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**Solution thermodynamics theory—Part I**

Chapter 11

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**topics Fundamental equations for mixtures Chemical potential**

Properties of individual species in solution (partial properties) Mixtures of real gases Mixtures of real liquids

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**A few equations For a closed system**

Total differential form, what are (nV) and (nS) Which are the main variables for G?? What are the main variables for G in an open system of k components?

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**G in a mixture (open system)**

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**G in a mixture of k components at T and P**

How is this equation reduced if n =1?

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**2 phases (each at T and P) in a closed system**

Apply this equation to each phase Sum the equations of both phases, take into account that In a closed system:

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We end up with How are dnia and dnib related at constant n?

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**For 2 phases, k components at equilibrium**

Thermal equilibrium Mechanical equilibrium Chemical equilibrium For all i = 1, 2,…k

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**In order to solve the VLE problem**

Need models for mi in each phase Examples of models of mi in the vapor phase Examples of models of mi in the liquid phase

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**Now we are going to learn:**

Partial molar properties Because the chemical potential is a partial molar property At the end of this section think about this What is the chemical potential in physical terms What are the units of the chemical potential How do we use the chemical potential to solve a VLE (vapor-liquid equilibrium) problem

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**Partial molar property**

Solution property Partial property Pure-species property

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**example Open beaker: ethanol + water, equimolar Total volume nV**

T and P Add a drop of pure water, Dnw Mix, allow for heat exchange, until temp T Change in volume ?

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**Total vs. partial properties**

See derivation page 384

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**Derivation of Gibbs-Duhem equation**

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**Gibbs-Duhem at constant T&P**

Useful for thermodynamic consistency tests

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Binary solutions See derivation page 386

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Obtain dM/dx1 from (a)

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Example 11.3 We need 2,000 cm3 of antifreeze solution: 30 mol% methanol in water. What volumes of methanol and water (at 25oC) need to be mixed to obtain 2,000 cm3 of antifreeze solution at 25oC Data:

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**solution Calculate total molar volume of the 30% mixture**

We know the total volume, calculate the number of moles required, n Calculate n1 and n2 Calculate the total volume of each pure species needed to make that mixture

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**Note curves for partial molar volumes**

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From Gibbs-Duhem: Divide by dx1, what do you conclude respect to the slopes?

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Example 11.4 Given H=400x1+600x2+x1x2(40x1+20x2) determine partial molar enthalpies as functions of x1, numerical values for pure-species enthalpies, and numerical values for partial enthalpies at infinite dilution Also show that the expressions for the partial molar enthalpies satisfy Gibbs-Duhem equation, and they result in the same expression given for total H.

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