| Molar concentration | |
|---|---|
Common symbols | c,[chemical symbol or formula] |
| SI unit | mol/m3 |
Other units | mol/L |
Derivations from other quantities | c =n/V |
| Dimension | |
Molar concentration (also calledmolarity,amount concentration orsubstance concentration) 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 in SI units. A solution with a concentration of 1 mol/L is said to be 1 molar, commonly designated as 1 M or 1 M. Molarity is often depicted with square brackets around the substance of interest; for example, the molarity of the hydrogen ion is depicted as [H+].
Molar concentration or molarity is most commonly expressed in units of moles ofsolute per litre ofsolution.[1] 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:[2]
Here, is the amount of the solute in moles,[3] 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.[3]
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.[4]
In theInternational System of Units (SI), thecoherent unit for molar concentration ismol/m3. However, most chemical literature traditionally usesmol/dm3, which is the same asmol/L. This traditional unit is often called amolar and denoted by the letter M, for example:
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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