Concentration

For other uses, see Concentration (disambiguation).

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. 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 either coexisting phases or 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

Main article: Mass concentration (chemistry)

The mass concentration ρ_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/m³.

Molar concentration

Main article: Molar concentration

The molar concentration c_i is defined as the amount of a constituent n_i 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

Main article: 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/m³.

Volume concentration

Main article: Volume concentration

The volume concentration ϕ_i (also called volume fraction) is defined as the volume of a constituent V_i 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

Main article: Normality (chemistry)

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

Molality

Main article: Molality

The molality of a solution m_i is defined as the amount of a constituent n_i divided by the mass of the solvent m_solvent (not the mass of the solution):

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

The SI-unit for molality is mol/kg.

Mole fraction

Main article: Mole fraction

The mole fraction x_i is defined as the amount of a constituent n_i divided by the total amount of all constituents in a mixture n_tot:

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

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

Mole ratio

Main article: Mixing 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:

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

If n_i is much smaller than n_tot, 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

Main article: Mass fraction (chemistry)

The mass fraction w_i is the fraction of one substance with mass m_i to the mass of the total mixture m_tot, 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

Main article: Mixing ratio

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

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

If m_i is much smaller than m_tot, 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	UNIQ4dac9b9627032aa3-math-000000AC-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 / (ntot − ni)	mol/mol	ppm, ppb, ppt
mass fraction	wi	mi / mtot	kg/kg	ppm, ppb, ppt
mass ratio	ζi	mi / (mtot − mi)	kg/kg	ppm, ppb, ppt

See also

• Serial dilution
• Practical examples of 1 and 2 normal acids in biochemistry