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 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 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).^[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).

Formulation

There are four quantities that describe concentration:

Mass concentration

The mass concentration Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \rho_i} is defined as the mass of a constituent Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle m_i} divided by the volume of the mixture Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle V} :

Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \rho_i = \frac {m_i}{V}.}

The SI unit is kg/m³ (equal to g/L).

Molar concentration

The molar concentration Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle c_i} is defined as the amount of a constituent Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle n_i} (in moles) divided by the volume of the mixture Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle V} :

Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\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 Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle C_i} is defined as the number of entities of a constituent Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle N_i} in a mixture divided by the volume of the mixture Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle V} :

Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle C_i = \frac{N_i}{V}.}

The SI unit is 1/m³.

Volume concentration

The volume concentration Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \sigma_i} (not to be confused with volume fraction^[3]) is defined as the volume of a constituent Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle V_i} divided by the volume of the mixture Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle V} :

Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\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 Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \sigma_i} used here is normative in German literature^[4] (see Volumenkonzentration in the German Wikipedia).

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 Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle c_i} divided by an equivalence factor Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle 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

The molality of a solution Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle b_i} is defined as the amount of a constituent Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle n_i} (in moles) divided by the mass of the solvent Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle m_\mathrm{solvent}} (not the mass of the solution):

Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle b_i = \frac{n_i}{m_\mathrm{solvent}}.}

The SI unit for molality is mol/kg.

Mole fraction

The mole fraction Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle x_i} is defined as the amount of a constituent Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle 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 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	$\rho _{i}$ or $\gamma _{i}$	$m_{i}/V$	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	$\sigma _{i}$	$V_{i}/V$	m³/m³
Related quantities	Symbol	Definition	SI unit	other unit(s)
normality		$c_{i}/f_{\mathrm {eq} }$	mol/m³	N (= mol/L)
molality	$b_{i}$	$n_{i}/m_{\mathrm {solvent} }$	mol/kg	m
mole fraction	Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle x_i}	Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle n_i/n_\mathrm{tot}}	mol/mol	ppm, ppb, ppt
mole ratio	$r_{i}$	Failed to parse (Conversion error. Server ("https://wikimedia.org/api/rest_") reported: "Cannot get mml. Server problem."): {\displaystyle n_{i}/(n_{\mathrm {tot} }-n_{i})}	mol/mol	ppm, ppb, ppt
mass fraction	Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle w_i}	Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle m_i/m_\mathrm{tot}}	kg/kg	ppm, ppb, ppt
mass ratio	Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \zeta_i}	Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle m_i/(m_\mathrm{tot}-m_i)}	kg/kg	ppm, ppb, ppt
volume fraction	Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \phi_i}	Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle V_i/\sum_j V_j}	m³/m³	ppm, ppb, ppt

References

↑ ^1.0 ^1.1 Template:GoldBookRef
↑ "concentration". Oxford English Dictionary (Online ed.). Oxford University Press. (Subscription or participating institution membership required.)
↑ Template:GoldBookRef
↑ Norm DIN 1310 [de]: Zusammensetzung von Mischphasen (Gasgemische, Lösungen, Mischkristalle); Begriffe, Formelzeichen. 1984.

External links

Media related to Concentration (chemistry) at Wikimedia Commons

Template:Chemical solutions

[goldbook-1] 1.0 ^1.1 Template:GoldBookRef

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

[goldbook2-3] Template:GoldBookRef

[DIN_1310-4] Norm DIN 1310 [de]: Zusammensetzung von Mischphasen (Gasgemische, Lösungen, Mischkristalle); Begriffe, Formelzeichen. 1984.

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Concentration

Contents

Etymology

Qualitative description