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In chemistry, concentration is the abundance of a constituent divided by the total volume of a mixture. Several types of mathematical description can be distinguished: mass concentration, molar concentration, number concentration, and volume concentration.^[1] A concentration can be any kind of chemical mixture, but most frequently solutes and solvents in solutions. The molar (amount) concentration has variants such as normal concentration and osmotic concentration.

Qualitative description

These glasses containing red dye demonstrate qualitative changes in concentration. The solutions on the left are more dilute, compared to the more concentrated solutions on the right.

Often in informal, non-technical language, concentration is described in a qualitative way, through the use of adjectives such as "dilute" for solutions of relatively low concentration and "concentrated" for solutions of relatively high concentration. To concentrate a solution, one must add more solute (for example, alcohol), or reduce the amount of solvent (for example, water). By contrast, to dilute a solution, one must add more solvent, or reduce the amount of solute. Unless two substances are fully miscible there exists a concentration at which no further solute will dissolve in a solution. At this point, the solution is said to be saturated. If additional solute is added to a saturated solution, it will not dissolve, except in certain circumstances, when supersaturation may occur. Instead, phase separation will occur, leading to coexisting phases, either completely separated or mixed as a suspension. The point of saturation depends on many variables such as ambient temperature and the precise chemical nature of the solvent and solute.

Concentrations are often called levels, reflecting the mental schema of levels on the vertical axis of a graph, which can be high or low (for example, "high serum levels of bilirubin" are concentrations of bilirubin in the blood serum that are greater than normal).

Quantitative notation

There are four quantities that describe concentration:

Mass concentration

The mass concentration ρi{displaystyle rho _{i}} is defined as the mass of a constituent mi{displaystyle m_{i}} divided by the volume of the mixture V{displaystyle V}:

ρi=miV.{displaystyle rho _{i}={frac {m_{i}}{V}}.}

The SI unit is kg/m³ (equal to g/L).

Molar concentration

The molar concentration ci{displaystyle c_{i}} is defined as the amount of a constituent ni{displaystyle n_{i}} (in moles) divided by the volume of the mixture V{displaystyle V}:

ci=niV.{displaystyle c_{i}={frac {n_{i}}{V}}.}

The SI unit is mol/m³. However, more commonly the unit mol/L (= mol/dm³) is used.

Number concentration

The number concentration Ci{displaystyle C_{i}} is defined as the number of entities of a constituent Ni{displaystyle N_{i}} in a mixture divided by the volume of the mixture V{displaystyle V}:

Ci=NiV.{displaystyle C_{i}={frac {N_{i}}{V}}.}

The SI unit is 1/m³.

Volume concentration

The volume concentration σi{displaystyle sigma _{i}} (not to be confused with volume fraction^[2]) is defined as the volume of a constituent Vi{displaystyle V_{i}} divided by the volume of the mixture V{displaystyle V}:

σi=ViV.{displaystyle sigma _{i}={frac {V_{i}}{V}}.}

Being dimensionless, it is expressed as a number, e.g., 0.18 or 18%; its unit is 1.

There seems to be no standard notation in the English literature.
The letter σi{displaystyle sigma _{i}} used here is normative in German literature (see Volumenkonzentration).

Related quantities

Several other quantities can be used to describe the composition of a mixture. Note that these should not be called concentrations.^[1]

Normality

Normality is defined as the molar concentration ci{displaystyle c_{i}} divided by an equivalence factor feq{displaystyle f_{mathrm {eq} }}. Since the definition of the equivalence factor depends on context (which reaction is being studied), IUPAC and NIST discourage the use of normality.

Molality

(Not to be confused with Molarity)

The molality of a solution bi{displaystyle b_{i}} is defined as the amount of a constituent ni{displaystyle n_{i}} (in moles) divided by the mass of the solvent msolvent{displaystyle m_{mathrm {solvent} }} (not the mass of the solution):

bi=nimsolvent.{displaystyle b_{i}={frac {n_{i}}{m_{mathrm {solvent} }}}.}

The SI unit for molality is mol/kg.

