Concentration

Saturday, 23 June 2012

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Branches of Mathematics

Pure mathematics

Applied mathematics

Qualitative description [link]

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 [link]

There are four quantities that describe concentration:

Mass concentration [link]

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.

Molar concentration [link]

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 (= mol/dm³) is used.

Number concentration [link]

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 [link]

The volume concentration $\phi_i$ (also called volume fraction) is defined as the volume of a constituent $V_i$ divided by the volume of all constituents of the mixture $V$ prior to mixing:

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

The SI-unit is m³/m³.

Related quantities [link]

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

Normality [link]

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 [link]

(Not to be confused with Molarity)

The molality of a solution $b_i$ 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):

: $b_i = \frac{n_i}{m_{solvent}}$

The SI-unit for molality is mol/kg.

Mole fraction [link]

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 [link]

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 [link]

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 [link]

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:

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

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 [link]

Concentration depends on the variation of the volume of the solution due mainly to thermal expansion.

Table of concentrations and related quantities [link]

! 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		$c_i/f_{eq}$	mol/m³	N (=mol/L)
molality	$b_i$	$n_i/m_{solvent}$	mol/kg
mole fraction	$x_i$	$n_i/n_{tot}$	mol/mol	ppm, ppb, ppt
mole ratio	$r_i$	$n_i/(n_{tot}-n_i)$	mol/mol	ppm, ppb, ppt
mass fraction	$w_i$	$m_i/m_{tot}$	kg/kg	ppm, ppb, ppt
mass ratio	$\zeta_i$	$m_i/(m_{tot}-m_i)$	kg/kg	ppm, ppb, ppt

References [link]

Category:Analytical chemistry Category:Chemical properties

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