Concentration

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Concentration

In chemistry, concentration is defined as the abundance of a constituent divided by the total volume of a mixture. Four types 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 in homogeneous solutions.

Qualitative description

These glasses containing red dye demonstrate qualitative changes in concentration. The solutions on the left are more dilute, compared to the more concentrated solutions on the right.

Often in informal, non-technical 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 ρi is defined as the mass of a constituent mi divided by the volume of the mixture V:

$\rho_i = \frac {m_i}{V}$

The SI-unit is kg/m3.

Molar concentration

The molar concentration ci is defined as the amount of a constituent ni divided by the volume of the mixture V:

$c_i = \frac {n_i}{V}$

The SI-unit is mol/m3. However, more commonly the unit mol/L is used.

Number concentration

The number concentration Ci is defined as the number of entities of a constituent Ni in a mixture divided by the volume of the mixture V:

$C_i = \frac{N_i}{V}$

The SI-unit is 1/m3.

Volume concentration

The volume concentration ϕi (also called volume fraction) is defined as the volume of a constituent Vi divided by the volume of all consituents of the mixture V prior to mixing:

$\phi_i = \frac {V_i}{V}$

The SI-unit is m3/m3.

Related Quantities

Several other quantities can be used to describe the composition of a mixture. Note that these should not be called concentrations.

Normality

Normality is defined as the molar concentration ci divided by an equivalence factor feq. Since the definition of the equivalence factor may not be unequivocal, IUPAC and NIST discourage the use of normality.

Molality

The molality of a solution mi is defined as the amount of a constituent ni divided by the mass of the solvent msolvent (not the mass of the solution):

$m_i = \frac{n_i}{m_{solvent}}$

The SI-unit for molality is mol/kg.

Mole fraction

The mole fraction xi is defined as the amount of a constituent ni divided by the total amount of all constituents in a mixture ntot:

$x_i = \frac {n_i}{n_{tot}}$

The SI-unit is mol/mol. However, the deprecated parts-per notation is often used to describe small mole fractions.

Mole ratio

The mole ratio ri is defined as the amount of a constituent ni divided by the total amount of all other constituents in a mixture:

$r_i = \frac{n_i}{n_{tot}-n_i}$

If ni is much smaller than ntot, the mole ratio is almost identical to the mole fraction.

The SI-unit is mol/mol. However, the deprecated parts-per notation is often used to describe small mole ratios.

Mass fraction

The mass fraction wi is the fraction of one substance with mass mi to the mass of the total mixture mtot, defined as:

$w_i = \frac {m_i}{m_{tot}}$

The SI-unit is kg/kg. However, the deprecated parts-per notation is often used to describe small mass fractions.

Mass ratio

The mass ratio ζi is defined as the mass of a constituent mi divided by the total mass of all other constituents in a mixture:

$\zeta_i = \frac{m_i}{m_{tot}-m_i}$

If mi is much smaller than mtot, the mass ratio is almost identical to the mass fraction.

The SI-unit is kg/kg. However, the deprecated parts-per 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.

Table of concentrations and related quantities

Concentration type Symbol Definition SI-unit other unit(s)
mass concentration ρi or γi mi / V kg/m3 g/100mL (=g/dL)
molar concentration ci ni / V mol/m3 M (=mol/L)
number concentration Ci Ni / V 1/m3 1/cm3
volume concentration ϕi Vi / V m3/m3
Related quantities Symbol Definition SI-unit other unit(s)
normality UNIQ4e0e247d5b017e86-math-0000003E-QINU ci / feq mol/m3 M (=mol/L)
molality mi ni / msolvent mol/kg
mole fraction xi ni / ntot mol/mol ppm, ppb, ppt
mole ratio ri ni / (ntotni) mol/mol ppm, ppb, ppt
mass fraction wi mi / mtot kg/kg ppm, ppb, ppt
mass ratio ζi mi / (mtotmi) kg/kg ppm, ppb, ppt

References

1. ^ IUPAC, Compendium of Chemical Terminology, 2nd ed. (the "Gold Book") (1997). Online corrected version:  (2006–) "concentration".

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