Internal category

Excess molar quantities are properties of mixtures which characterize the nonideal behaviour of real mixtures. They are the difference between the partial molar property of a component in a real mixture and that of the component in an ideal mixture. By definition, excess properties of a mixture are related to those of the pure substances in an ideal mixture by:

$z^{E}=z-\sum _{i}x_{i}z_{i}^{id}.$

Here $*$ denotes the pure substance, $E$ the excess molar property, and $z$ corresponds to the specific property under consideration. From the definition of partial molar properties,

$z=\sum _{i}x_{i}{\bar {Z_{i}}},$

substitution yields:

$z^{E}=\sum _{i}x_{i}({\bar {Z_{i}}}-z_{i}^{id}).$

For volumes, internal energies and enthalpies the excess quantities are identical to the mixing quantities.

Examples

The volume of a mixture from the sum of the excess volumes of the components of a mixture is given by the formula:

${V}=\sum _{i}V_{i}+\sum _{i}V_{i}^{E}$

Deriving by temperature the thermal expansivities of the components in a mixture can be related to the expansivity of the mixture:

${\frac {\partial V}{\partial T}}=\sum _{i}{\frac {\partial V_{i}}{\partial T}}+\sum _{i}{\frac {\partial V_{i}^{E}}{\partial T}}$

Equivalently: $:\alpha _{V}V=\sum _{i}\alpha _{V,i}V_{i}+\sum _{i}{\frac {\partial V_{i}^{E}}{\partial T}}$

Substituting the excess molar volume

${\frac {\partial {\bar {V^{E}}}_{i}}{\partial T}}=R{\frac {\partial (ln(\gamma _{i}))}{\partial P}}+RT{\partial ^{2} \over \partial T\partial P}ln(\gamma _{i})$

one can relate activity coefficients to thermal expansivity.

See also

• Apparent molar property
• Heat of mixing

References

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External links

• [1]
• excess quantities for electrolyte mixtures