A partial molar property of a component in a mixture may be either greater than or less than the corresponding pure-component molar property. Furthermore, the partial molar property may vary with composition in a complicated way. Show this to be the case by computing (a) the partial molar volumes and (b) the partial molar enthalpies of ethanol and water in an ethanol-water mixture. (The data that follow are from Volumes 3 and 5 of the International Critical Tables, McGraw-Hill, New York, 1929.)

Partial molar volumes help to assess the influence of pressure on phase equilibria or reaction equilibria. The prediction of partial molar volumes or excess volumes is a sharp test for theories of the fluid state.

On the other hand, the interpretation of partial molar volumes or excess volumes is usually difficult, if not impossible. Many mixtures exhibit positive and negative excess volumes, depending on composition, temperature, and pressure. Speculations why some mixture exhibits positive or negative excess volumina are futile, particularly if they are based on measurements at ambient pressure and temperature only.

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