Molar concentration

Molar concentration or molarity is most commonly expressed in units of moles of solute per litre of solution.{{Cite book|title=Introductory chemistry essentials|last=Tro, Nivaldo J.|date=6 January 2014|isbn=9780321919052|edition= Fifth|location=Boston|pages=457|oclc=857356651}} 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 $c$:{{GoldBookRef|title=amount concentration, c|file=A00295}}

:$c\; =\; \backslash frac\{n\}\{V\}\; =\; \backslash frac\{N\}\{N\_\backslash text\{A\}\backslash ,V\}\; =\; \backslash frac\{C\}\{N\_\backslash text\{A\}\}.$

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 $N\_\backslash text\{A\}$ is the Avogadro constant, since 2019 defined as exactly {{physconst|NA|ref=no}}. The ratio $\backslash frac\{N\}\{V\}$ 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.{{Cite book| author = Kaufman, Myron| title = Principles of thermodynamics| page = 213| publisher = CRC Press| year = 2002| isbn = 0-8247-0692-7}}

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

{{anchor|Formal}}

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 ({{chem2|Na2CO3}}) has a formal concentration of c({{chem2|Na2CO3}}) = 1 mol/L, the molar concentrations are c({{chem2|Na+}}) = 2 mol/L and c({{chem2|CO3(2−)}}) = 1 mol/L because the salt dissociates into these ions.{{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}}

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:

:1 mol/m³ = 10⁻³ mol/dm³ = 10⁻³ mol/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:

The conversion to number concentration $C\_i$ is given by

:$C\_i\; =\; c\_i\; N\_\backslash text\{A\},$

where $N\_\backslash text\{A\}$ is the Avogadro constant.

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

:$\backslash rho\_i\; =\; c\_i\; M\_i,$

where $M\_i$ is the molar mass of constituent $i$.

The conversion to mole fraction $x\_i$ is given by

:$x\_i\; =\; c\_i\; \backslash frac\{\backslash overline\{M\}\}\{\backslash rho\},$

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

:$x\_i\; =\; \backslash frac\{c\_i\}\{c\}\; =\; \backslash frac\{c\_i\}\{\backslash sum\_j\; c\_j\}.$

The conversion to mass fraction $w\_i$ is given by

:$w\_i\; =\; c\_i\; \backslash frac\{M\_i\}\{\backslash rho\}.$

For binary mixtures, the conversion to molality $b\_2$ is

:$b\_2\; =\; \backslash frac\{c\_2\}\{\backslash rho\; -\; c\_1\; M\_1\},$

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

For solutions with more than one solute, the conversion is

:$b\_i\; =\; \backslash frac\{c\_i\}\{\backslash rho\; -\; \backslash sum\_\{j\backslash neq\; i\}\; c\_j\; M\_j\}.$

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.

The sum of products between these quantities equals one:

:$\backslash sum\_i\; c\_i\; \backslash overline\{V\_i\}\; =\; 1.$

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

:$c\_i\; =\; \backslash frac\; \{c\_\{i,T\_0\}\}\{1\; +\; \backslash alpha\backslash Delta\; T\},$

where $c\_\{i,T\_0\}$ is the molar concentration at a reference temperature, $\backslash alpha$ is the thermal expansion coefficient of the mixture.

{{bulleted list

|1= 11.6 g of NaCl is dissolved in 100 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 g/mol is the molar mass of NaCl.

|2= 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.

|3= 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) = {{sfrac|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) = {{sfrac|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) = {{sfrac|5.1 kg/L |254.23 g/mol}} = 20.1 mol/L.

|4= 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 C is

:C = 60 / (10⁻¹⁵ L) = 6{{e|16}} L⁻¹.

The molar concentration is

:c = {{sfrac|C|N_A}} = {{sfrac|6{{e|16}} L⁻¹ |6{{e|23}} mol⁻¹}} = 10⁻⁷ 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=}}

}}

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

{{Reflist}}

• [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}}

Category:Concentration

Category:Molar quantities