Partial gibbs free energy and gibbs duhem equation

Partial gibbs free energy and gibbs duhem equation,relation between binary solution,relation between partiaL properties,PARTIAL PROPERTIES,PARTIAL PROPERTIES IN BINARY SOLUTION,RELATIONS AMONG PARTIAL PROPERTIES,Maxwell relation,Examples

1. Partial gibbes free energy and gibbes / duhem equation, relation between binary solution , relation between partiaL properties

2. PARTIAL PROPERTIES Define the partial molar property of species i A  partial molar property  is a  thermodynamic  quantity which indicates how an  extensive property  of a  solution  or  mixture  varies with changes in the  molar  composition of the mixture at constant  temperature  and pressure .  When one mole of water is added to a large volume of water at 25 °C, the volume increases by 18 cm 3 . The molar volume of pure water would thus be reported as 18 cm 3  mol −1 . However, addition of one mole of water to a large volume of pure  ethanol  results in an increase in volume of only 14 cm 3 . The reason that the increase is different is that the volume occupied by a given number of water molecules depends upon the identity of the surrounding molecules. The value 14 cm 3  is said to be the partial molar volume of water in ethanol.

3. THE GIBBS/DUHEM EQUATION Define the partial molar property of species i : the chemical potential and the particle molar Gibbs energy are identical: for thermodynamic property M :

4. and Calculation of mixture properties from partial properties The Gibbs/ Duhem equation

5. Binary solution is a mixture of two liquids that are completely miscible one with another. The boiling point of binary solution depends upon the solution composition and there can be three cases: 1. the boiling points of solutions of all compositions lie between the boiling points of clean liquids 2. the boiling points of solutions of any composition lie above the boiling points of clean liquids 3. the boiling points of solutions of some compositions lie below the boiling points of clean liquids WHAT IS BINARY SOLUTION

6. PARTIAL PROPERTIES IN BINARY SOLUTION For binary system Const. P and T, using Gibbs/Duhem equation

7. EXAMPLE : 1 The need arises in a laboratory for 2000 cm 3 of an antifreeze solution consisting of 30 mol-% methanol in water. What volumes of pure methanol and of pure water at 25°C must be mixed to form the 2000 cm 3 of antifreeze at 25°C? The partial and pure molar volumes are given. Methanol (1): V 1 = 38.632 cm 3 /mol V 1 = 40.727 cm 3 /mol Water (2) : V 2 = 17.765 cm 3 /mol V 2 = 18.068 cm 3 /mol The total number of moles required is : Now, Volume of the each species:

8. Fig 11.2

9. The enthalpy of a binary liquid system of species 1 and 2 at fixed T and P is: Determine expressions for and as functions of x 1 , numerical values for the pure-species enthalpies H 1 and H 2 , and numerical values for the partial enthalpies at infinite dilution and EXAMPLE : 2

10. RELATIONS AMONG PARTIAL PROPERTIES Maxwell relation:

11. Every equation that provides the linear relation among thermodynamics properties if a constant composition solution has as it’s counterpart an equation connecting corresponding partial properties of each species in that solution.

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