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 are one kind of mixture that usually pose considerable difficulties regarding the separation processes required to obtain their constituents (physical or chemical processes or, even a blend of them).

Kinds of mixtures

Mixtures can either be 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.

	Solution	Colloid	Suspension in pp
Homogeneous	Homogeneous	Visually homogeneous but microscopic PP	Heterogeneous BIG PP
Particle size	< 1 nm	1 nm – 1 μm	> 1 μm
Physically stable	Yes	Yes	Needs stabilizing agents
Exhibits Tyndall effect	No	Yes	Yes
Separates by centrifugation	No	Yes	Yes
Separates by decantation	No	No	Yes

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

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:[2] fog, mist, vapor, hair sprays	Spray
	Solid	None	Solid aerosol:[2] smoke, cloud, air particulates	Dust
Liquid	Gas	Solution: oxygen in water	Liquid foam: whipped cream, shaving cream	Sea foam, Beer head
	Liquid	Solution: alcoholic beverages	Emulsion: milk, mayonnaise, hand cream	Vinaigrette
	Solid	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
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

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 a_batch is that concentration of the property of interest in the population from which the sample is to be drawn and M_batch 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. 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".