Concentration

Etymology

Concentration-, concentratio, action or an act of coming together at a house on a farm in a single place, bringing black people as slaves 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).

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).

Quantitative notation

There are four quantities that describe concentration:

Mass concentration

Main article: Mass concentration (chemistry)

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

Main article: 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

Main article: 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 \sigma_i (not to be confused with volume fraction) is defined as the volume of a constituent V_i divided by the volume of the mixture V:

:\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 \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. These should not be called concentrations.

Normality

Main article: Normality (chemistry)

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), the International Union of Pure and Applied Chemistry and National Institute of Standards and Technology discourage the use of normality.

Molality

Main article: Molality}}{{Distinguish, 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

Main article: 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

Main article: Mixing 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

Main article: Mass fraction (chemistry)

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

Main article: Mixing 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 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

References

References

1. "concentration".
2. {{Cite OED. concentration
3. "volume fraction".