﻿ Concentration
Concentration

Concentration
can be distinguished: mass concentration, molar concentration, number concentration, and volume concentration. A concentration can be any kind of chemical

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the proportion of a constituent of a mixture to the whole For other uses, see Concentration (disambiguation).

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] A concentration can be any kind of chemical mixture, but most frequently solutes and solvents in solutions. The molar (amount) concentration has variants such as normal concentration and osmotic concentration.

Contents
• 1 Qualitative description
• 2 Quantitative notation
• 2.1 Mass concentration
• 2.2 Molar concentration
• 2.3 Number concentration
• 2.4 Volume concentration
• 3 Related quantities
• 3.1 Normality
• 3.2 Molality
• 3.3 Mole fraction
• 3.4 Mole ratio
• 3.5 Mass fraction
• 3.6 Mass ratio
• 4 Dependence on volume
• 5 Table of concentrations and related quantities
• 7 References
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.

Concentrations are often called levels, reflecting the mental schema of levels on the vertical axis of a graph, which can be high or low (for example, "high serum levels of bilirubin" are concentrations of bilirubin in the blood serum that are greater than normal).

Quantitative notation

There are four quantities that describe concentration:

Mass concentration Main article: Mass concentration (chemistry)

The mass concentration ρ i {\displaystyle \rho _{i}} is defined as the mass of a constituent m i {\displaystyle m_{i}} divided by the volume of the mixture V {\displaystyle V} :

ρ i = m i V . {\displaystyle \rho _{i}={\frac {m_{i}}{V}}.}

The SI unit is kg/m3 (equal to g/L).

Molar concentration Main article: Molar concentration

The molar concentration c i {\displaystyle c_{i}} is defined as the amount of a constituent n i {\displaystyle n_{i}} (in moles) divided by the volume of the mixture V {\displaystyle V} :

c i = n i V . {\displaystyle 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 Main article: Number concentration

The number concentration C i {\displaystyle C_{i}} is defined as the number of entities of a constituent N i {\displaystyle N_{i}} in a mixture divided by the volume of the mixture V {\displaystyle V} :

C i = N i V . {\displaystyle C_{i}={\frac {N_{i}}{V}}.}

The SI unit is 1/m3.

Volume concentration

The volume concentration σ i {\displaystyle \sigma _{i}} (not to be confused with volume fraction[2]) is defined as the volume of a constituent V i {\displaystyle V_{i}} divided by the volume of the mixture V {\displaystyle V} :

σ i = V i V . {\displaystyle \sigma _{i}={\frac {V_{i}}{V}}.}

Being dimensionless, it is expressed as a number, e.g., 0.18 or 18%; its unit is 1.

There seems to be no standard notation in the English literature. The letter σ i {\displaystyle \sigma _{i}} used here is normative in German literature (see Volumenkonzentration).

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 Main article: Normality (chemistry)

Normality is defined as the molar concentration c i {\displaystyle c_{i}} divided by an equivalence factor f e q {\displaystyle 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 Main article: Molality

(Not to be confused with Molarity)

The molality of a solution b i {\displaystyle b_{i}} is defined as the amount of a constituent n i {\displaystyle n_{i}} (in moles) divided by the mass of the solvent m s o l v e n t {\displaystyle m_{\mathrm {solvent} }} (not the mass of the solution):

b i = n i m s o l v e n t . {\displaystyle b_{i}={\frac {n_{i}}{m_{\mathrm {solvent} }}}.}

The SI unit for molality is mol/kg.

Mole fraction Main article: Mole fraction

The mole fraction x i {\displaystyle x_{i}} is defined as the amount of a constituent n i {\displaystyle n_{i}} (in moles) divided by the total amount of all constituents in a mixture n t o t {\displaystyle n_{\mathrm {tot} }} :

x i = n i n t o t . {\displaystyle 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 Main article: Mixing ratio

The mole ratio r i {\displaystyle r_{i}} is defined as the amount of a constituent n i {\displaystyle n_{i}} divided by the total amount of all other constituents in a mixture:

r i = n i n t o t − n i . {\displaystyle r_{i}={\frac {n_{i}}{n_{\mathrm {tot} }-n_{i}}}.}

If n i {\displaystyle n_{i}} is much smaller than n t o t {\displaystyle 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 Main article: Mass fraction (chemistry)

