8.17. Two liquids 1 and 2 arc mixcd, and it is found that the molar volumc of themixture follows the relationvxix2vz x1x2cand v are the molar volumes of pure 1where the x terms are mole fractions,and 2, and c is a constant with units of volume per mole. Find expressions forthe P dependence of the chemical potentials and in terms of the pure-speciesproperties and the constant c.

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Asked Oct 6, 2019
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This problem is (8.17) from a book  "Thermodynamics and Statistical Mechanics An Integrated Approach by M. Scott Shell"

8.17. Two liquids 1 and 2 arc mixcd, and it is found that the molar volumc of the
mixture follows the relation
vxix2vz x1x2c
and v are the molar volumes of pure 1
where the x terms are mole fractions,
and 2, and c is a constant with units of volume per mole. Find expressions for
the P dependence of the chemical potentials and in terms of the pure-species
properties and the constant c.
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8.17. Two liquids 1 and 2 arc mixcd, and it is found that the molar volumc of the mixture follows the relation vxix2vz x1x2c and v are the molar volumes of pure 1 where the x terms are mole fractions, and 2, and c is a constant with units of volume per mole. Find expressions for the P dependence of the chemical potentials and in terms of the pure-species properties and the constant c.

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Expert Answer

Step 1

Where x denotes mole fraction of liquids (1 and 2) in the solution

ʋ1* denotes molar volume of pure 1

ʋ2*denotes molar volume of pure 2

C is constant (volume/mol)

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--(a) v=xv +x^v^ +xx,c -

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Step 2

From the fundamental thermodynamic relation in terms of Gibbs free energy and use Maxwell relation to find out pressure dependence of chemical potential

For mixture thermodynamic relation is written as follows:

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dG VdP-SdT+HdN - OG -(2) =V -- OP TN OG (3) =-S- -(4)

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Step 3

From Maxwell relation equati...

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o'G aN, ӘP ОРОN, OG OG -(5) ДР дN, ON, ОР

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