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{{Short description|Ratio of part of a mixture to the whole}}
{{other uses}}
In [[chemistry]], '''concentration''' is the [[Abundance (chemistry)|abundance]] of a constituent divided by the total volume of a mixture. Several types of mathematical description can be distinguished: ''[[mass concentration (chemistry)|mass concentration]]'', ''[[molar concentration]]'', ''[[number concentration]]'', and ''[[volume concentration]]''.<ref name="goldbook">{{GoldBookRef | file = C01222 | title = concentration}}</ref> The concentration can refer to any kind of chemical mixture, but most frequently refers to solutes and [[Solvent|solvents]] in [[Solution (chemistry)|solution]]s. The molar (amount) concentration has variants, such as [[normal concentration]] and [[osmotic concentration]]. '''Dilution''' is reduction of concentration, e.g. by adding solvent to a solution. The verb [[Wikt:concentrate|to concentrate]] means to increase concentration, the opposite of dilute.

==Etymology==
''Concentration-'', ''concentratio'', action or an act of coming together at a single place, bringing to a common center, was used in [[Neo-Latin|post-classical Latin]] in 1550 or earlier, similar terms attested in Italian (1589), Spanish (1589), English (1606), French (1632).<ref>{{Cite OED|concentration|id=38114}}</ref>

==Qualitative description==

[[Image:Dilution-concentration simple example.jpg|frame|right|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 data|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 [[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 solution|saturated]]. If additional solute is added to a saturated solution, it will not dissolve, except in certain circumstances, when [[supersaturation]] may occur. Instead, [[Phase (matter)#Phase separation|phase separation]] will occur, leading to coexisting phases, either completely separated or mixed as a [[suspension (chemistry)|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 (psychology)|schema]] of [[ordinate|levels on the vertical axis]] of a [[chart|graph]], which can be [[height|high or low]] (for example, "high serum levels of bilirubin" are concentrations of [[bilirubin]] in the [[serum (blood)|blood serum]] that are greater [[Reference ranges for blood tests#Bilirubin reference ranges|than normal]]).

==Quantitative notation==

There are four quantities that describe concentration:

===Mass concentration===
{{main|Mass concentration (chemistry)}}

The mass concentration <math>\rho_i</math> is defined as the [[mass]] of a constituent <math>m_i</math> divided by the volume of the mixture <math>V</math>:

:<math>\rho_i = \frac {m_i}{V}.</math>

The [[International System of Units|SI unit]] is kg/m<sup>3</sup> (equal to g/L).

===Molar concentration===
{{main|Molar concentration}}

The molar concentration <math>c_i</math> is defined as the [[amount of substance|amount]] of a constituent <math>n_i</math> (in moles) divided by the volume of the mixture <math>V</math>:

:<math>c_i = \frac {n_i}{V}.</math>

The SI unit is mol/m<sup>3</sup>. However, more commonly the unit mol/L (= mol/dm<sup>3</sup>) is used.

===Number concentration===
{{main|Number concentration}}

The number concentration <math>C_i</math> is defined as the number of entities of a constituent <math>N_i</math> in a mixture divided by the volume of the mixture <math>V</math>:

:<math>C_i = \frac{N_i}{V}.</math>

The SI unit is 1/m<sup>3</sup>.

===Volume concentration===

The '''volume concentration''' <math>\sigma_i</math> (not to be confused with [[volume fraction]]<ref name="goldbook2">{{GoldBookRef | file = V06643 | title = volume fraction}}</ref>) is defined as the volume of a constituent <math>V_i</math> divided by the volume of the mixture <math>V</math>:

:<math>\sigma_i = \frac {V_i}{V}.</math>

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

There seems to be no standard notation in the English literature. The letter <math>\sigma_i</math> used here is normative in German literature (see [[:de:Volumenkonzentration|Volumenkonzentration]]).

==Related quantities==

Several other quantities can be used to describe the composition of a mixture. These should '''not''' be called concentrations.<ref name="goldbook" />

===Normality===
{{main|Normality (chemistry)}}

Normality is defined as the molar concentration <math>c_i</math> divided by an equivalence factor <math>f_\mathrm{eq}</math>. Since the definition of the equivalence factor depends on context (which reaction is being studied), the [[IUPAC|International Union of Pure and Applied Chemistry]] and [[NIST|National Institute of Standards and Technology]] discourage the use of normality.

