View source for Molar concentration

{{Short description|Measure of concentration of a chemical}}
{{Redirect-distinguish|Molarity|Molality|Morality}}
{{Infobox physical quantity
| name = Molar concentration
| width =
| background =
| image =
| caption =
| symbols = {{mvar|c}}, {{nobr|[chemical symbol or formula]}}
| unit = mol/m<sup>3</sup>
| otherunits = mol/L
| dimension = wikidata
| extensive =
| intensive =
| conserved =
| transformsas =
| derivations = {{math|1=''c'' = ''n''/''V''}}
}}
'''Molar concentration''' (also called '''molarity''', '''amount concentration''' or '''substance concentration''') is the number of moles of solute per liter of solution.<ref>{{Cite web |title=Dictionary.com {{!}} Meanings & Definitions of English Words |url=https://www.dictionary.com/browse/molarity |access-date=2025-05-15 |website=Dictionary.com |language=en}}</ref> Specifically, It is a measure of the [[concentration]] of a [[chemical species]], in particular, of a [[solute]] in a [[Solution (chemistry)|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 [[Mole (unit)|moles]] per [[liter]], having the unit symbol mol/L or [[Mole (unit)|mol]]/[[Decimetre|dm]]<sup>3</sup> (1000&nbsp;mol/[[Cubic metre|m<sup>3</sup>]]) in SI units. A solution with a concentration of 1&nbsp;mol/L is said to be 1&nbsp;'''molar''', commonly designated as 1&nbsp;M or 1&nbsp;<u>M</u>. Molarity is often depicted with square brackets around the substance of interest; for example, the molarity of the hydrogen ion is depicted as [H<sup>+</sup>].

==Definition==
Molar concentration or molarity is most commonly expressed in units of moles of [[solute]] per litre of [[Solution (chemistry)|solution]].<ref>{{Cite book|title=Introductory chemistry essentials|last=Tro, Nivaldo J.|date=6 January 2014|isbn=9780321919052|edition= Fifth|location=Boston|pages=457|oclc=857356651}}</ref> 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 <math>c</math>:<ref name="GoldBook">{{GoldBookRef|title=amount concentration, ''c''|file=A00295}}</ref>

:<math>c = \frac{n}{V} = \frac{N}{N_\text{A}\,V} = \frac{C}{N_\text{A}}.</math>

Here, <math>n</math> is the amount of the solute in moles,<ref name=kaufman/> <math>N</math> is the number of [[particle number|constituent particle]]s present in volume <math>V</math> (in litres) of the solution, and <math>N_\text{A}</math> is the [[Avogadro constant]], since 2019 defined as exactly {{physconst|NA|ref=no}}. The ratio <math>\frac{N}{V}</math> is the [[number density]] <math>C</math>.

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 [[coefficient|factors]], or by using a temperature-independent measure of concentration such as [[molality]].<ref name=kaufman>{{Cite book| author = Kaufman, Myron| title = Principles of thermodynamics| page = 213| publisher = CRC Press| year = 2002| isbn = 0-8247-0692-7}}</ref>

The [[wikt: reciprocal|reciprocal]] quantity represents the dilution (volume) which can appear in Ostwald's [[law of dilution]].

===Formality or analytical concentration===
{{anchor|Formal}}<!--[[Formal concentration]] redirects here --><!--[[Analytical concentration]] redirects here -->
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''<sub>A</sub>) or '''analytical concentration''' (''c''<sub>A</sub>). For example, if a sodium carbonate solution ({{chem2|Na2CO3}}) has a formal concentration of ''c''({{chem2|Na2CO3}}) = 1&nbsp;mol/L, the molar concentrations are ''c''({{chem2|Na+}}) = 2&nbsp;mol/L and ''c''({{chem2|CO3(2−)}}) = 1&nbsp;mol/L because the salt dissociates into these ions.<ref name="Harvey_2020">{{Cite web |title=2.2: Concentration |last=Harvey |first=David |work=Chemistry LibreTexts |date=2020-06-15 |access-date=2021-12-15 |url= https://chem.libretexts.org/Courses/BethuneCookman_University/B-CU%3A_CH-345_Quantitative_Analysis/Book%3A_Analytical_Chemistry_2.1_(Harvey)/02%3A_Basic_Tools_of_Analytical_Chemistry/2.02%3A_Concentration}}</ref>

==Units==
In the [[International System of Units]] (SI), the [[Coherence (units of measurement)|coherent unit]] for molar concentration is [[Mole (unit)|mol]]/[[Metre|m]]<sup>3</sup>. However, most chemical literature traditionally uses [[Mole (unit)|mol]]/[[Decimetre|dm]]<sup>3</sup>, which is the same as [[Mole (unit)|mol]]/[[Litre|L]]. This traditional unit is often called a '''molar''' and denoted by the letter M, for example:
:1 [[Mole (unit)|mol]]/[[Metre|m]]<sup>3</sup> = 10<sup>−3</sup> [[Mole (unit)|mol]]/[[Decimetre|dm]]<sup>3</sup> = 10<sup>−3</sup> [[Mole (unit)|mol]]/[[Litre|L]] = 10<sup>−3</sup>&nbsp;M = 1&nbsp;mM = 1&nbsp;mmol/L.

