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.)

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Alcohol wt% 0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 100 Density at 20°C mol % (kg m-3) x 10-3 Water 0.9982 0.9894 0.9819 0.9751 0.9686 0.9617 0.9538 0.9449 0.9352 0.9247 0.9138 0.9026 0.8911 0.8795 0.8677 0.8556 0.8434 0.8310 0.8180 0.8042 0.7893 5 10 15 20 25 30 35 40 45 50 5 60 5 70 75 80 35 90 95 55 65 85 Heat Evolved on Mixing at 17.33°C (kJ/mol of Ethanol) 0.042 0.092 0.167 0.251 0.335 0.423 0.519 0.636 0.757 0.946 1.201 1.507 1.925 2.478 3.218 4.269 5.821 7.801 9.818