Concentration

For other uses, seeConcentration (disambiguation).

Inchemistry,concentrationis theabundanceof a constituent divided by the total volume of a mixture. Several types of mathematical description can be distinguished:mass concentration,molar concentration,number concentration,andvolume concentration.The concentration can refer to any kind of chemical mixture, but most frequently refers to solutes andsolventsinsolutions.The molar (amount) concentration has variants, such asnormal concentrationandosmotic concentration.Dilutionis reduction of concentration, e.g. by adding solvent to a solution. The verbto concentratemeans 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 inpost-classical Latinin 1550 or earlier, similar terms attested in Italian (1589), Spanish (1589), English (1606), French (1632).

Qualitative description

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 aqualitativeway, through the use of adjectives such as "dilute" for solutions of relatively low concentration and "concentrated" for solutions of relatively high concentration. Toconcentratea solution, one must add moresolute(for example, alcohol), or reduce the amount ofsolvent(for example, water). By contrast, todilutea solution, one must add more solvent, or reduce the amount of solute. Unless two substances aremiscible,there exists a concentration at which no further solute will dissolve in a solution. At this point, the solution is said to besaturated.If additional solute is added to a saturated solution, it will not dissolve, except in certain circumstances, whensupersaturationmay occur. Instead,phase separationwill occur, leading to coexisting phases, either completely separated or mixed as asuspension.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 calledlevels,reflecting the mentalschemaoflevels on the vertical axisof agraph,which can behigh or low(for example, "high serum levels of bilirubin" are concentrations ofbilirubinin theblood serumthat are greaterthan 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 themassof a constituent$m_{i}$divided by the volume of the mixture$V$:

$\rho _{i}={\frac {m_{i}}{V}}.$

TheSI unitis kg/m³(equal to g/L).

Molar concentration

Main article:Molar concentration

The molar concentration$c_{i}$is defined as theamountof 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

Thevolume concentration$\sigma _{i}$(not to be confused withvolume 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%; its unit is 1.

There seems to be no standard notation in the English literature. The letter$\sigma _{i}$used here is normative in German literature (seeVolumenkonzentration).

Related quantities

Several other quantities can be used to describe the composition of a mixture. These shouldnotbe 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), theInternational Union of Pure and Applied ChemistryandNational Institute of Standards and Technologydiscourage the use of normality.

Molality

Main article:Molality

Not to be confused withMolarity.

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$m_{\mathrm {solvent} }$(notthe 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 deprecatedparts-per notationis 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 allotherconstituents 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 allotherconstituents 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 tothermal 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	M (= mol/L)
molality	$b_{i}$	$n_{i}/m_{\mathrm {solvent} }$	mol/kg	m
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
volume fraction	$\phi _{i}$	$V_{i}/\sum _{j}V_{j}$	m3/m3	ppm, ppb, ppt

See also

• Dilution ratio– Change in concentration when mixing two liquids
• Dose concentration– Ratio of part of a mixture to the wholePages displaying short descriptions of redirect targets
• Serial dilution– Step-wise dilution of a substance in solution
• Wine/water mixing problem
• Standard state § Solutes

External links

• Media related toConcentration (chemistry)at Wikimedia Commons