Molar concentration

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"Molarity" redirects here. It is not to be confused with Molality.


c_i = \frac {n_i}{V}

It is also called molarity, amount-of-substance concentration, amount concentration, substance concentration, or simply concentration. Whereas mole fraction is a ratio of moles to moles, molar concentration is a ratio of moles to volume. The volume V in the definition c_i = n_i/V refers to the volume of the solution, not the volume of the solvent. One litre of a solution usually contains either slightly more or slightly less than 1 liter of solvent because the process of dissolution causes volume of liquid to increase or decrease (discussed further at volume fraction).


Units and notation[edit]

In addition to the notation c_i there is a notation using brackets and the formula of a compound like [A]. This notation is encountered especially in equilibrium constants and reaction quotients.

The SI unit is mol/m3. However, more commonly the unit mol/L is used. A solution of concentration 1 mol/L is also denoted as "1 molar" (1M). In many publication styles, the "M" symbol (as well as mM, µM, and so on) is like the degree (°) and percent (%) symbols in that it is closed up to the number, whereas most unit symbols (for example, cm, mm, L, mL, g, kg, s) take an intervening space. Some styles deprecate the M, mM, µM notation and replace it with mol/L, mmol/L, or µmol/L.



Name Abbreviation Concentration Concentration (SI unit)
millimolar mM 10−3 mol/dm3 100 mol/m3
yoctomolar yM[2] 10−24 mol/dm3
(1 particle per 1.6 L)
10−21 mol/m3

Related quantities[edit]

Number concentration[edit]

Main article: Number concentration

The conversion to number concentration C_i is given by:

C_i = c_i \cdot N_{\rm A}


Mass concentration[edit]

The conversion to mass concentration \rho_i is given by:

\rho_i = c_i \cdot M_i

where M_i is the molar mass of constituent i.

Mole fraction[edit]

Main article: Mole fraction

The conversion to mole fraction x_i is given by:

x_i = c_i \cdot \frac{M}{\rho} = c_i \cdot \frac{\sum_i x_i M_i}{\rho}
x_i= c_i \cdot \frac{\sum x_j M_j}{\rho - c_i M_i}

where M is the average molar mass of the solution, \rho is the density of the solution and j is the index of other solutes.

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 c_i}

Mass fraction[edit]

The conversion to mass fraction w_i is given by:

w_i = c_i \cdot \frac{M_i}{\rho}


Main article: Molality

The conversion to molality (for binary mixtures) is:


where the solute is assigned the subscript 2.

For solutions with more than one solute, the conversion is:



Sum of molar concentrations – normalizing relation[edit]

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 molar concentration of salts.

Sum of products molar concentrations-partial molar volumes[edit]

The sum of products between these quantities equals one.

\sum_i c_i \cdot \bar{V_i} = 1

Dependence on volume[edit]


c_i = \frac {{c_{i,T_0}}}{{(1 + \alpha \cdot \Delta T)}}

where c_{i,T_0} is the molar concentration at a reference temperature, \alpha is the thermal expansion coefficient of the mixture.

Spatial variation and diffusion[edit]







The molar concentration of NaCl in the solution is therefore:




m(NaCl) = 2 mol/L x 0.1 L x 58 g/mol = 11.6 g










The molar concentration is:

Reference ranges for blood tests, sorted by molar concentration.




External links[edit]