| Molar concentration | |
|---|---|
Common symbols | c,[chemical symbol or formula] |
| SI unit | mol/m3 |
Other units | mol/L, M |
Derivations from other quantities | c =n/V |
| Dimension | |
Molar concentration (also calledamount-of-substance concentration ormolarity) is the number of moles of solute per liter of solution.[1] Specifically, It is a measure of theconcentration of achemical species, in particular, of asolute in asolution, in terms ofamount of substance per unitvolume of solution. Inchemistry, the most commonly used unit for molarity is the number ofmoles perliter, having the unit symbol mol/L ormol/dm3 (1000 mol/m3) in SI units. Molar concentration is often depicted with square brackets around the substance of interest; for example with the hydronium ion [H3O+] = 4.57 x 10-9 mol/L.[2]
Molar concentration or molarity is most commonly expressed in units of moles ofsolute per litre ofsolution.[3] For use in broader applications, it is defined asamount of substance of solute per unit volume of solution, or per unit volume available to the species, represented by lowercase:[4]
Here, is the amount of the solute in moles,[5] is the number ofconstituent particles present in volume (in litres) of the solution, and is theAvogadro constant, since 2019 defined as exactly6.02214076×1023 mol−1. The ratio is thenumber density.
Inthermodynamics, the use of molar concentration is often not convenient because the volume of most solutions slightly depends ontemperature due tothermal expansion. This problem is usually resolved by introducing temperature correctionfactors, or by using a temperature-independent measure of concentration such asmolality.[5]
Thereciprocal quantity represents the dilution (volume) which can appear in Ostwald'slaw of dilution.
If a molecule or salt dissociates in solution, the concentration refers to the original chemical formula in solution, the molar concentration is sometimes calledformal concentration orformality (FA) oranalytical concentration (cA). For example, if a sodium carbonate solution (Na2CO3) has a formal concentration ofc(Na2CO3) = 1 mol/L, the molar concentrations arec(Na+) = 2 mol/L andc(CO2−3) = 1 mol/L because the salt dissociates into these ions.[6]
While there is clear consensus on the equivalence of units:
1mol/m3 = 10−3mol/dm3 = 10−3mol/L = 10−3 M = 1 mM = 1 mmol/L
guidance on unit names and abbreviations varies:
[A]mount concentration ...[a]lso called amount-of-substance concentration, substance concentration (in clinical chemistry) and in older literature molarity. ...The common unit is mole per cubic decimetre (mol dm−3) or mole per litre (mol L−1) sometimes denoted by M.
In the older literature this quantity was often calledmolarity, a usage that should be avoided due to the risk of confusion with the quantitymolality. Units commonly used for amount concentration are mol L−1 (or mol dm−3), mmol L−1, mmol L−1 etc., often denoted M, mM, uM etc. (pronounced molar, millimolar, micromolar).
The term molarity and the symbol M should no longer be used because they, too, are obsolete. One should use instead amount-of-substance concentration of B and such units as mol/dm3, kmol/m3, or mol/L. (A solution of, for example, 0.1 mol/dm3 was often called a 0.1 molar solution, denoted 0.1 M solution. The molarity of the solution was said to be 0.1 M.)
TheSI prefix "mega" (symbol M) has the same symbol. However, the prefix is never used alone, so "M" unambiguously denotes molar.Sub-multiples, such as "millimolar" (mM) and "nanomolar" (nM), consist of the unit preceded by anSI prefix:
| Name | Abbreviation | Concentration | |
|---|---|---|---|
| (mol/L) | (mol/m3) | ||
| millimolar | mM | 10−3 | 100=1 |
| micromolar | μM | 10−6 | 10−3 |
| nanomolar | nM | 10−9 | 10−6 |
| picomolar | pM | 10−12 | 10−9 |
| femtomolar | fM | 10−15 | 10−12 |
| attomolar | aM | 10−18 | 10−15 |
| zeptomolar | zM | 10−21 | 10−18 |
| yoctomolar | yM | 10−24 (6 particles per 10 L) | 10−21 |
| rontomolar | rM | 10−27 | 10−24 |
| quectomolar | qM | 10−30 | 10−27 |
The conversion tonumber concentration is given by
where is theAvogadro constant.
The conversion tomass concentration is given by
where is themolar mass of constituent.
The conversion tomole fraction is given by
where is the average molar mass of the solution, is thedensity of the solution.
A simpler relation can be obtained by considering the total molar concentration, namely, the sum of molar concentrations of all the components of the mixture:
The conversion tomass fraction is given by
For binary mixtures, the conversion tomolality is
where the solvent is substance 1, and the solute is substance 2.
For solutions with more than one solute, the conversion is
The sum of molar concentrations gives the total molar concentration, namely the density of the mixture divided by the molar mass of the mixture or by another name the reciprocal of the molar volume of the mixture. In an ionic solution, ionic strength is proportional to the sum of the molar concentration of salts.
The sum of products between these quantities equals one:
The molar concentration depends on the variation of the volume of the solution due mainly to thermal expansion. On small intervals of temperature, the dependence is
where is the molar concentration at a reference temperature, is thethermal expansion coefficient of the mixture.
The volume of such a solution is 104.3mL (volume is directly observable); its density is calculated to be 1.07 (111.6g/104.3mL)
The molar concentration of NaCl in the solution is therefore
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