Mixture

Mixtures can be characterized by being separable by mechanical means e.g. heat, filtration, gravitational sorting, centrifugation etc.[8] Mixtures can be either homogeneous or heterogeneous': a mixture in which constituents are distributed uniformly is called homogeneous, such as salt in water, otherwise it is called heterogeneous, such as sand in water.

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.

Mixtures are unlike chemical compounds, because:

• 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.[9]

The following table shows the main properties of the three families of mixtures and examples of the three types of mixture.

A homogeneous mixture has the same proportions of its components throughout any given sample and is also referred to as a solution. Conversely, a heterogeneous mixture has components of which proportions vary throughout the sample. "Homogeneous" and "heterogeneous" are not absolute terms, but are dependent on context and the size of the sample.

In chemistry, if the volume of a homogeneous suspension is divided in half, the same amount of material is suspended in both halves of the substance. An example of a homogeneous mixture is air.

In physical chemistry and materials science this refers to substances and mixtures which are in a single phase. This is in contrast to a substance that is heterogeneous.[11]

A diagram representing at the microscopic level the differences between homogeneous mixtures, heterogeneous mixtures, compounds, and 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 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 quantitavely defines the heterogeneity of a particle as:[13]

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

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 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.

• Chemical substance

• IUPAC, Compendium of Chemical Terminology, 2nd ed. (the "Gold Book") (1997). Online corrected version:  (2006–) "mixture". doi:10.1351/goldbook.M03949