, molar concentration
, also called molarity
, is a measure of the concentration
of a solute
in a solution
, or of any molecular
, 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
Molar concentration is sometimes denoted by C
, 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.
or molarity C
is defined as moles
per unit volume of solution
, or per unit volume available to the species:
Here, 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.
The SI units
for molar concentration are mol
. However, most chemical literature traditionally uses mol
, which is the same as mol
. 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.
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
) = 10-7
M = 100 nM. (Here, nM is "nanomolar", i.e.
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.