Molar concentration explained

Molar concentration (also called amount-of-substance concentration or molarity) is the number of moles of solute per liter of solution.^[1] Specifically, it is a measure of the concentration of a chemical species, in particular, of a solute in a solution, in terms of amount of substance per unit volume of solution. In chemistry, the most commonly used unit for molarity is the number of moles per liter, having the unit symbol mol/L or mol/dm³ (1000 mol/m³) in SI units. Molar concentration is often depicted with square brackets around the substance of interest; for example, the molarity of the hydronium ion is denoted as [H₃O⁺].

Definition

Molar concentration or molarity is most commonly expressed in units of moles of solute per litre of solution.^[2] For use in broader applications, it is defined as amount of substance of solute per unit volume of solution, or per unit volume available to the species, represented by lowercase

:

Here,

is the amount of the solute in moles, is the number of constituent particles present in volume (in litres) of the solution, and is the Avogadro constant, since 2019 defined as exactly . The ratio is the number density .

In thermodynamics, the use of molar concentration is often not convenient because the volume of most solutions slightly depends on temperature due to thermal expansion. This problem is usually resolved by introducing temperature correction factors, or by using a temperature-independent measure of concentration such as molality.^[3]

The reciprocal quantity represents the dilution (volume) which can appear in Ostwald's law of dilution.

Formality or analytical concentration

If a molecule or salt dissociates in solution, the concentration refers to the original chemical formula in solution, the molar concentration is sometimes called formal concentration or formality (F_A) or analytical concentration (c_A). For example, if a sodium carbonate solution has a formal concentration of c = 1 mol/L, the molar concentrations are c = 2 mol/L and c = 1 mol/L because the salt dissociates into these ions.^[4]

Units

While there is clear consensus on the equivalence of units:

1 mol/m³ = 10⁻³ mol/dm³ = 10⁻³ mol/L = 10⁻³ M = 1 mM = 1 mmol/L,guidance on unit names and abbreviations varies:

The SI prefix "mega" (symbol M) has the same symbol. However, the prefix is never used alone, so "M" unambiguously denotes molar.Sub-multiples, such as "millimolar" (mM) and "nanomolar" (nM), consist of the unit preceded by an SI prefix:

Name	Abbreviation	Concentration
		(mol/L)	(mol/m3)
millimolar	mM	10−3	100=1
micromolar	μM	10−6	10−3
nanomolar	nM	10−9	10−6
picomolar	pM	10−12	10−9
femtomolar	fM	10−15	10−12
attomolar	aM	10−18	10−15
zeptomolar	zM	10−21	10−18
yoctomolar	yM	10−24 (6 particles per 10 L)	10−21
rontomolar	rM	10−27	10−24
quectomolar	qM	10−30	10−27

Related quantities

Number concentration

is given by where is the Avogadro constant.

Mass concentration

is given by where is the molar mass of constituent .

Mole fraction

is given by },where is the average molar mass of the solution, is the density of the solution.

A simpler relation can be obtained by considering the total molar concentration, namely, the sum of molar concentrations of all the components of the mixture:

Mass fraction

is given by

Molality

is where the solvent is substance 1, and the solute is substance 2.

For solutions with more than one solute, the conversion is

Properties

Sum of molar concentrations – normalizing relations

The sum of molar concentrations gives the total molar concentration, namely the density of the mixture divided by the molar mass of the mixture or by another name the reciprocal of the molar volume of the mixture. In an ionic solution, ionic strength is proportional to the sum of the molar concentration of salts.

Sum of products of molar concentrations and partial molar volumes

The sum of products between these quantities equals one:

Dependence on volume

The molar concentration depends on the variation of the volume of the solution due mainly to thermal expansion. On small intervals of temperature, the dependence is

where is the molar concentration at a reference temperature, is the thermal expansion coefficient of the mixture.

See also

• Molality
• Normality
• Orders of magnitude (molar concentration)

External links

• Molar Solution Concentration Calculator
• Experiment to determine the molar concentration of vinegar by titration

Notes and References

1. Web site: Dictionary.com Meanings & Definitions of English Words . 2025-05-15 . Dictionary.com . en.
2. Book: Tro, Nivaldo J.. Introductory chemistry essentials. 6 January 2014. 9780321919052. Fifth. Boston. 457. 857356651.
3. Book: Kaufman, Myron. Principles of thermodynamics. 213. CRC Press. 2002. 0-8247-0692-7.
4. Web site: 2.2: Concentration . Harvey . David . Chemistry LibreTexts . 2020-06-15 . 2021-12-15 .