Molar concentration

Template:Short description Template:Redirect-distinguish Template:Infobox physical quantity Molar concentration (also called amount-of-substance concentration or molarity) is the number of moles of solute per liter of solution. Specifically, it 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 (1000 mol/m³) (really (mol/m³)/1000) in SI units. Molar concentration is often depicted with square brackets around the substance of interest; for example, the molarity of the hydronium ion is denoted as [H₃O⁺].

Definition

Molar concentration, or molarity, is most commonly expressed in units of moles of solute per litre of solution. 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 $c$:

$c=\frac{n}{V}=\frac{N}{N_{\text{A}}V}=\frac{C}{N_{\text{A}}}.$

Here, $n$ is the amount of the solute in moles, $N$ is the number of constituent particles present in volume $V$ (in litres) of the solution, and $N_{\text{A}}$ is the Avogadro constant, since 2019 defined as exactly Template:Physconst. The ratio $N/V$ is the number density $C$.

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.

The reciprocal quantity represents the dilution (volume) which can appear in Ostwald's law of dilution.

Formality or analytical concentration

Template:Anchor 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 (F_A) or analytical concentration (c_A). For example, if a sodium carbonate solution (Template:Chem2) has a formal concentration of c(Template:Chem2) = 1 mol/L, the molar concentrations are c(Template:Chem2) = 2 mol/L and c(Template:Chem2) = 1 mol/L because the salt dissociates into these ions.

Units

While there is clear consensus on the equivalence of units:

1 mol/m³ = 10⁻³ mol/dm³ = 10⁻³ mol/L = 10⁻³ M = 1 mM = 1 mmol/L,

guidance on unit names and abbreviations varies:

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: Template:Table alignment

Name	Abbre- viation	Concentration		Number of particles
		(mol/L)	(mol/m3)	per L	per m3
Template:Anchormillimolar	mM	10−3	100 = 1	~6Template:E	~6Template:E
micromolar	μM	10−6	10−3	~6Template:E	~6Template:E
nanomolar	nM	10−9	10−6	~6Template:E	~6Template:E
picomolar	pM	10−12	10−9	~6Template:E	~6Template:E
femtomolar	fM	10−15	10−12	~6Template:E	~6Template:E
attomolar	aM	10−18	10−15	~6Template:E	~6Template:E
zeptomolar	zM	10−21	10−18	~600	~6Template:E
yoctomolar	yM	10−24	10−21	~0.6	~600
rontomolar	rM	10−27	10−24	~6Template:E	~0.6
quectomolar	qM	10−30	10−27	~6Template:E	~6Template:E

Related quantities

Number concentration

The conversion to number concentration $C_i$ is given by

$C_i=c_i{N}_{\text{A}},$

where $N_{\text{A}}$ is the Avogadro constant.

Mass concentration

The conversion to mass concentration ${\rho }_i$ is given by

${\rho }_i=c_i{M}_i,$

where $M_i$ is the molar mass of constituent $i$.

Mole fraction

The conversion to mole fraction $x_i$ is given by

$x_i=c_i\frac{\bar{M}}{\rho },$

where $\bar{M}$ is the average molar mass of the solution, $\rho$ 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:

$x_i=\frac{c_i}{c}=\frac{c_i}{\sum _j{c}_j}.$

Mass fraction

The conversion to mass fraction $w_i$ is given by

$w_i=c_i\frac{M_i}{\rho }.$

Molality

For binary mixtures, the conversion to molality $b_2$ is

$b_2=\frac{c_2}{\rho -c_1{M}_1},$

where the solvent is substance 1, and the solute is substance 2.

For solutions with more than one solute, the conversion is

$b_i=\frac{c_i}{\rho -\sum _{j\ne i}{c}_j{M}_j}.$

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:

$\sum _i{c}_i\overline{V_i}=1.$

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

$c_i=\frac{c_{i,T_0}}{1+\alpha \mathrm{\Delta }T},$

where $c_{i,T_0}$ is the molar concentration at a reference temperature, $\alpha$ is the thermal expansion coefficient of the mixture.

See also

• Molality
• Normality
• Orders of magnitude (molar concentration)

External links

• Molar Solution Concentration Calculator
• Experiment to determine the molar concentration of vinegar by titration