# Concentration

### 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. 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.

## 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 \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/m3 (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/m3. However, more commonly the unit mol/L (= mol/dm3) 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/m3.

### Volume concentration

The volume concentration \phi_i (do not confuse with volume fraction) is defined 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.

### 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 parts-per 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 parts-per 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 parts-per 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 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 \rho_i or \gamma_i m_i/V kg/m3 g/100mL (= g/dL)
molar concentration c_i n_i/V mol/m3 M (= mol/L)
number concentration C_i N_i/V 1/m3 1/cm3
volume concentration \phi_i V_i/V m3/m3
Related quantities Symbol Definition SI unit other unit(s)
normality c_i/f_\mathrm{eq} mol/m3 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