding solvent lowers concentration while the amount of solute is unchanged, giving \( C_1 V_1 = C_2 V_2 \)[5](https://openstax.org/books/chemistry-2e/pages/3-3-molarity) |
| Standard value | The standard amount concentration \( c^{\ominus} \) is usually chosen as 1 mol dm−3 • [6](https://goldbook.iupac.org/terms/view/15363) |
| Obsolete terms | Molarity (M) and normality (N) are deprecated by NIST in favor of amount-of-substance concentration and its units[2](https://www.nist.gov/pml/special-publication-811/nist-guide-si-chapter-8) |
## The family of concentration quantities
Because several different quantities share the name, precision requires naming what is divided by what. The IUPAC group of four volume-based quantities comprises mass concentration \( \rho_{\mathrm{B}} = m_{\mathrm{B}}/V \), amount concentration \( c_{\mathrm{B}} = n_{\mathrm{B}}/V \), volume concentration, and number concentration \( C_{\mathrm{B}} = N_{\mathrm{B}}/V \), where \( N_{\mathrm{B}} \) counts molecules[3](https://goldbook.iupac.org/terms/view/C01222) • [2](https://www.nist.gov/pml/special-publication-811/nist-guide-si-chapter-8). NIST notes that the bare phrase "concentration of B" can cause confusion for exactly this reason and prefers the unambiguous name amount-of-substance concentration[2](https://www.nist.gov/pml/special-publication-811/nist-guide-si-chapter-8).
A second family divides one extensive quantity by another, giving dimensionless fractions. The amount fraction (synonym mole fraction) is the amount of a constituent divided by the total amount of all constituents, \( x_{\mathrm{B}} = n_{\mathrm{B}}/\sum n_i \)[7](https://goldbook.iupac.org/terms/view/A00296), and the mass fraction is the mass of a constituent divided by the total mass[8](https://goldbook.iupac.org/terms/view/M03722). Molality, the amount of solute divided by the mass of solvent, \( b_{\mathrm{B}} = n_{\mathrm{B}}/m_{\mathrm{A}} \) in mol/kg, belongs to this mass-based group[2](https://www.nist.gov/pml/special-publication-811/nist-guide-si-chapter-8).
## Units and notation
The SI unit of amount-of-substance concentration is the mole per cubic meter[9](https://www.nist.gov/pml/owm/si-units-amount-substance). Laboratory practice almost always uses mol/dm3 or mol/L, and since 1 mol/dm3 = 1 kmol/m3 = 1 mol/L these are numerically identical[2](https://www.nist.gov/pml/special-publication-811/nist-guide-si-chapter-8). For entity B the concentration is often written \( c_{\mathrm{B}} \) or [B]; the bracketed form is the standard shorthand in kinetics and equilibrium expressions[1](https://goldbook.iupac.org/terms/view/A00295).
**Obsolete names.** NIST states that the terms molarity and normality and the symbols M and N should no longer be used because they are obsolete; a "0.1 M solution" should be written as a solution with an amount-of-substance concentration of 0.1 mol/dm3, and a "0.5 N solution of H2SO4" as \( c[(1/2)\mathrm{H_2SO_4}] = 0.5 \) mol/dm3 • [2](https://www.nist.gov/pml/special-publication-811/nist-guide-si-chapter-8). The IUPAC Gold Book still records molarity as the older-literature name for the same quantity[1](https://goldbook.iupac.org/terms/view/A00295). In clinical chemistry the recommended abbreviation is substance concentration[10](https://doi.org/10.1039/bk9781788012881-00001).
For very low concentrations, environmental and medical work commonly uses parts per million (ppm) and parts per billion (ppb), defined on a mass basis as \( \text{ppm} = (\text{mass solute}/\text{mass solution}) \times 10^{6} \) and \( \text{ppb} = (\text{mass solute}/\text{mass solution}) \times 10^{9} \)[11](https://openstax.org/books/chemistry-2e/pages/3-4-other-units-for-solution-concentrations). IUPAC and ISO deprecate ppm and ppb, while the units percent and per mille are accepted by ISO[10](https://doi.org/10.1039/bk9781788012881-00001).
## Temperature dependence
Any concentration defined against the volume of the mixture changes when the mixture expands or contracts. OpenStax gives the example that a solution with identical numbers of solute and solvent species has different molar concentrations at different temperatures because of contraction and expansion of the solution[4](https://openstax.org/books/chemistry-2e/pages/11-4-colligative-properties). Mass-based and mole-based quantities avoid this: molality and mole fraction are computed from masses and molar amounts only, so they do not vary with temperature, which is why colligative-property calculations such as freezing-point depression use molality[4](https://openstax.org/books/chemistry-2e/pages/11-4-colligative-properties).
## Dilution and solution preparation
Dilution is the process whereby the concentration of a solution is lessened by the addition of solvent[5](https://openstax.org/books/chemistry-2e/pages/3-3-molarity). Because the amount of solute is unchanged, the product of concentration and volume is conserved, giving the dilution equation \( C_1 V_1 = C_2 V_2 \)[5](https://openstax.org/books/chemistry-2e/pages/3-3-molarity). The equation holds for any concentration and volume units that cancel properly, not only molarity and liters[5](https://openstax.org/books/chemistry-2e/pages/3-3-molarity). In the laboratory, solutions of known concentration are prepared in [volumetric flasks](https://www.edgepedia.org/volumetric-flask), either by dissolving a weighed amount of solute and filling to the mark or by diluting a stock solution[12](https://chem.libretexts.org/Courses/Western_Oregon_University/Introduction_to_Chemistry_and_the_Environment/08%3A_Chapter_8_-_Solutions/8.08%3A_Dilutions).
