# Mixture

In chemistry, a mixture is a material made up of two or more different chemical substance/substances which are not chemically combined.[1] A mixture is the physical combination of two or more substances in which the identities are retained and are mixed in the form of solutions, suspensions and colloids.[2][3]

Mixtures are one product of mechanically blending or mixing chemical substances such as elements and compounds, without chemical bonding or other chemical change, so that each ingredient substance retains its own chemical properties and makeup.[4] Despite the fact that there are no chemical changes to its constituents, the physical properties of a mixture, such as its melting point, may differ from those of the components. Some mixtures can be separated into their components by using physical (mechanical or thermal) means. Azeotropes are one kind of mixture that usually poses considerable difficulties regarding the separation processes required to obtain their constituents (physical or chemical processes or, even a blend of them).[5][6][7]

## Characteristics of mixtures

All mixtures can be characterized as being separable by mechanical means (e.g. purification, distillation, electrolysis, chromatography, heat, filtration, gravitational sorting, centrifugation).[8][9] Mixtures differ from chemical compounds in the following ways:

• the substances in a mixture can be separated using physical methods such as filtration, freezing, and distillation;
• there is little or no energy change when a mixture forms (see Enthalpy of mixing);
• mixtures have variable compositions, while compounds have a fixed, definite formula;
• when mixed, individual substances keep their properties in a mixture, while if they form a compound their properties can change.[10]

The following table shows the main properties and examples for all possible phase combinations of the three "families" of mixtures:

Mixtures Table
Dispersion medium (mixture phase) Dissolved or dispersed phase Solution Colloid Suspension (coarse dispersion)
Gas Gas Gas mixture: air (oxygen and other gases in nitrogen) None None
Liquid None Liquid aerosol:[11]
fog, mist, vapor, hair sprays
Spray
Solid None Solid aerosol:[11]
smoke, ice cloud, air particulates
Dust
Liquid Gas Solution:
oxygen in water
Liquid foam:
whipped cream, shaving cream
Liquid Solution:
alcoholic beverages
Emulsion:
milk, mayonnaise, hand cream
Vinaigrette
Solid Solution:
sugar in water
Liquid sol:
pigmented ink, blood
Suspension:
mud (soil particles suspended in water), chalk powder suspended in water
Solid Gas Solution:
hydrogen in metals
Solid foam:
aerogel, styrofoam, pumice
Foam:
dry sponge
Liquid Solution:
amalgam (mercury in gold), hexane in paraffin wax
Gel:
agar, gelatin, silicagel, opal
Wet sponge
Solid Solution:
alloys, plasticizers in plastics
Solid sol:
cranberry glass
Clay, silt, sand, gravel, granite

## Homogeneous and heterogeneous mixtures

Mixtures can be either homogeneous or heterogeneous: a mixture in which constituents are distributed uniformly, such as salt in water, is called homogeneous, whereas a mixture whose constituents are clearly separate from one another, such as sand in water, it is called heterogeneous.

In addition, "uniform mixture" is another term for homogenous mixture and "non-uniform mixture" is another term for heterogeneous mixture. These terms are derived from the idea that a homogeneous mixture has a uniform appearance, or only one visible phase, because the particles are evenly distributed. However, a heterogeneous mixture has non-uniform composition and its constituent substances are easily distinguishable from one another (often, but not always, in different phases).

Several solid substances, such as salt and sugar, dissolve in water to form a special type of homogeneous mixture called a solution, in which there is both a solute (dissolved substance) and solvent (dissolving medium) present. Air is an example of a solution as well: a homogeneous mixture of gaseous nitrogen solvent, in which oxygen and smaller amounts of other gaseous solutes are dissolved. Mixtures are not limited in either their number of substances or the amounts of those substances, though in a homogeneous mixture the solute-to-solvent proportion can only reach a certain point before the mixture separates and becomes heterogeneous.

A homogeneous mixture is characterized by uniform dispersion of its constituent substances throughout; the substances exist in equal proportion everywhere within the mixture. Differently put, a homogeneous mixture will be the same no matter from where in the mixture it is sampled. For example, if a solid-liquid solution is divided into two halves of equal volume, the halves will contain equal amounts of both the liquid medium and dissolved solid (solvent and solute).

In physical chemistry and materials science, "homogeneous" more narrowly describes substances and mixtures which are in a single phase.[12]

A diagram representing at the microscopic level the differences between homogeneous mixtures, heterogeneous mixtures, compounds, and elements

### Solution

A solution is a special type of homogeneous mixture where the ratio of solute to solvent remains the same throughout the solution and the particles are not visible with the naked eye, even if homogenized with multiple sources. In solutions, solutes will not settle out after any period of time and they can't be removed by physical methods, such as a filter or centrifuge.[13] As a homogeneous mixture, a solution has one phase (solid, liquid, or gas), although the phase of the solute and solvent may initially have been different (e.g., salt water).

### Gases

Gases exhibit by far the greatest space (and, consequently, the weakest intermolecular forces) between their atoms or molecules; since intermolecular interactions are miniscule in comparison to those in liquids and solids, dilute gases very easily form solutions with one another. Air is one such example: it can be more specifically described as a gaseous solution of oxygen and other gases dissolved in nitrogen (its major component).

## Distinguishing between mixture types

Making a distinction between homogeneous and heterogeneous mixtures is a matter of the scale of sampling. On a coarse enough scale, any mixture can be said to be homogeneous, if the entire article is allowed to count as a "sample" of it. On a fine enough scale, any mixture can be said to be heterogeneous, because a sample could be as small as a single molecule. In practical terms, if the property of interest of the mixture is the same regardless of which sample of it is taken for the examination used, the mixture is homogeneous.

