Definition
Molar concentration, or molarity, is most commonly expressed in units of moles of solute per litre of solution.2 For use in broader applications, it is defined as amount of substance of solute per unit volume of solution, or per unit volume available to the species, represented by lowercase :3
Here, is the amount of the solute in moles,4 is the number of constituent particles present in volume (in litres) of the solution, and is the Avogadro constant, since 2019 defined as exactly 6.02214076×1023 mol−1. The ratio is the number density .
In thermodynamics, the use of molar concentration is often not convenient because the volume of most solutions slightly depends on temperature due to thermal expansion. This problem is usually resolved by introducing temperature correction factors, or by using a temperature-independent measure of concentration such as molality.4
The reciprocal quantity represents the dilution (volume) which can appear in Ostwald's law 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 called formal concentration or formality (FA) or analytical concentration (cA). For example, if a sodium carbonate solution (Na2CO3) has a formal concentration of c(Na2CO3) = 1 mol/L, the molar concentrations are c(Na+) = 2 mol/L and c(CO2−3) = 1 mol/L because the salt dissociates into these ions.5
Units
While there is clear consensus on the equivalence of units:
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.
— IUPAC, "Gold Book" 5ed
In the older literature this quantity was often called molarity, a usage that should be avoided due to the risk of confusion with the quantity molality. 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, μM etc. (pronounced molar, millimolar, micromolar).
— IUPAC, "Green Book" 3ed
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/dm, kmol/m, or mol/L. (A solution of, for example, 0.1 mol/dm 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.)
Properties
Sum of molar concentrations – normalizing relations
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.
Sum of products of molar concentrations and partial molar volumes
The sum of products between these quantities equals one:
Dependence on volume
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 the thermal expansion coefficient of the mixture.
Examples
- 11.6 g of NaCl is dissolved in 100 g of water. The final mass concentration ρ(NaCl) is 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
Here, 58 g/mol is the molar mass of NaCl.- ρ(NaCl) = 11.6 g/11.6 g + 100 g = 0.104 g/g = 10.4 %.
- c(NaCl) = 11.6 g/58 g/mol / 104.3 mL = 0.00192 mol/mL = 1.92 mol/L.
- A typical task in chemistry is the preparation of 100 mL (= 0.1 L) of a 2 mol/L solution of NaCl in water. The mass of salt needed is To create the solution, 11.6 g NaCl is placed in a volumetric flask, dissolved in some water, then followed by the addition of more water until the total volume reaches 100 mL.
- m(NaCl) = 2 mol/L × 0.1 L × 58 g/mol = 11.6 g.
- The density of water is approximately 1000 g/L and its molar mass is 18.02 g/mol (or 1/18.02 = 0.055 mol/g). Therefore, the molar concentration of water is Likewise, the concentration of solid hydrogen (molar mass = 2.02 g/mol) is The concentration of pure osmium tetroxide (molar mass = 254.23 g/mol) is
- c(H2O) = 1000 g/L/18.02 g/mol ≈ 55.5 mol/L.
- c(H2) = 88 g/L/2.02 g/mol = 43.7 mol/L.
- c(OsO4) = 5.1 kg/L/254.23 g/mol = 20.1 mol/L.
- A typical protein in bacteria, such as , may have about 60 copies, and the volume of a bacterium is about 10 L. Thus, the number concentration is = 60 / (10 L) = 6×10 L. The molar concentration is
The SI 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 an SI prefix:
E. coli
