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 litre, having the unit symbol mol/L. A solution with a concentration of 1 mol/L is said to be 1 molar, commonly designated as 1 M.
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:^{[2]}
Here, n is the amount of the solute in moles,^{[3]}N is the number of molecules present in vol (in litres), the ratio N/V is the number concentration C, and N_{A} is the Avogadro constant, approximately 6.022×10^{23}mol^{−1}.
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.^{[3]}
The reciprocal quantity represents the dilution (volume) which can appear in Ostwald's law of dilution.
In the International System of Units (SI) the base unit for molar concentration is mol/m^{3}. However, this is impractical for most laboratory purposes and most chemical literature traditionally uses mol/dm^{3}, which is the same as mol/L. These traditional units are often denoted by the letter M, optionally preceded by an SI prefix as needed to denote sub-multiples, for example:
The adjectives "millimolar" and "micromolar" refer to mM and ?M (10^{-3}mol/L and 10^{-6}mol/L), respectively.
Name | Abbreviation | Concentration | Concentration (SI unit) |
---|---|---|---|
millimolar | mM | 10^{-3} mol/L | 10^{0} mol/m^{3} |
micromolar | ?M | 10^{-6} mol/L | 10^{-3} mol/m^{3} |
nanomolar | nM | 10^{-9} mol/L | 10^{-6} mol/m^{3} |
picomolar | pM | 10^{-12} mol/L | 10^{-9} mol/m^{3} |
femtomolar | fM | 10^{-15} mol/L | 10^{-12} mol/m^{3} |
attomolar | aM | 10^{-18} mol/L | 10^{-15} mol/m^{3} |
zeptomolar | zM | 10^{-21} mol/L | 10^{-18} mol/m^{3} |
yoctomolar | yM^{[4]} | 10^{-24} mol/L (6 particles per 10 L) |
10^{-21} mol/m^{3} |
The conversion to number concentration is given by
where is the Avogadro constant.
The conversion to mass concentration is given by
where is the molar mass of constituent .
The conversion to mole fraction is given by
where is the average molar mass of the solution, 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:
The conversion to mass fraction is given by
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
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.
The sum of products between these quantities equals one:
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
where is the molar concentration at a reference temperature, is the thermal expansion coefficient of the mixture.
Molar and mass concentration have different values in space where diffusion happens.
The density of such a solution is 1.07 g/mL, thus its volume is:
The molar concentration of NaCl in the solution is therefore:
Here, 58 g/mol is the molar mass of NaCl.
To create the solution, 11.6 g NaCl are placed in a volumetric flask, dissolved in some water, then followed by the addition of more water until the total volume reaches 100 mL.
Likewise, the concentration of solid hydrogen (molar mass = 2.02 g/mol) is:
The concentration of pure osmium tetroxide (molar mass = 254.23 g/mol) is:
The molar concentration is:
If the concentration refers to original chemical formula in solution, the molar concentration is sometimes called formal concentration. For example, if a sodium carbonate solution (Na_{2}CO_{3}) has a formal concentration of c(Na_{2}CO_{3}) = 1 mol/L, the molar concentrations are c(Na^{+}) = 2 mol/L and c(CO^{2-}
_{3}) = 1 mol/L because the salt dissociates into these ions.