The [[SI prefix]] "[[Mega-|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]]:

{| class="wikitable" style="text-align:center;" border="0"
|-
! rowspan=2 | Name
! rowspan=2 | Abbreviation
! colspan=2 | Concentration
|-
! (mol/L)
! (mol/m<sup>3</sup>)
|-
|{{anchor|millimolar}}millimolar
|mM
|10<sup>−3</sup>
|10<sup>0</sup>=1
|-
|micromolar
|μM
|10<sup>−6</sup>
|10<sup>−3</sup>
|-
|nanomolar
|nM
|10<sup>−9</sup>
|10<sup>−6</sup>
|-
|picomolar
|pM
|10<sup>−12</sup>
|10<sup>−9</sup>
|-
|femtomolar
|fM
|10<sup>−15</sup>
|10<sup>−12</sup>
|-
|attomolar
|aM
|10<sup>−18</sup>
|10<sup>−15</sup>
|-
|zeptomolar
|zM
|10<sup>−21</sup>
|10<sup>−18</sup>
|-
|yoctomolar
|yM
|10<sup>−24</sup><br />(6 particles per 10 L)
|10<sup>−21</sup>
|-
|rontomolar
|rM
|10<sup>−27</sup>
|10<sup>−24</sup>
|-
|quectomolar
|qM
|10<sup>−30</sup>
|10<sup>−27</sup>
|}

== Related quantities ==
=== Number concentration ===
The conversion to [[number concentration]] <math>C_i</math> is given by

:<math>C_i = c_i N_\text{A},</math>

where <math>N_\text{A}</math> is the [[Avogadro constant]].

=== Mass concentration ===
The conversion to [[mass concentration (chemistry)|mass concentration]] <math>\rho_i</math> is given by

:<math>\rho_i = c_i M_i,</math>

where <math>M_i</math> is the [[molar mass]] of constituent <math>i</math>.

=== Mole fraction ===
The conversion to [[mole fraction]] <math>x_i</math> is given by

:<math>x_i = c_i \frac{\overline{M}}{\rho},</math>

where <math>\overline{M}</math> is the average molar mass of the solution, <math>\rho</math> 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:

:<math>x_i = \frac{c_i}{c} = \frac{c_i}{\sum_j c_j}.</math>

=== Mass fraction ===
The conversion to [[mass fraction (chemistry)|mass fraction]] <math>w_i</math> is given by

:<math>w_i = c_i \frac{M_i}{\rho}.</math>

=== Molality ===
For binary mixtures, the conversion to [[molality]] <math>b_2</math> is

:<math>b_2 = \frac{c_2}{\rho - c_1 M_1},</math>

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

For solutions with more than one solute, the conversion is

:<math>b_i = \frac{c_i}{\rho - \sum_{j\neq i} c_j M_j}.</math>

== 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:
:<math>\sum_i c_i \overline{V_i} = 1.</math>

=== 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

:<math>c_i = \frac {c_{i,T_0}}{1 + \alpha\Delta T},</math>

where <math>c_{i,T_0}</math> is the molar concentration at a reference temperature, <math>\alpha</math> is the [[thermal expansion coefficient]] of the mixture.

== Examples ==
{{bulleted list
|1= 11.6&nbsp;g of [[NaCl]] is dissolved in 100&nbsp;g of water. The final mass concentration ''ρ''(NaCl) is
:''ρ''(NaCl) = {{sfrac|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) = {{sfrac|11.6 g |58 g/mol}} / 104.3 mL = 0.00192 mol/mL = 1.92 mol/L.

Here, 58&nbsp;g/mol is the [[molar mass]] of NaCl.
|2= A typical task in chemistry is the preparation of 100&nbsp;mL (= 0.1 L) of a 2&nbsp;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&nbsp;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&nbsp;mL.
|3= The density of [[water]] is approximately 1000 g/L and its molar mass is 18.02&nbsp;g/mol (or 1/18.02 = 0.055&nbsp;mol/g). Therefore, the molar concentration of water is
:''c''(H<sub>2</sub>O) = {{sfrac|1000 g/L |18.02 g/mol}} ≈ 55.5 mol/L.

Likewise, the concentration of [[solid hydrogen]] (molar mass = 2.02&nbsp;g/mol) is
:''c''(H<sub>2</sub>) = {{sfrac|88 g/L |2.02 g/mol}} = 43.7 mol/L.

The concentration of pure [[osmium tetroxide]] (molar mass = 254.23&nbsp;g/mol) is
:''c''(OsO<sub>4</sub>) = {{sfrac|5.1 kg/L |254.23 g/mol}} = 20.1 mol/L.
|4= A typical protein in [[bacterium|bacteria]], such as ''[[Escherichia coli|E. coli]]'', may have about 60 copies, and the volume of a bacterium is about 10<sup>−15</sup>&nbsp;L. Thus, the number concentration ''C'' is
:''C'' = 60 / (10<sup>−15</sup> L) = 6{{e|16}} L<sup>−1</sup>.

The molar concentration is
:''c'' = {{sfrac|''C''|''N''<sub>A</sub>}} = {{sfrac|6{{e|16}} L<sup>−1</sup> |6{{e|23}} mol<sup>−1</sup>}} = 10<sup>−7</sup> mol/L = 100 nmol/L.
|5= [[Reference ranges for blood tests]], sorted by molar concentration:
{{Wide image|Reference ranges for blood tests - by molarity.png|3000px|alt=}}
}}

==See also==
* [[Molality]]
* [[Normality (chemistry)|Normality]]
* [[Orders of magnitude (molar concentration)]]

== References ==
{{Reflist}}

== External links ==
* [http://www.physiologyweb.com/calculators/molar_solution_concentration_calculator.html Molar Solution Concentration Calculator]
* [http://web.lemoyne.edu/~giunta/chm151L/vinegar.html Experiment to determine the molar concentration of vinegar by titration]
{{Mole concepts}}
{{Chemical solutions}}

{{DEFAULTSORT:Molar Concentration}}
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[[Category:Concentration]]
[[Category:Molar quantities]]