Concentration

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 fraction, mass concentration, molar concentration, number concentration, and volume concentration.^[1] The concentration can refer to any kind of chemical mixture, but most frequently refers to solutes and solvents in solutions. 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 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 post-classical Latin in 1550 or earlier, similar terms attested in Italian (1589), Spanish (1589), English (1606), French (1632).^[2]

Qualitative description

File:Dilution-concentration simple example.jpg

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 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 five quantities that describe concentration:

Mass fraction

Mass concentration

The mass concentration $ρ_{i}$ (not to be confused with mass fraction) is defined as the mass of a constituent $m_{i}$ divided by the volume of the mixture $V$ :

ρ_{i} = \frac{m_{i}}{V} .

The SI unit is kg/m³ (equal to g/L).

Molar concentration

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

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 $C_{i}$ is defined as the number of entities of a constituent $N_{i}$ in a mixture divided by the volume of the mixture $V$ :

C_{i} = \frac{N_{i}}{V} .

The SI unit is 1/m³.

Volume concentration

The volume concentration $σ_{i}$ (not to be confused with volume fraction^[3]) is defined as the volume of a constituent $V_{i}$ divided by the volume of the mixture $V$ :

σ_{i} = \frac{V_{i}}{V} .

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 $σ_{i}$ used here is normative in German literature (see Volumenkonzentration).

Related quantities

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

Normality

Normality is defined as the molar concentration $c_{i}$ divided by an equivalence factor $f_{e q}$ . Since the definition of the equivalence factor depends on context (which reaction is being studied), the International Union of Pure and Applied Chemistry and National Institute of Standards and Technology discourage the use of normality.

Molality

The molality of a solution $b_{i}$ is defined as the amount of a constituent $n_{i}$ (in moles) divided by the mass of the solvent $m_{s o l v e n t}$ (not the mass of the solution):

b_{i} = \frac{n_{i}}{m_{s o l v e n t}} .

The SI unit for molality is mol/kg.

Mole fraction

The mole fraction $x_{i}$ is defined as the amount of a constituent $n_{i}$ (in moles) divided by the total amount of all constituents in a mixture $n_{t o t}$ :

x_{i} = \frac{n_{i}}{n_{t o t}} .

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 $r_{i}$ is defined as the amount of a constituent $n_{i}$ divided by the total amount of all other constituents in a mixture:

r_{i} = \frac{n_{i}}{n_{t o t} - n_{i}} .

If $n_{i}$ is much smaller than $n_{t o t}$ , 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 $w_{i}$ is the fraction of one substance with mass $m_{i}$ to the mass of the total mixture $m_{t o t}$ , defined as:

w_{i} = \frac{m_{i}}{m_{t o t}} .

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 $ζ_{i}$ is defined as the mass of a constituent $m_{i}$ divided by the total mass of all other constituents in a mixture:

ζ_{i} = \frac{m_{i}}{m_{t o t} - m_{i}} .

If $m_{i}$ is much smaller than $m_{t o t}$ , 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

Concentration type	Symbol	Definition	SI unit	other unit(s)
mass concentration	$ρ_{i}$ or $γ_{i}$	$m_{i} / V$	kg/m³	g/100mL (= g/dL)
molar concentration	$c_{i}$	$n_{i} / V$	mol/m³	M (= mol/L)
number concentration	$C_{i}$	$N_{i} / V$	1/m³	1/cm³
volume concentration	$σ_{i}$	$V_{i} / V$	m³/m³
Related quantities	Symbol	Definition	SI unit	other unit(s)
normality		$c_{i} / f_{e q}$	mol/m³	M (= mol/L)
molality	$b_{i}$	$n_{i} / m_{s o l v e n t}$	mol/kg	m
mole fraction	$x_{i}$	$n_{i} / n_{t o t}$	mol/mol	ppm, ppb, ppt
mole ratio	$r_{i}$	$n_{i} / (n_{t o t} - n_{i})$	mol/mol	ppm, ppb, ppt
mass fraction	$w_{i}$	$m_{i} / m_{t o t}$	kg/kg	ppm, ppb, ppt
mass ratio	$ζ_{i}$	$m_{i} / (m_{t o t} - m_{i})$	kg/kg	ppm, ppb, ppt
volume fraction	$ϕ_{i}$	$V_{i} / \sum_{j} V_{j}$	m³/m³	ppm, ppb, ppt

References

↑ ^1.0 ^1.1 IUPAC, Compendium of Chemical Terminology, 2nd ed. (the "Gold Book") (1997). Online corrected version: (2006–) "concentration". doi:10.1351/goldbook.C01222
↑ "concentration". Oxford English Dictionary (Online ed.). Oxford University Press. (Subscription or participating institution membership required.)
↑ IUPAC, Compendium of Chemical Terminology, 2nd ed. (the "Gold Book") (1997). Online corrected version: (2006–) "volume fraction". doi:10.1351/goldbook.V06643

External links

File:Commons-logo.svg Media related to Concentration (chemistry) at Wikimedia Commons

[goldbook-1] 1.0 ^1.1 IUPAC, Compendium of Chemical Terminology, 2nd ed. (the "Gold Book") (1997). Online corrected version: (2006–) "concentration". doi:10.1351/goldbook.C01222

[2] "concentration". Oxford English Dictionary (Online ed.). Oxford University Press. (Subscription or participating institution membership required.)

[goldbook2-3] IUPAC, Compendium of Chemical Terminology, 2nd ed. (the "Gold Book") (1997). Online corrected version: (2006–) "volume fraction". doi:10.1351/goldbook.V06643

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v t e Chemical solutions
Solution	Ideal solution Aqueous solution Solid solution Buffer solution Flory–Huggins Mixture Suspension Colloid Phase diagram Phase separation Eutectic point Alloy Saturation Supersaturation Serial dilution Dilution (equation) Apparent molar property Miscibility gap
Concentration and related quantities	Molar concentration Mass concentration Number concentration Volume concentration Normality Molality Mole fraction Mass fraction Isotopic abundance Mixing ratio Ternary plot
Solubility	Solubility equilibrium Total dissolved solids Solvation Solvation shell Enthalpy of solution Lattice energy Raoult's law Henry's law Solubility table (data) Solubility chart Miscibility
Solvent	(Category) Acid dissociation constant Protic solvent Polar aprotic solvent Inorganic nonaqueous solvent Solvation List of boiling and freezing information of solvents Partition coefficient Polarity Hydrophobe Hydrophile Lipophilic Amphiphile Lyonium ion Lyate ion

Concentration

Contents

Etymology

Qualitative description

Quantitative notation

Mass fraction

Mass concentration

Molar concentration

Number concentration

Volume concentration

Related quantities

Normality

Molality

Mole fraction

Mole ratio

Mass fraction

Mass ratio

Dependence on volume and temperature

Table of concentrations and related quantities

See also

References

External links

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