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 concentration, molar concentration, number concentration, and volume concentration.^[1] The term concentration can be applied to any kind of chemical mixture, but most frequently it refers to solutes and solvents in solutions. The molar (amount) concentration has variants such as normal concentration and osmotic concentration.

Qualitative description

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.

Quantitative notation

There are four quantities that describe concentration:

Mass concentration

The mass concentration $\rho_i$ is defined as the mass of a constituent $m_i$ divided by the volume of the mixture $V$:

$\rho_i = \frac {m_i}{V}.$

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 $\phi_i$ (do not confuse with volume fraction^[2]) is defined as the volume of a constituent $V_i$ divided by the volume of the mixture $V$:

$\phi_i = \frac {V_i}{V}.$

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

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 $c_i$ divided by an equivalence factor $f_\mathrm{eq}$. 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 $b_i$ is defined as the amount of a constituent $n_i$ (in moles) divided by the mass of the solvent $m_\mathrm{solvent}$ (not the mass of the solution):

$b_i = \frac{n_i}{m_\mathrm{solvent}}.$

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 $n_\mathrm{tot}$:

$x_i = \frac {n_i}{n_\mathrm{tot}}.$

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 $r_i$ is defined as the amount of a constituent $n_i$ divided by the total amount of all other constituents in a mixture:

$r_i = \frac{n_i}{n_\mathrm{tot}-n_i}.$

If $n_i$ is much smaller than $n_\mathrm{tot}$, 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 $w_i$ is the fraction of one substance with mass $m_i$ to the mass of the total mixture $m_\mathrm{tot}$, defined as:

$w_i = \frac {m_i}{m_\mathrm{tot}}.$

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 $\zeta_i$ is defined as the mass of a constituent $m_i$ divided by the total mass of all other constituents in a mixture:

$\zeta_i = \frac{m_i}{m_\mathrm{tot}-m_i}.$

If $m_i$ is much smaller than $m_\mathrm{tot}$, 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 due mainly to thermal expansion.

Table of concentrations and related quantities

Concentration type	Symbol	Definition	SI unit	other unit(s)
mass concentration	$\rho_i$ or $\gamma_i$	$m_i/V$	kg/m^3	g/100mL (= g/dL)
molar concentration	$c_i$	$n_i/V$	mol/m^3	M (= mol/L)
number concentration	$C_i$	$N_i/V$	1/m^3	1/cm^3
volume concentration	$\phi_i$	$V_i/V$	m^3/m^3
Related quantities	Symbol	Definition	SI unit	other unit(s)
normality		$c_i/f_\mathrm{eq}$	mol/m^3	N (= mol/L)
molality	$b_i$	$n_i/m_\mathrm{solvent}$	mol/kg
mole fraction	$x_i$	$n_i/n_\mathrm{tot}$	mol/mol	ppm, ppb, ppt
mole ratio	$r_i$	$n_i/(n_\mathrm{tot}-n_i)$	mol/mol	ppm, ppb, ppt
mass fraction	$w_i$	$m_i/m_\mathrm{tot}$	kg/kg	ppm, ppb, ppt
mass ratio	$\zeta_i$	$m_i/(m_\mathrm{tot}-m_i)$	kg/kg	ppm, ppb, ppt

See also

• Dilution ratio
• Dose concentration
• Serial dilution
• Wine/water mixing problem

References

1. IUPAC, Compendium of Chemical Terminology, 2nd ed. (the "Gold Book") (1997). Online corrected version:  (2006–) "concentration".
2. IUPAC, Compendium of Chemical Terminology, 2nd ed. (the "Gold Book") (1997). Online corrected version:  (2006–) "volume fraction".