Molar concentration

In chemistry, molar concentration (also called molarity, amount concentration or substance concentration) 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.

Definition

Molar concentration or molarity is most commonly in units of moles of solute per liter of solution. For use in broader applications, it is defined as amount of solute per unit volume of solution, or per unit volume available to the species, represented by lowercase c:

$c={\frac {n}{V}}={\frac {N}{N_{\rm {A}}\,V}}={\frac {C}{N_{\rm {A}}}}.$

Here, n is the amount of the solute in moles, N is the number of molecules present in the volume V (in litres), the ratio N/V is the number concentration C, and N_A is the Avogadro constant, approximately 6.022×10²³ mol⁻¹.
Or more simply: 1 molar = 1 M = 1 mole/litre.

Units

The SI units for molar concentration are mol/m³. However, most chemical literature traditionally uses mol/dm³, or mol dm^-3, 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 .

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

Name	Abbreviation	Concentration
Millimolar	mM	10-3 molar
Micromolar	μM	10-6 molar
Nanomolar	nM	10-9 molar
Picomolar	pM	10-12 molar
Femtomolar	fM	10-15 molar
Attomolar	aM	10-18 molar
Zeptomolar	zM	10-21 molar
Yoctomolar	yM	10-24 molar (1 molecule per 1.6 liters)

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/(N_A V) = 10⁻⁷ M = 100 nM. (Here, nM is "nanomolar", i.e. 10^-9 moles per liter).

Consider the preparation of 100 ml of a 2 M solution of NaCl in water. Since the molar mass of NaCl is 58 g/mol, the total mass needed is 2*(58 g)*(100 ml)/(1000 ml) = 11.6 g. Dissolve this in ~80 ml of water, and add water until the total volume reaches 100 ml.

By contrast, consider 11.6 g of NaCl dissolved in 100 ml of water. The density of water is about 1 g/ml, meaning that the final concentration of NaCl by mass will be (11.6 g)/(11.6 g + 100 g) = 10.4 %. The density of such a solution is 1.07 g/ml, and its volume will be (11.6 g + 100 g)/(1.07 g/ml) = 104.3 ml. The molar concentration of NaCl in the solution will therefore be (11.6 g)/(58 g/mol)/(104.3 ml)*1000 = 1.92 M.

Water approximates 1 kilogram (1000 grams) per liter under usual circumstances with a molecular mass of 18.0153. So the concentration of water in pure water is 55.5 molar. Likewise the concentration of hydrogen in solid hydrogen is 88 grams per liter / molecular weight 2.016 = 43.7 molar, and the concentration of osmium tetroxide in osmium tetroxide is 5.1 kilograms per liter / molecular weight 254.23 = 20.1 molar.

Reference ranges for blood tests, sorted by molar concentration.

See also

• Normality
• Osmolarity
• Molecular weight

External links

• Experiment to determine the molar concentration of vinegar by titration