In chemistry, the molar concentration, is defined as the amount of a constituent divided
by the volume of the mixture :
It is also called molarity, amount-of-substance concentration, amount concentration, substance
concentration, or simply concentration. The volume in the definition 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. The reciprocal quantity represents the dilution
which can appear in Ostwald's law of dilution.
Notation In addition to the notation 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. Units
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". 1 mol/L = 1 mol/dm3 = 1 mol dm−3 = 1 M = 1000
mol/m3. An SI prefix is often used to denote concentrations.
Commonly used units are listed in the table hereafter:
Related quantities Number concentration
The conversion to number concentration is given by:
where is the Avogadro constant, approximately 6.022×1023 mol−1.
Mass concentration
The conversion to mass concentration is given by:
where is the molar mass of constituent . Mole fraction
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.
Mass fraction
The conversion to mass fraction is given by:
Molality
The conversion to molality is:
where the solute is assigned the subscript 2.
For solutions with more than one solute, the conversion is:
Properties Sum of molar concentrations – normalizing
relation 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
The sum of products between these quantities equals one.
Dependence on volume 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. Spatial variation and diffusion
Molar and mass concentration have different values in space where diffusion happens.
Examples Example 1: Consider 11.6 g of NaCl dissolved
in 100 g of water. The final mass concentration will be:
(NaCl) = 11.6 g / = 0.104 g/g = 10.4 % The density of such a solution is 1.07 g/mL,
thus its volume will be: = / = 104.3 mL
The molar concentration of NaCl in the solution is therefore:
(NaCl) = / 104.3 mL = 0.00192 mol/mL = 1.92 mol/L
Here, 58 g/mol is the molar mass of NaCl. Example 2: Another typical task in chemistry
is the preparation of 100 mL of a 2 mol/L solution of NaCl in water. The mass of salt
needed is: (NaCl) = 2 mol/L * 0.1 L * 58 g/mol = 11.6
g 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. Example 3: The density of water is approximately
1000 g/L and its molar mass is 18.02 g/mol. Therefore, the molar concentration of water
is: (H2O) = 1000 g/L / = 55.5 mol/L
Likewise, the concentration of solid hydrogen is:
(H2) = 88 g/L / = 43.7 mol/L The concentration of pure osmium tetroxide
is: (OsO4) = 5.1 kg/L / = 20.1 mol/L.
Example 4: A typical protein in bacteria, such as E. coli, may have about 60 copies,
and the volume of a bacterium is about L. Thus, the number concentration is:
= 60 /= 6×1016 L−1 The molar concentration is:
= 6×1016 L−1 / = 10−7 mol/L = 100 nmol/L
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
has a formal concentration of = 1 mol/L, the molar concentrations are = 2 mol/L and
= 1 mol/L because the salt dissociates into these ions.
References
External links Molar Solution Concentration Calculator
Experiment to determine the molar concentration of vinegar by titration