# Mixture

In chemistry, a mixture is a material system made up of two or more different substances which are mixed but are not combined chemically. A mixture refers to the physical combination of two or more substances on which the identities are retained and are mixed in the form of solutions, suspensions, and colloids.

Mixtures are the one product of a mechanical blending or mixing of chemical substances like elements and compounds, without chemical bonding or other chemical change, so that each ingredient substance retains its own chemical properties and makeup.[1] Despite 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 physical (mechanical or thermal) means. Azeotropes can be considered as a kind of mixture which usually pose considerable difficulties regarding the separation processes required to obtain their constituents (physical or chemical processes or, even a blend of them).

## Examples of mixtures

Mixtures can be either homogeneous or heterogeneous. A homogeneous mixture is a type of mixture in which the composition is uniform and every part of the solution has the same properties. A heterogeneous mixture is a type of mixture in which the components can be seen, as there are two or more phases present. One example of a mixture is air. Air is a homogeneous mixture of the gaseous substances nitrogen, oxygen, and smaller amounts of other substances. Salt, sugar, and many other substances dissolve in water to form homogeneous mixtures. A homogeneous mixture in which there is both a solute and solvent present is also a solution. Mixtures can have any amounts of ingredients.

The following table shows the main properties of the three families of mixtures.

 Mixture homogeneity Homogeneous (Solution) Visually homogeneous but microscopically heterogeneous (Colloid) Heterogeneous (Suspension) Particle size < 1 nanometer between 1 nanometer and 1 micrometer > 1 micrometer Physical stability Yes Yes No: needs stabilizing agents Tyndall effect No Yes Yes Separates by centrifugation No Yes - Separates by decantation No No Yes

The following table shows examples of the three types of mixtures.

 Dissolved or dispersed phase Dispersion medium (Mixture phase) Solution Colloid Suspension (Coarse dispersion) Gas Gas Gas mixture: air (oxygen and other gases in nitrogen) None None Liquid Gas None Liquid aerosol:[2] fog, mist, vapor, hair sprays Aerosol Solid Gas None Solid aerosol:[2] smoke, cloud, air particulates Solid aerosol: dust Gas Liquid Solution: oxygen in water Liquid foam: whipped cream, shaving cream Foam Liquid Liquid Solution: alcoholic beverages Emulsion: miniemulsion, microemulsion Emulsion: milk, mayonnaise, hand cream Solid Liquid Solution: sugar in water Liquid sol: pigmented ink, blood Suspension: mud (soil, clay or silt particles are suspended in water), chalk powder suspended in water Gas Solid Solution: hydrogen in metals Solid foam: aerogel, styrofoam, pumice Foam: dry sponge Liquid Solid Solution: amalgam (mercury in gold), hexane in paraffin wax Gel: agar, gelatin, silicagel, opal Wet sponge Solid Solid Solution: alloys, plasticizers in plastics Solid sol: cranberry glass Clay, Silt, Sand, Gravel, Granite

## Physics and chemistry

A heterogeneous mixture is a mixture of two or more chemical substances (elements or compounds). Examples are: mixtures of sand and water or sand and iron filings, a conglomerate rock, water and oil, a portion salad, trail mix, and concrete (not cement). A mixture of powdered silver metal and powdered gold metal would represent a heterogeneous mixture of two elements.

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 you'll allow the entire article 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 [3] quantitavely defines the heterogeneity of a particle as:

$h_i = \frac{(c_i - c_\text{batch})m_i}{c_\text{batch} m_\text{aver}} .$

where $h_i$, $c_i$, $c_\text{batch}$, $m_i$, and $m_\text{aver}$ are respectively: the heterogeneity of the $i$th particle of the population, the mass concentration of the property of interest in the $i$th particle of the population, the mass concentration of the property of interest in the population, the mass of the $i$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:

$V = \frac{1}{(\sum_{i=1}^N q_i m_i)^2} \sum_{i=1}^N q_i(1-q_i) m_{i}^{2} \left(a_i - \frac{\sum_{j=1}^N q_j a_j m_j}{\sum_{j=1}^N q_j m_j}\right)^2 .$

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:

$V = \frac{1-q}{q M_\text{batch}^2} \sum_{i=1}^N m_{i}^{2} \left(a_i - a_\text{batch} \right)^2 .$

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. ^ Atkins' Physical Chemistry, 7th Ed. by Julio De Paula, P.W. Atkins ISBN 0-19-879285-9
2. ^ a b http://iupac.org/publications/pac/pdf/1972/pdf/3104x0577.pdf
3. ^ Gy, P (1979) Sampling of Particulate Materials: Theory and Practice, Elsevier: Amsterdam

IUPAC, Compendium of Chemical Terminology, 2nd ed. (the "Gold Book") (1997). Online corrected version:  (2006–) "mixture".