Molar concentration

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 . 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

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 (FA) or analytical concentration (cA). For example, if a sodium carbonate solution () has a formal concentration of c() = 1 mol/L, the molar concentrations are c() = 2 mol/L and c() = 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:

title=Guide to the SI, Chapter 8| text=The term molarity and the symbol M should no longer be used because they, too, are obsolete. One should use instead amount-of-substance concentration of B and such units as mol/dm3, kmol/m3, or mol/L. (A solution of, for example, 0.1 mol/dm3 was often called a 0.1 molar solution, denoted 0.1 M solution. The molarity of the solution was said to be 0.1 M.)}}

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:

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{\overline{M}}{\rho}, where \overline{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\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 the thermal expansion coefficient of the mixture.

Examples

: ρ(NaCl) = = 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) = / 104.3 mL = 0.00192 mol/mL = 1.92 mol/L.

Here, 58 g/mol is the molar mass of NaCl. : 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. : c(H2O) = ≈ 55.5 mol/L.

Likewise, the concentration of solid hydrogen (molar mass = 2.02 g/mol) is : c(H2) = = 43.7 mol/L.

The concentration of pure osmium tetroxide (molar mass = 254.23 g/mol) is : c(OsO4) = = 20.1 mol/L. : C = 60 / (10−15 L) = 6 L−1.

The molar concentration is : c = = = 10−7 mol/L = 100 nmol/L.

References

References

1. "Dictionary.com {{!}} Meanings & Definitions of English Words".
2. Tro, Nivaldo J.. (6 January 2014). "Introductory chemistry essentials".
3. "amount concentration, ''c''".
4. Kaufman, Myron. (2002). "Principles of thermodynamics". CRC Press.
5. Harvey, David. (2020-06-15). "2.2: Concentration". Chemistry LibreTexts.