Mixture

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

Mixtures are the 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).

Mixtures can be either homogeneous or heterogeneous. An homogeneous mixture is a type of mixture in which the composition is uniform. An heterogeneous mixture is a type of mixture in which the components can easily be identified, as there are two or more phases present. 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. The following table shows the main properties of the three families of mixtures.

	Solution	Colloid	Coarse dispersion
Mixture homogeneity	Homogeneous	Visually homogeneous but microscopically heterogeneous	Heterogeneous
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	Yes
Separates by decantation	No	No	Yes

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

Dissolved or dispersed phase	Continuous medium	Solution	Colloid	Coarse dispersion
Gas	Gas	Gas mixture: air (oxygen and other gases in nitrogen)	None	None
Liquid	Gas	None	Aerosol: fog, mist, vapor, hair sprays	Aerosol
Solid	Gas	None	Solid aerosol: smoke, cloud, air particulates	Solid aerosol: dust
Gas	Liquid	Solution: oxygen in water	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	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	Gravel, granite

Physics and chemistry

A heterogeneous mixture is a mixture of two or more compounds. Examples are: mixtures of sand and water or sand and iron filings, a conglomerate rock, water and oil, a salad, trail mix, and concrete (not cement).

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 ^[2] quantitatively 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.

It must be noted that 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

^ Atkins' Physical Chemistry, 7th Ed. by Julio De Paula, P.W. Atkins ISBN 0-19-879285-9
^ 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".