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 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).

Formulation

There are four quantities that describe concentration:

Mass concentration

The mass concentration ${\displaystyle {\rho }_i}$ is defined as the mass of a constituent ${\displaystyle m_i}$ divided by the volume of the mixture ${\displaystyle V}$:

${\displaystyle {\rho }_i=\frac{m_i}{V}.}$

The SI unit is kg/m³ (equal to g/L).

Molar concentration

The molar concentration ${\displaystyle c_i}$ is defined as the amount of a constituent ${\displaystyle n_i}$ (in moles) divided by the volume of the mixture ${\displaystyle V}$:

${\displaystyle c_i=\frac{n_i}{V}.}$

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

Number concentration

The number concentration ${\displaystyle C_i}$ is defined as the number of entities of a constituent ${\displaystyle N_i}$ in a mixture divided by the volume of the mixture ${\displaystyle V}$:

${\displaystyle C_i=\frac{N_i}{V}.}$

The SI unit is 1/m³.

Volume concentration

The volume concentration ${\displaystyle {\sigma }_i}$ (not to be confused with volume fraction) is defined as the volume of a constituent ${\displaystyle V_i}$ divided by the volume of the mixture ${\displaystyle V}$:

${\displaystyle {\sigma }_i=\frac{V_i}{V}.}$

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 ${\displaystyle {\sigma }_i}$ used here is normative in German literature ().

Related quantities

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

Normality

Normality is defined as the molar concentration ${\displaystyle c_i}$ divided by an equivalence factor ${\displaystyle f_{\mathrm{e}\mathrm{q}}}$. 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 ${\displaystyle b_i}$ is defined as the amount of a constituent ${\displaystyle n_i}$ (in moles) divided by the mass of the solvent ${\displaystyle m_{\mathrm{s}\mathrm{o}\mathrm{l}\mathrm{v}\mathrm{e}\mathrm{n}\mathrm{t}}}$ (not the mass of the solution):

${\displaystyle b_i=\frac{n_i}{m_{\mathrm{s}\mathrm{o}\mathrm{l}\mathrm{v}\mathrm{e}\mathrm{n}\mathrm{t}}}.}$

The SI unit for molality is mol/kg.

Mole fraction

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

${\displaystyle x_i=\frac{n_i}{n_{\mathrm{t}\mathrm{o}\mathrm{t}}}.}$

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

${\displaystyle r_i=\frac{n_i}{n_{\mathrm{t}\mathrm{o}\mathrm{t}}-n_i}.}$

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

${\displaystyle w_i=\frac{m_i}{m_{\mathrm{t}\mathrm{o}\mathrm{t}}}.}$

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 ${\displaystyle {\zeta }_i}$ is defined as the mass of a constituent ${\displaystyle m_i}$ divided by the total mass of all other constituents in a mixture:

${\displaystyle {\zeta }_i=\frac{m_i}{m_{\mathrm{t}\mathrm{o}\mathrm{t}}-m_i}.}$

If ${\displaystyle m_i}$ is much smaller than ${\displaystyle m_{\mathrm{t}\mathrm{o}\mathrm{t}}}$, 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