## Concentration in thermodynamics and kinetics
Concentration enters rate laws and equilibrium expressions, but for real (non-ideal) solutions the thermodynamically correct variable is the activity, often described as the effective concentration of a species; activity replaces concentration so that the equations of ideal thermodynamics remain usable for real systems[13](https://chem.libretexts.org/Bookshelves/Physical_and_Theoretical_Chemistry_Textbook_Maps/Supplemental_Modules_%28Physical_and_Theoretical_Chemistry%29/Physical_Properties_of_Matter/Solutions_and_Mixtures/Nonideal_Solutions/Activities_and_their_Effects_on_Equilibria). The activity coefficient \( \gamma_{\mathrm{B}} \) of a solute is a dimensionless quantity defined in terms of the chemical potential \( \mu_{\mathrm{B}} \), and it approaches 1 in the infinitely dilute limit[14](https://goldbook.iupac.org/terms/view/A00116). Thermodynamic standard states are built on a chosen standard amount concentration \( c^{\ominus} \), most commonly 1 mol dm−3, a choice that must be specified although it is widely accepted[6](https://goldbook.iupac.org/terms/view/15363).
A further distinction matters in analysis of salts and their derivatives. The stoichiometric concentration of a component, \( c_{\mathrm{B}} = n_{\mathrm{B}}/V \) with \( n_{\mathrm{B}} \) the stoichiometric amount of the component, must be distinguished from the amount-of-substance concentration of the free form of that component in the system, since a dissolved salt partly dissociates or complexes[15](https://goldbook.iupac.org/terms/view/S06023).
## Measurement context
A central task of analytical chemistry is to provide information on the quantitative composition of a substance, expressed through quantities such as concentration, content, amount fraction, or mass fraction[10](https://doi.org/10.1039/bk9781788012881-00001). Reported concentrations should carry a number of significant digits appropriate to the measurement uncertainty, and suitable unit prefixes or scientific notation should be used to avoid insignificant figures[10](https://doi.org/10.1039/bk9781788012881-00001).
## References
1. [IUPAC Gold Book: amount concentration (A00295)](https://goldbook.iupac.org/terms/view/A00295)
2. [NIST Guide to the SI, Chapter 8](https://www.nist.gov/pml/special-publication-811/nist-guide-si-chapter-8)
3. [IUPAC Gold Book: concentration (C01222)](https://goldbook.iupac.org/terms/view/C01222)
4. [OpenStax Chemistry 2e, 11.4 Colligative Properties](https://openstax.org/books/chemistry-2e/pages/11-4-colligative-properties)
5. [OpenStax Chemistry 2e, 3.3 Molarity](https://openstax.org/books/chemistry-2e/pages/3-3-molarity)
6. [IUPAC Gold Book: standard amount concentration (15363)](https://goldbook.iupac.org/terms/view/15363)
7. [IUPAC Gold Book: amount fraction (A00296)](https://goldbook.iupac.org/terms/view/A00296)
8. [IUPAC Gold Book: mass fraction (M03722)](https://goldbook.iupac.org/terms/view/M03722)
9. [NIST SI Units: Amount of Substance](https://www.nist.gov/pml/owm/si-units-amount-substance)
10. [IUPAC Compendium of Terminology in Analytical Chemistry, Fundamental and Metrological Concepts](https://doi.org/10.1039/bk9781788012881-00001)
11. [OpenStax Chemistry 2e, 3.4 Other Units for Solution Concentrations](https://openstax.org/books/chemistry-2e/pages/3-4-other-units-for-solution-concentrations)
12. [Chemistry LibreTexts: Dilutions](https://chem.libretexts.org/Courses/Western_Oregon_University/Introduction_to_Chemistry_and_the_Environment/08%3A_Chapter_8_-_Solutions/8.08%3A_Dilutions)
13. [Chemistry LibreTexts: Activities and their Effects on Equilibria](https://chem.libretexts.org/Bookshelves/Physical_and_Theoretical_Chemistry_Textbook_Maps/Supplemental_Modules_%28Physical_and_Theoretical_Chemistry%29/Physical_Properties_of_Matter/Solutions_and_Mixtures/Nonideal_Solutions/Activities_and_their_Effects_on_Equilibria)
14. [IUPAC Gold Book: activity coefficient (A00116)](https://goldbook.iupac.org/terms/view/A00116)
15. [IUPAC Gold Book: stoichiometric concentration (S06023)](https://goldbook.iupac.org/terms/view/S06023)
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*Topic: Encyclopedia › Physical world and mathematics › Chemistry › Chemical principles and methods › Stoichiometry and composition › Measures of composition*
*Initially written Sep 17, 2026 · Reviewed: Oct 15, 2026 · Edited: Oct 15, 2026; Oct 25, 2026 · Last review: Oct 15, 2026*
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