| Molar concentration | |
| Symbols: | , |
| Unit: | mol/m3 |
| Otherunits: | mol/L |
| Dimension: | wikidata |
Molar concentration (also called molarity, amount concentration or substance concentration) 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 in SI units. A solution with a concentration of 1 mol/L is said to be 1 molar, commonly designated as 1 M or 1 M. 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>].
Molar concentration or molarity is most commonly expressed in units of moles of solute per litre of solution.[1] 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=
| n | |
| V |
=
| N | |
| NAV |
=
| C | |
| NA |
.
Here,
n
N
V
NA
| N | |
| V |
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.[2]
The reciprocal quantity represents the dilution (volume) which can appear in Ostwald's law of dilution.
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:
| 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 | |
Ci
Ci=ciNA,
where
NA
\rhoi
\rhoi=ciMi,
where
Mi
i
xi
xi=ci
| \overline{M | |
where
\overline{M}
\rho
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:
xi=
| ci | |
| c |
=
| ci | |
| \sumjcj |
.
wi
wi=ci
| Mi | |
| \rho |
.
b2
b2=
| c2 | |
| \rho-c1M1 |
,
where the solvent is substance 1, and the solute is substance 2.
For solutions with more than one solute, the conversion is
bi=
| ci | |
| \rho-\sumj ≠ cjMj |
.
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:
\sumici\overline{Vi}=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
ci=
| |||||
| 1+\alpha\DeltaT |
,
where
| c | |
| i,T0 |
\alpha