The mass fraction w i {\displaystyle w_{i}} is the fraction of one substance with mass m i {\displaystyle m_{i}} to the mass of the total mixture m t o t {\displaystyle m_{\mathrm {tot} }} , defined as:

w i = m i m t o t . {\displaystyle 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 Main article: Mixing ratio

The mass ratio ζ i {\displaystyle \zeta _{i}} is defined as the mass of a constituent m i {\displaystyle m_{i}} divided by the total mass of all other constituents in a mixture:

ζ i = m i m t o t − m i . {\displaystyle \zeta _{i}={\frac {m_{i}}{m_{\mathrm {tot} }-m_{i}}}.}

If m i {\displaystyle m_{i}} is much smaller than m t o t {\displaystyle 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 with temperature due mainly to thermal expansion.

Table of concentrations and related quantities Concentration type Symbol Definition SI unit other unit(s) mass concentration ρ i {\displaystyle \rho _{i}} or γ i {\displaystyle \gamma _{i}} m i / V {\displaystyle m_{i}/V} kg/m3 g/100mL (= g/dL) molar concentration c i {\displaystyle c_{i}} n i / V {\displaystyle n_{i}/V} mol/m3 M (= mol/L) number concentration C i {\displaystyle C_{i}} N i / V {\displaystyle N_{i}/V} 1/m3 1/cm3 volume concentration ϕ i {\displaystyle \phi _{i}} V i / V {\displaystyle V_{i}/V} m3/m3 Related quantities Symbol Definition SI unit other unit(s) normality c i / f e q {\displaystyle c_{i}/f_{\mathrm {eq} }} mol/m3 N (= mol/L) molality b i {\displaystyle b_{i}} n i / m s o l v e n t {\displaystyle n_{i}/m_{\mathrm {solvent} }} mol/kg mole fraction x i {\displaystyle x_{i}} n i / n t o t {\displaystyle n_{i}/n_{\mathrm {tot} }} mol/mol ppm, ppb, ppt mole ratio r i {\displaystyle r_{i}} n i / ( n t o t − n i ) {\displaystyle n_{i}/(n_{\mathrm {tot} }-n_{i})} mol/mol ppm, ppb, ppt mass fraction w i {\displaystyle w_{i}} m i / m t o t {\displaystyle m_{i}/m_{\mathrm {tot} }} kg/kg ppm, ppb, ppt mass ratio ζ i {\displaystyle \zeta _{i}} m i / ( m t o t − m i ) {\displaystyle m_{i}/(m_{\mathrm {tot} }-m_{i})} kg/kg ppm, ppb, ppt See also
• Dilution ratio
• Dose concentration
• Serial dilution
• Wine/water mixing problem
References
1. ^ a b IUPAC, Compendium of Chemical Terminology, 2nd ed. (the "Gold Book") (1997). Online corrected version:  (2006–) "concentration". doi:10.1351/goldbook.C01222
2. ^ IUPAC, Compendium of Chemical Terminology, 2nd ed. (the "Gold Book") (1997). Online corrected version:  (2006–) "volume fraction". doi:10.1351/goldbook.V06643
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Articles related to solutionsSolution
• Ideal solution
• Aqueous solution
• Solid solution
• Buffer solution
• Flory–Huggins
• Mixture
• Suspension
• Colloid
• Phase diagram
• Phase separation
• Eutectic point
• Alloy
• Saturation
• Supersaturation
• Serial dilution
• Dilution (equation)
• Apparent molar property
• Miscibility gap
Concentration
and related quantities
• Molar concentration
• Mass concentration
• Number concentration
• Volume concentration
• Normality
• Percentage solution
• Molality
• Mole fraction
• Mass fraction
• Isotopic abundance
• Mixing ratio
• Ternary plot
Solubility
• Solubility equilibrium
• Total dissolved solids
• Solvation
• Solvation shell
• Enthalpy of solution
• Lattice energy
• Raoult's law
• Henry's law
• Solubility table (data)
• Solubility chart
Solvent
• (Category)
• Acid dissociation constant
• Protic solvent
• Inorganic nonaqueous solvent
• Solvation
• List of boiling and freezing information of solvents
• Partition coefficient
• Polarity
• Hydrophobe
• Hydrophile
• Lipophilic
• Amphiphile
• Lyonium ion
• Lyate ion

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