Molar concentration (also called molarity, amount concentration or substance concentration) 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?dm^-3 in SI unit. A solution with a concentration of 1 mol/L is said to be 1 molar, commonly designated as 1 M. To avoid confusion with SI prefix mega, which has the same abbreviation, small caps ? or italicized M are also used in journals and textbooks.^[1]

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 c:^[3]

${\displaystyle c={\frac {n}{V}}={\frac {N}{N_{\rm {A}}\,V}}={\frac {C}{N_{\rm {A}}}}.}$

Here, n is the amount of the solute in moles,^[4]N is the number of constituent particles present in volume V (in litres) of the solution, and N_A is the Avogadro constant, since 20 May 2019 defined as exactly . The ratio N/V is the number density C.

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.^[4]

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

Formality or analytical concentration

If a molecular entity 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 (Na₂CO₃) has a formal concentration of c(Na₂CO₃) = 1 mol/L, the molar concentrations are c(Na⁺) = 2 mol/L and c(CO^2-
₃) = 1 mol/L because the salt dissociates into these ions.

Units

In the International System of Units (SI) the coherent unit for molar concentration is mol/m³. However, this is inconvenient for most laboratory purposes and most chemical literature traditionally uses mol/dm³, which is the same as mol/L. This traditional unit is often denoted by the letter M, optionally preceded by an SI prefix as needed to denote sub-multiples, for example:

mol/m³ = 10^-3mol/dm³ = 10^-3mol/L = 10^-3 M = 1 mmol/L = 1 mM.

The units millimolar and micromolar refer to mM and ?M (10^-3 mol/L and 10^-6 mol/L), respectively.

Related quantities

Number concentration

The conversion to number concentration ${\displaystyle C_{i}}$ is given by

${\displaystyle C_{i}=c_{i}N_{\text{A}},}$

where ${\displaystyle N_{\text{A}}}$ is the Avogadro constant.

Mass concentration

The conversion to mass concentration ${\displaystyle \rho _{i}}$ is given by

${\displaystyle \rho _{i}=c_{i}M_{i},}$

where ${\displaystyle M_{i}}$ is the molar mass of constituent ${\displaystyle i}$.

Mole fraction

The conversion to mole fraction ${\displaystyle x_{i}}$ is given by

${\displaystyle x_{i}=c_{i}{\frac {\overline {M}}{\rho }},}$

where ${\displaystyle {\overline {M}}}$ is the average molar mass of the solution, ${\displaystyle \rho }$ 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:

${\displaystyle x_{i}={\frac {c_{i}}{c}}={\frac {c_{i}}{\sum _{j}c_{j}}}.}$

Mass fraction

The conversion to mass fraction ${\displaystyle w_{i}}$ is given by

${\displaystyle w_{i}=c_{i}{\frac {M_{i}}{\rho }}.}$

Molality

The conversion to molality (for binary mixtures) is

${\displaystyle b_{2}={\frac {c_{2}}{\rho -c_{1}M_{1}}},}$

where the solute is assigned the subscript 2.

For solutions with more than one solute, the conversion is

${\displaystyle b_{i}={\frac {c_{i}}{\rho _{i}}}={\frac {c_{i}}{\rho -\sum _{j\neq i}c_{j}M_{j}}}.}$

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:

${\displaystyle \sum _{i}c_{i}{\overline {V_{i}}}=1.}$

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

${\displaystyle c_{i}={\frac {c_{i,T_{0}}}{1+\alpha \Delta T}},}$

where ${\displaystyle c_{i,T_{0}}}$ is the molar concentration at a reference temperature, ${\displaystyle \alpha }$ is the thermal expansion coefficient of the mixture.

Examples

See also

• Orders of magnitude (molar concentration)

References

External links

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