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# Molar concentration

In chemistry, molar concentration, also called molarity, is a measure of the concentration of a solute in a solution, or of any molecular, ionic, or atomic species in a given volume. However, in thermodynamics the use of molar concentration is often not very 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.

## Notation

Molar concentration is sometimes denoted by C or M, but more often by simply placing square brackets around the chemical formula or element symbol. For example,
CNa+ = [Na+]

denotes the molar concentration of sodium ions.

## Definition

Molar concentration or molarity C is defined as moles of solute per unit volume of solution, or per unit volume available to the species:

$C=frac\left\{nu\right\}\left\{V\right\}=frac\left\{N\right\}\left\{N_A,V\right\}=frac\left\{n\right\}\left\{N_A\right\}$ .

Here, $nu$ is the number of moles of the solute, N is the number of molecules present in the volume V, the ratio N/V is the number density n, and NA is the Avogadro's number, approximately 6.022×1023 mol-1.

## Units

The SI units for molar concentration are mol/m3. However, most chemical literature traditionally uses mol/dm3, which is the same as mol/L. These traditional units are often denoted by a capital letter M (pronounced "molar"), sometimes preceded by an SI prefix, as in:

mol/m3 = 10-3 mol/dm3 = 10-3 mol/L = 10-3 M = 1 mM .

This way, words "millimolar" and "micromolar" refer to mM and μM (10-3 mol/L and 10-6 mol/L) respectively.

## Examples

Most proteins are present in the bacteria such as E. coli at 60 copies or fewer. The volume of a bacterium is 10-15 L, which gives us C = N / (NA·V) = 10-7 M = 100 nM. (Here, nM is "nanomolar", i.e. 10-9 moles per litre).

Consider 2 grams of NaCl dissolved in 15 mL of water. As 58 grams of NaCl is 1 mole of molecules (since molar mass of NaCl is 58 g/mol), and 1 millilitre is 0.001 litre, this gives C = (2/58 mol)/(0.015 L) = 2.3 M.