Gy's sampling theory quantitatively defines the heterogeneity of a particle as:[14]

${\displaystyle h_{i}={\frac {(c_{i}-c_{\text{batch}})m_{i}}{c_{\text{batch}}m_{\text{aver}}}},}$

where ${\displaystyle h_{i}}$, ${\displaystyle c_{i}}$, ${\displaystyle c_{\text{batch}}}$, ${\displaystyle m_{i}}$, and ${\displaystyle m_{\text{aver}}}$ are respectively: the heterogeneity of the ${\displaystyle i}$th particle of the population, the mass concentration of the property of interest in the ${\displaystyle i}$th particle of the population, the mass concentration of the property of interest in the population, the mass of the ${\displaystyle i}$th particle in the population, and the average mass of a particle in the population.

During sampling of heterogeneous mixtures of particles, the variance of the sampling error is generally non-zero.

Pierre Gy derived, from the Poisson sampling model, the following formula for the variance of the sampling error in the mass concentration in a sample:

${\displaystyle V={\frac {1}{(\sum _{i=1}^{N}q_{i}m_{i})^{2}}}\sum _{i=1}^{N}q_{i}(1-q_{i})m_{i}^{2}\left(a_{i}-{\frac {\sum _{j=1}^{N}q_{j}a_{j}m_{j}}{\sum _{j=1}^{N}q_{j}m_{j}}}\right)^{2},}$

in which V is the variance of the sampling error, N is the number of particles in the population (before the sample was taken), q i is the probability of including the ith particle of the population in the sample (i.e. the first-order inclusion probability of the ith particle), m i is the mass of the ith particle of the population and a i is the mass concentration of the property of interest in the ith particle of the population.

The above equation for the variance of the sampling error is an approximation based on a linearization of the mass concentration in a sample.

In the theory of Gy, correct sampling is defined as a sampling scenario in which all particles have the same probability of being included in the sample. This implies that q i no longer depends on i, and can therefore be replaced by the symbol q. Gy's equation for the variance of the sampling error becomes:

${\displaystyle V={\frac {1-q}{qM_{\text{batch}}^{2}}}\sum _{i=1}^{N}m_{i}^{2}\left(a_{i}-a_{\text{batch}}\right)^{2},}$

where abatch is that concentration of the property of interest in the population from which the sample is to be drawn and Mbatch is the mass of the population from which the sample is to be drawn.

## References

1. ^ IUPAC, Compendium of Chemical Terminology, 2nd ed. (the "Gold Book") (1997). Online corrected version:  (2006–) "mixture". doi:10.1351/goldbook.M03949
2. ^ Whitten K.W., Gailey K. D. and Davis R. E. (1992). General chemistry (4th ed.). Philadelphia: Saunders College Publishing. ISBN 978-0-03-072373-5.[page needed]
3. ^ Petrucci, Ralph H.; Harwood, William S.; Herring, F. Geography (2002). General chemistry: principles and modern applications (8th ed.). Upper Saddle River, N.J: Prentice Hall. ISBN 978-0-13-014329-7. LCCN 2001032331. OCLC 46872308.[page needed]
4. ^ De Paula, Julio; Atkins, P. W. (2002). Atkins' Physical Chemistry (7th ed.). ISBN 978-0-19-879285-7.[page needed]
5. ^ Alberts B.; et al. (2002). Molecular Biology of the Cell, 4th Ed. Garland Science. ISBN 978-0-8153-4072-0.[page needed]
6. ^ Laidler K. J. (1978). Physical chemistry with biological applications. Benjamin/Cummings. Menlo Park. ISBN 978-0-8053-5680-9.[page needed]
7. ^ Weast R. C., Ed. (1990). CRC Handbook of chemistry and physics. Boca Raton: Chemical Rubber Publishing Company. ISBN 978-0-8493-0470-5.[page needed]
8. ^ Pleasants, Julian M, ed. (2017). "A Call to Duty". Home Front. doi:10.5744/florida/9780813054254.003.0003. ISBN 9780813054254.
9. ^ Ashworth, William; Littl1, Charles E., eds. (2001). "Mixture". The Encyclopedia of Environmental Studies. Online publisher:Science Online. Facts on File, Inc.
10. ^ "Definition of mixture - Chemistry Dictionary". www.chemicool.com. Retrieved 30 November 2018.
11. ^ a b Everett, D. H. (23 July 1971). Manual of Symbols and Terminology for Physicochemical Quantities and Units. Appendix II Definitions, Terminology and Symbols in Colloid and Surface Chemistry. Part I (PDF) (Report). London: International Union of Pure and Applied Chemistry: Division of Physical Chemistry. Archived (PDF) from the original on 28 October 2016. Retrieved 28 October 2016.
12. ^ Lew, Kristi (2009). "Homogeneous". Acids and Bases, Essential Chemistry. New York: Chelsea House Publishing. Online publisher: Science Online. Facts on File, Inc. ISBN 978-0-7910-9783-0. access date: 2010–01-01
13. ^ "Solution (chemistry)" (authors: William Ashworth and Charles E. Little) |chapter-format= requires |chapter-url= (help). Encyclopedia of Environmental Studies, New Edition. Online publisher:Science Online. Facts on File, Inc. 2001. access date: 2010–01-01
14. ^ Gy, P (1979). Sampling of Particulate Materials: Theory and Practice. Amsterdam: Elsevier.