Concentration
In chemistry, concentration is the abundance of a constituent divided by the total volume of a mixture. Several types of mathematical description can be distinguished: mass concentration, molar concentration, number concentration, and volume concentration.^{[1]} The term concentration can be applied to any kind of chemical mixture, but most frequently it refers to solutes and solvents in solutions. The molar (amount) concentration has variants such as normal concentration and osmotic concentration.
Contents
Qualitative description
Often in informal, nontechnical language, concentration is described in a qualitative way, through the use of adjectives such as "dilute" for solutions of relatively low concentration and "concentrated" for solutions of relatively high concentration. To concentrate a solution, one must add more solute (for example, alcohol), or reduce the amount of solvent (for example, water). By contrast, to dilute a solution, one must add more solvent, or reduce the amount of solute. Unless two substances are fully miscible there exists a concentration at which no further solute will dissolve in a solution. At this point, the solution is said to be saturated. If additional solute is added to a saturated solution, it will not dissolve, except in certain circumstances, when supersaturation may occur. Instead, phase separation will occur, leading to coexisting phases, either completely separated or mixed as a suspension. The point of saturation depends on many variables such as ambient temperature and the precise chemical nature of the solvent and solute.
Quantitative notation
There are four quantities that describe concentration:
Mass concentration
The mass concentration \rho_i is defined as the mass of a constituent m_i divided by the volume of the mixture V:
 \rho_i = \frac {m_i}{V}.
The SI unit is kg/m^{3} (equal to g/L).
Molar concentration
The molar concentration c_i is defined as the amount of a constituent n_i (in moles) divided by the volume of the mixture V:
 c_i = \frac {n_i}{V}.
The SI unit is mol/m^{3}. However, more commonly the unit mol/L (= mol/dm^{3}) is used.
Number concentration
The number concentration C_i is defined as the number of entities of a constituent N_i in a mixture divided by the volume of the mixture V:
 C_i = \frac{N_i}{V}.
The SI unit is 1/m^{3}.
Volume concentration
The volume concentration \phi_i (do not confuse with volume fraction) is defined^{[1]} as the volume of a constituent V_i divided by the volume of the mixture V:
 \phi_i = \frac {V_i}{V}.
Being dimensionless, it is expressed as a number, e.g., 0.18 or 18%; its unit is 1.
Related quantities
Several other quantities can be used to describe the composition of a mixture. Note that these should not be called concentrations.^{[1]}
Normality
Normality is defined as the molar concentration c_i divided by an equivalence factor f_\mathrm{eq}. Since the definition of the equivalence factor depends on context (which reaction is being studied), IUPAC and NIST discourage the use of normality.
Molality
(Not to be confused with Molarity)
The molality of a solution b_i is defined as the amount of a constituent n_i (in moles) divided by the mass of the solvent m_\mathrm{solvent} (not the mass of the solution):
 b_i = \frac{n_i}{m_\mathrm{solvent}}.
The SI unit for molality is mol/kg.
Mole fraction
The mole fraction x_i is defined as the amount of a constituent n_i (in moles) divided by the total amount of all constituents in a mixture n_\mathrm{tot}:
 x_i = \frac {n_i}{n_\mathrm{tot}}.
The SI unit is mol/mol. However, the deprecated partsper notation is often used to describe small mole fractions.
Mole ratio
The mole ratio r_i is defined as the amount of a constituent n_i divided by the total amount of all other constituents in a mixture:
 r_i = \frac{n_i}{n_\mathrm{tot}n_i}.
If n_i is much smaller than n_\mathrm{tot}, the mole ratio is almost identical to the mole fraction.
The SI unit is mol/mol. However, the deprecated partsper notation is often used to describe small mole ratios.
Mass fraction
The mass fraction w_i is the fraction of one substance with mass m_i to the mass of the total mixture m_\mathrm{tot}, defined as:
 w_i = \frac {m_i}{m_\mathrm{tot}}.
The SI unit is kg/kg. However, the deprecated partsper notation is often used to describe small mass fractions.
Mass ratio
The mass ratio \zeta_i is defined as the mass of a constituent m_i divided by the total mass of all other constituents in a mixture:
 \zeta_i = \frac{m_i}{m_\mathrm{tot}m_i}.
If m_i is much smaller than m_\mathrm{tot}, the mass ratio is almost identical to the mass fraction.
The SI unit is kg/kg. However, the deprecated partsper notation is often used to describe small mass ratios.
Dependence on volume
Concentration depends on the variation of the volume of the solution due mainly to thermal expansion.
Concentration type  Symbol  Definition  SI unit  other unit(s) 

mass concentration  \rho_i or \gamma_i  m_i/V  kg/m^{3}  g/100mL (= g/dL) 
molar concentration  c_i  n_i/V  mol/m^{3}  M (= mol/L) 
number concentration  C_i  N_i/V  1/m^{3}  1/cm^{3} 
volume concentration  \phi_i  V_i/V  m^{3}/m^{3}  
Related quantities  Symbol  Definition  SI unit  other unit(s) 
normality  c_i/f_\mathrm{eq}  mol/m^{3}  N (= mol/L)  
molality  b_i  n_i/m_\mathrm{solvent}  mol/kg  
mole fraction  x_i  n_i/n_\mathrm{tot}  mol/mol  ppm, ppb, ppt 
mole ratio  r_i  n_i/(n_\mathrm{tot}n_i)  mol/mol  ppm, ppb, ppt 
mass fraction  w_i  m_i/m_\mathrm{tot}  kg/kg  ppm, ppb, ppt 
mass ratio  \zeta_i  m_i/(m_\mathrm{tot}m_i)  kg/kg  ppm, ppb, ppt 
See also
References
 ^ ^{a} ^{b} ^{c} IUPAC, Compendium of Chemical Terminology, 2nd ed. (the "Gold Book") (1997). Online corrected version: (2006–) "concentration".