===Molality===
{{main|Molality}}{{Distinguish|Molarity}}
The molality of a solution <math>b_i</math> is defined as the amount of a constituent <math>n_i</math> (in moles) divided by the mass of the solvent <math>m_\mathrm{solvent}</math> ('''not''' the mass of the solution):

:<math>b_i = \frac{n_i}{m_\mathrm{solvent}}.</math>

The SI unit for molality is mol/kg.

===Mole fraction===
{{main|Mole fraction}}

The mole fraction <math>x_i</math> is defined as the amount of a constituent <math>n_i</math> (in moles) divided by the total amount of all constituents in a mixture <math>n_\mathrm{tot}</math>:

:<math>x_i = \frac {n_i}{n_\mathrm{tot}}.</math>

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

===Mole ratio===
{{main|Mixing ratio}}

The mole ratio <math>r_i</math> is defined as the amount of a constituent <math>n_i</math> divided by the total amount of all ''other'' constituents in a mixture:

:<math>r_i = \frac{n_i}{n_\mathrm{tot}-n_i}.</math>

If <math>n_i</math> is much smaller than <math>n_\mathrm{tot}</math>, 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===
{{main|Mass fraction (chemistry)}}

The mass fraction <math>w_i</math> is the fraction of one substance with mass <math>m_i</math> to the mass of the total mixture <math>m_\mathrm{tot}</math>, defined as:

:<math>w_i = \frac {m_i}{m_\mathrm{tot}}.</math>

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

===Mass ratio===
{{main|Mixing ratio}}

The mass ratio <math>\zeta_i</math> is defined as the mass of a constituent <math>m_i</math> divided by the total mass of all ''other'' constituents in a mixture:

:<math>\zeta_i = \frac{m_i}{m_\mathrm{tot}-m_i}.</math>

If <math>m_i</math> is much smaller than <math>m_\mathrm{tot}</math>, 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 and temperature==
Concentration depends on the variation of the volume of the solution with temperature, due mainly to [[thermal expansion]].

== Table of concentrations and related quantities ==

{| class="wikitable"
|-
! Concentration type
! Symbol
! Definition
! SI unit
! other unit(s)
|-
| mass concentration
| <math>\rho_i</math> or <math>\gamma_i</math>
| <math>m_i/V</math>
| kg/m<sup>3</sup>
| g/100mL (=&nbsp;g/dL)
|-
| molar concentration
| <math>c_i</math>
| <math>n_i/V</math>
| mol/m<sup>3</sup>
| M (=&nbsp;mol/L)
|-
| number concentration
| <math>C_i</math>
| <math>N_i/V</math>
| 1/m<sup>3</sup>
| 1/cm<sup>3</sup>
|-
| volume concentration
| <math>\sigma_i</math>
| <math>V_i/V</math>
| m<sup>3</sup>/m<sup>3</sup>
| 
|-
! Related quantities
! Symbol
! Definition
! SI unit
! other unit(s)
|-
| normality
| 
| <math>c_i/f_\mathrm{eq}</math>
| mol/m<sup>3</sup>
| M (=&nbsp;mol/L)
|-
| molality
| <math>b_i</math>
| <math>n_i/m_\mathrm{solvent}</math>
| mol/kg
| m
|-
| mole fraction
| <math>x_i</math>
| <math>n_i/n_\mathrm{tot}</math>
| mol/mol
| ppm, ppb, ppt
|-
| mole ratio
| <math>r_i</math>
| <math>n_i/(n_\mathrm{tot}-n_i)</math>
| mol/mol
| ppm, ppb, ppt
|-
| mass fraction
| <math>w_i</math>
| <math>m_i/m_\mathrm{tot}</math>
| kg/kg
| ppm, ppb, ppt
|-
| mass ratio
| <math>\zeta_i</math>
| <math>m_i/(m_\mathrm{tot}-m_i)</math>
| kg/kg
| ppm, ppb, ppt
|-
| volume fraction
| <math>\phi_i</math>
| <math>V_i/\sum_j V_j</math>
| m<sup>3</sup>/m<sup>3</sup>
| ppm, ppb, ppt
|}

==See also==
* {{annotated link|Dilution ratio}}
* {{annotated link|Dose concentration}}
* {{annotated link|Serial dilution}}
* {{annotated link|Wine/water mixing problem}}
* {{section link|Standard state|Solutes}}

==References==
{{Reflist}}

==External links==
*{{Commonscatinline|Concentration (chemistry)}}

{{Chemical solutions}}
{{authority control}}

[[Category:Concentration| ]]