Molar concentration (also called molarity, amount concentrationorsubstance concentration) is a measure of the concentration of a chemical species, in particular, of a solute in a solution, in terms of amount of substance per unit volume of solution. In chemistry, the most commonly used unit for molarity is the number of moles per liter, having the unit symbol mol/L or mol/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 of solute per litre of solution.[1] 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 :[2]
Here, is the amount of the solute in moles,[3] 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.
Inthermodynamics 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.[3]
The reciprocal quantity represents the dilution (volume) which can appear in Ostwald's law of dilution.
Formality or analytical concentration
If a molecular entity dissociates in solution, the concentration refers to the original chemical formula in solution, the molar concentration is sometimes called formal concentrationorformality (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.[4]
In the International System of Units (SI), the coherent unit for molar concentration is mol/m3. However, most chemical literature traditionally uses mol/dm3, which is the same as mol/L. This traditional unit is often called a molar and denoted by the letter M, for example:
1mol/m3 = 10−3mol/dm3 = 10−3mol/L = 10−3 M = 1 mM = 1 mmol/L.
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:
where is the average molar mass of the solution, is the density 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:
Sum of molar concentrations – normalizing relations[edit]
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[edit]
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
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
m(NaCl) = 2 mol/L × 0.1 L × 58 g/mol = 11.6 g.
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.
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
c(H2O) = 1000 g/L/18.02 g/mol ≈ 55.5 mol/L.
Likewise, the concentration of solid hydrogen (molar mass = 2.02 g/mol) is
c(H2) = 88 g/L/2.02 g/mol = 43.7 mol/L.
The concentration of pure osmium tetroxide (molar mass = 254.23 g/mol) is
c(OsO4) = 5.1 kg/L/254.23 g/mol = 20.1 mol/L.
A typical protein in bacteria, such as E. coli, may have about 60 copies, and the volume of a bacterium is about 10−15 L. Thus, the number concentration Cis