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,

$z=\sum _i{x}_i\overline{Z_i},$

substitution yields:

$z^E=\sum _i{x}_i(\overline{Z_i}-z_i^{id}).$

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

$\frac{\partial {\overline{V^E}}_i}{\partial T}=R\frac{\partial (ln({\gamma }_i))}{\partial P}+RT\frac{{\partial }^2}{\partial T\partial P}ln({\gamma }_i)$

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