Molar concentration

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 <math>c</math>:

: <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,

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

Formality or analytical concentration

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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 () has a formal concentration of c() = 1&nbsp;mol/L, the molar concentrations are c() = 2&nbsp;mol/L and c() = 1&nbsp;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&nbsp;M = 1&nbsp;mM = 1&nbsp;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:

{| class="wikitable" style="text-align:center;" border="0"

|-

! rowspan=2 | Name

! rowspan=2 | Abbreviation

! colspan=2 | 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<br />(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 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 <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 <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

See also

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

References

External links

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

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