Mole fraction

The mole fraction xi{displaystyle x_{i}} is defined as the amount of a constituent ni{displaystyle n_{i}} (in moles) divided by the total amount of all constituents in a mixture ntot{displaystyle n_{mathrm {tot} }}:

xi=nintot.{displaystyle x_{i}={frac {n_{i}}{n_{mathrm {tot} }}}.}

The SI unit is mol/mol. However, the deprecated parts-per notation is often used to describe small mole fractions.

Mole ratio

The mole ratio ri{displaystyle r_{i}} is defined as the amount of a constituent ni{displaystyle n_{i}} divided by the total amount of all other constituents in a mixture:

ri=nintot−ni.{displaystyle r_{i}={frac {n_{i}}{n_{mathrm {tot} }-n_{i}}}.}

If ni{displaystyle n_{i}} is much smaller than ntot{displaystyle n_{mathrm {tot} }}, the mole ratio is almost identical to the mole fraction.

The SI unit is mol/mol. However, the deprecated parts-per notation is often used to describe small mole ratios.

Mass fraction

The mass fraction wi{displaystyle w_{i}} is the fraction of one substance with mass mi{displaystyle m_{i}} to the mass of the total mixture mtot{displaystyle m_{mathrm {tot} }}, defined as:

wi=mimtot.{displaystyle w_{i}={frac {m_{i}}{m_{mathrm {tot} }}}.}

The SI unit is kg/kg. However, the deprecated parts-per notation is often used to describe small mass fractions.

Mass ratio

The mass ratio ζi{displaystyle zeta _{i}} is defined as the mass of a constituent mi{displaystyle m_{i}} divided by the total mass of all other constituents in a mixture:

ζi=mimtot−mi.{displaystyle zeta _{i}={frac {m_{i}}{m_{mathrm {tot} }-m_{i}}}.}

If mi{displaystyle m_{i}} is much smaller than mtot{displaystyle m_{mathrm {tot} }}, the mass ratio is almost identical to the mass fraction.

The SI unit is kg/kg. However, the deprecated parts-per notation is often used to describe small mass ratios.

Dependence on volume

Concentration depends on the variation of the volume of the solution with temperature due mainly to thermal expansion.

Table of concentrations and related quantities

Concentration type	Symbol	Definition	SI unit	other unit(s)
mass concentration	ρi{displaystyle rho _{i}} or γi{displaystyle gamma _{i}}	mi/V{displaystyle m_{i}/V}	kg/m3	g/100mL (= g/dL)
molar concentration	ci{displaystyle c_{i}}	ni/V{displaystyle n_{i}/V}	mol/m3	M (= mol/L)
number concentration	Ci{displaystyle C_{i}}	Ni/V{displaystyle N_{i}/V}	1/m3	1/cm3
volume concentration	ϕi{displaystyle phi _{i}}	Vi/V{displaystyle V_{i}/V}	m3/m3
Related quantities	Symbol	Definition	SI unit	other unit(s)
normality		ci/feq{displaystyle c_{i}/f_{mathrm {eq} }}	mol/m3	N (= mol/L)
molality	bi{displaystyle b_{i}}	ni/msolvent{displaystyle n_{i}/m_{mathrm {solvent} }}	mol/kg
mole fraction	xi{displaystyle x_{i}}	ni/ntot{displaystyle n_{i}/n_{mathrm {tot} }}	mol/mol	ppm, ppb, ppt
mole ratio	ri{displaystyle r_{i}}	ni/(ntot−ni){displaystyle n_{i}/(n_{mathrm {tot} }-n_{i})}	mol/mol	ppm, ppb, ppt
mass fraction	wi{displaystyle w_{i}}	mi/mtot{displaystyle m_{i}/m_{mathrm {tot} }}	kg/kg	ppm, ppb, ppt
mass ratio	ζi{displaystyle zeta _{i}}	mi/(mtot−mi){displaystyle m_{i}/(m_{mathrm {tot} }-m_{i})}	kg/kg	ppm, ppb, ppt

See also

• Dilution ratio


• Dose concentration


• Serial dilution


• Wine/water mixing problem

References