Comelli and Francesconi examined mixtures of propionic acid with various other organic liquids at 313.15 K (F. Comelli and R. Francesconi, J. Chem. Eng. Data 41, 101 (1996)). They report the excess volume of mixing propionic acid with tetrahydropyran (THP, oxane) as VE = x1x2{a0 + a1(x1 − x2)}, where x1 is the mole fraction of propionic acid, x2 that of THP, a0 = −2.4697 cm3 mol−1, and a1 = 0.0608 cm3 mol−1. The density of propionic acid at this temperature is 0.971 74 g cm−3; that of THP is 0.863 98 g cm−3. (a) Derive an expression for the partial molar volume of each component at this temperature. (b) Compute the partial molar volume for each component in an equimolar mixture.

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Comelli and Francesconi examined mixtures of propionic acid with various other organic liquids at 313.15 K (F. Comelli and R. Francesconi, J. Chem. Eng. Data 41, 101 (1996)). They report the excess volume of mixing propionic acid with tetrahydropyran (THP, oxane) as VE = x1x2{a0 + a1(x1 − x2)}, where x1 is the mole fraction of propionic acid, x2 that of THP, a0 = −2.4697 cm3 mol−1, and a1 = 0.0608 cm3 mol−1. The density of propionic acid at this temperature is 0.971 74 g cm−3; that of THP is 0.863 98 g cm−3. (a) Derive an expression for the partial molar volume of each component at this temperature. (b) Compute the partial molar volume for each component in an equimolar mixture.

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