Molar concentration
In chemistry, the molar concentration, is defined as the amount of a constituent (usually measured in moles – hence the name) divided by the volume of the mixture :^{1}
It is also called molarity, amountofsubstance 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 (volume) which can appear in Ostwald's law of dilution.
Contents
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/m^{3}. However, more commonly the unit mol/L is used. A solution of concentration 1 mol/L is also denoted as "1 molar" (1 M).
 1 mol/L = 1 mol/dm^{3} = 1 mol dm^{−3} = 1 M = 1000 mol/m^{3}.
An SI prefix is often used to denote concentrations. Commonly used units are listed in the table hereafter:
Name  Abbreviation  Concentration  Concentration (SI unit) 

millimolar  mM  10^{−3} mol/dm^{3}  10^{0} mol/m^{3} 
micromolar  μM  10^{−6} mol/dm^{3}  10^{−3} mol/m^{3} 
nanomolar  nM  10^{−9} mol/dm^{3}  10^{−6} mol/m^{3} 
picomolar  pM  10^{−12} mol/dm^{3}  10^{−9} mol/m^{3} 
femtomolar  fM  10^{−15} mol/dm^{3}  10^{−12} mol/m^{3} 
attomolar  aM  10^{−18} mol/dm^{3}  10^{−15} mol/m^{3} 
zeptomolar  zM  10^{−21} mol/dm^{3}  10^{−18} mol/m^{3} 
yoctomolar  yM^{2}  10^{−24} mol/dm^{3} (1 particle per 1.6 L) 
10^{−21} mol/m^{3} 
Related quantities
Number concentration
The conversion to number concentration is given by:
where is the Avogadro constant, approximately 6.022×10^{23} 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 (for binary mixtures) 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 concentrationspartial 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 (NaCl) will be:
 (NaCl) = 11.6 g / (11.6 g + 100 g) = 0.104 g/g = 10.4 %
The density of such a solution is 1.07 g/mL, thus its volume will be:
 = (11.6 g + 100 g) / (1.07 g/mL) = 104.3 mL
The molar concentration of NaCl in the solution is therefore:
 (NaCl) = (11.6 g / 58 g/mol) / 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 (= 0.1 L) 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 (or 1/18.02=0.055 mol/g). Therefore, the molar concentration of water is:
 (H_{2}O) = 1000 g/L / (18.02 g/mol) = 55.5 mol/L
Likewise, the concentration of solid hydrogen (molar mass = 2.02 g/mol) is:
 (H_{2}) = 88 g/L / (2.02 g/mol) = 43.7 mol/L
The concentration of pure osmium tetroxide (molar mass = 254.23 g/mol) is:
 (OsO_{4}) = 5.1 kg/L / (254.23 g/mol) = 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 / (10^{−15} L)= 6×10^{16} L^{−1}
The molar concentration is:
 = 6×10^{16} L^{−1} / (6×10^{23} mol^{−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 (Na_{2}CO_{3}) = 1 mol/L, the molar concentrations are (Na^{+}) = 2 mol/L and (CO_{3}^{2}) = 1 mol/L because the salt dissociates into these ions.
References
 ^ IUPAC, Compendium of Chemical Terminology, 2nd ed. (the "Gold Book") (1997). Online corrected version: (2006–) "amount concentration, c".
 ^ David Bradley. "How low can you go? The Y to Y".
External links
 Molar Solution Concentration Calculator
 Experiment to determine the molar concentration of vinegar by titration

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