Molar concentration

"Molarity" redirects here. Not to be confused withMolalityorMorality.

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	${\mathsf {L}}^{-3}{\mathsf {N}}$

Molar concentration(also calledmolarity,amount concentrationorsubstance concentration) is a measure of theconcentrationof achemical species,in particular, of asolutein asolution,in terms ofamount of substanceper unitvolumeof solution. Inchemistry,the most commonly used unit for molarity is the number ofmolesperliter,having the unit symbol mol/L ormol/dm³in SI units. A solution with a concentration of 1 mol/L is said to be 1molar,commonly designated as 1 M or 1M.Molarity is often depicted with square brackets around the substance of interest; for example, the molarity of the hydrogen ion is depicted as [H⁺].

Definition

Molar concentration or molarity is most commonly expressed in units of moles ofsoluteper litre ofsolution.For use in broader applications, it is defined asamount of substanceof 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 ofconstituent particlespresent in volume$V$(in litres) of the solution, and$N_{\text{A}}$is theAvogadro constant,since 2019 defined as exactly6.02214076×10²³mol⁻¹.The ratio${\frac {N}{V}}$is thenumber density$C$.

Inthermodynamics,the use of molar concentration is often not convenient because the volume of most solutions slightly depends ontemperaturedue tothermal expansion.This problem is usually resolved by introducing temperature correctionfactors,or by using a temperature-independent measure of concentration such asmolality.

Thereciprocalquantity represents the dilution (volume) which can appear in Ostwald'slaw of dilution.

Formality or analytical concentration

If a molecule or salt dissociates in solution, the concentration refers to the original chemical formula in solution, the molar concentration is sometimes calledformal concentrationorformality(F_A) oranalytical concentration(c_A). 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.

Units

In theInternational System of Units(SI), thecoherent unitfor molar concentration ismol/m³.However, most chemical literature traditionally usesmol/dm³,which is the same asmol/L.This traditional unit is often called amolarand denoted by the letter M, for example:

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

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

Related quantities

Number concentration

The conversion tonumber concentration$C_{i}$is given by

$C_{i}=c_{i}N_{\text{A}},$

where$N_{\text{A}}$is theAvogadro constant.

Mass concentration

The conversion tomass concentration$\rho _{i}$is given by

$\rho _{i}=c_{i}M_{i},$

where$M_{i}$is themolar massof constituent$i$.

Mole fraction

The conversion tomole fraction$x_{i}$is given by

$x_{i}=c_{i}{\frac {\overline {M}}{\rho }},$

where${\overline {M}}$is the average molar mass of the solution,$\rho$is thedensityof 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 tomass fraction$w_{i}$is given by

$w_{i}=c_{i}{\frac {M_{i}}{\rho }}.$

Molality

For binary mixtures, the conversion tomolality$b_{2}$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

$b_{i}={\frac {c_{i}}{\rho -\sum _{j\neq i}c_{j}M_{j}}}.$

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

$c_{i}={\frac {c_{i,T_{0}}}{1+\alpha \Delta T}},$

where$c_{i,T_{0}}$is the molar concentration at a reference temperature,$\alpha$is thethermal expansion coefficientof the mixture.

Examples

• 11.6 g ofNaClis dissolved in 100 g of water. The final mass concentrationρ(NaCl) is

  ρ(NaCl) =⁠11.6 g/11.6 g + 100 g⁠= 0.104 g/g = 10.4 %.

  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

  c(NaCl) =⁠11.6 g/58 g/mol⁠/ 104.3 mL = 0.00192 mol/mL = 1.92 mol/L.

  Here, 58 g/mol is themolar massof NaCl.
• 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 avolumetric flask,dissolved in some water, then followed by the addition of more water until the total volume reaches 100 mL.
• The density ofwateris 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 ofsolid hydrogen(molar mass = 2.02 g/mol) is

  c(H₂) =⁠88 g/L/2.02 g/mol⁠= 43.7 mol/L.

  The concentration of pureosmium 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 inbacteria,such asE. coli,may have about 60 copies, and the volume of a bacterium is about 10⁻¹⁵L. Thus, the number concentrationCis
  C= 60 / (10⁻¹⁵L) = 6×10¹⁶L⁻¹.
  The molar concentration is

  c=⁠C/N_A⁠=⁠6×10¹⁶L⁻¹/6×10²³mol⁻¹⁠= 10⁻⁷mol/L = 100 nmol/L.

• Reference ranges for blood tests,sorted by molar concentration:
  

See also

• Molality
• Orders of magnitude (molar concentration)

External links

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