Partial Properties: Thought Experiment Suppose we add a drop of water to pure acetone. What change in volume would result? If the resulting water/acetone mixture is ideal the volume increase is simply that of the volume of the water droplet. If the mixture behaves non-ideally, the volume increase will not equal the volume of the water droplet. The effect may, in fact, be quite different. Non-ideality in mixtures results from complex intermolecular interactions that we cannot predict. We have to solve engineering problems (separations, property calculations, …) for these non-ideal systems. na moles Acetone nw moles H2O

Partial Properties: Thought Experiment The volume change of the acetone-water mixture does not equal the volume of the water droplet We like to assign values or “contributions” to each component in non-ideal mixtures to account for the variation of a property with respect to composition. This leads us to define partial molar properties, which in our thought experiment gives us the partial molar volume for water in an acetone-water solution. This quantity represents change in solution volume as the number of moles of water is varied at a given P,T, and nacetone.

Partial Molar Quantities We prefer to think of mixtures in terms of their components: An overall property like V or H has a contribution from each component in the mixture. In non-ideal systems, the properties of the pure components have little meaning, forcing us to find an alternative way of defining molar quantities. If nM is the total thermodynamic property of interest: where is a partial molar property, also a function of (T,P, nj) A partial molar property depends on the P,T and composition from which it is derived. It is difficult to predict, but can be measured experimentally.

Total Properties of Non-Ideal Mixtures Ideal mixtures result from a lack of molecular interactions (ideal gas) or equivalent molecular interactions (ideal solution). In these cases, a total thermodynamic property (nM) for a mixture is: nM =  ni Mi where Mi represents the pure component property of i. Non-ideal systems do not obey this simple formula, as cross-component molecular interactions differ from pure component interactions. nM =  ni where represents the partial molar property of component i. In terms of mole fractions: M =  xi If we know the partial properties of the components of the mixture (from experimental data) we can determine its total property.