Partial molar properties analytical determination

In view of the difficulty of determining the exact slope of the curve at all points, it is preferable to use an analytical procedure instead of the graphical one just described. The property G is then expressed as a function of the number of moles of one component, c.g., the molality, associated with a constant amount of the other component. Upon differentiation with respect to n, i.e., the molality, an expression for the partial molar property is obtained. 

Define a partial molar property and describe its role in determining the properties of mixtures. Calculate the value of a partial molar property for a species in a mixture from analytical and graphical methods. Apply the Gibbs-Duhem equation to relate the partial molar properties of different species. 

When the value of an intensive property / can be expressed as an algebraic function of the composition, the partial molar quantities can be determined analytically. 

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