1. Physical Transformations of Pure substances By Doba Jackson, Ph.D. Assistant Professor Huntingdon College

2. Some Definitions Phase- A form of matter that is uniform throughout in chemical composition and physical state Phase Transition- The spontaneous conversion of one phase to another Single PhaseMultiple Phase

3. Phase changes are spontaneous events depend on the temperature and pressure

4. Phase diagrams illustrates the most stable phase at a each temperature and pressure

5. The most stable phase can be determined by the Gibbs Energy Chemical Potential (μ = G m )

6. Chemical Potential Chemical Potential (μ)- is a measure of the potential that a substance has to undergo a change in state or composition Molar Gibbs energy (G m )- is the maximum energy that a system has available for non-expansion work. For all Pure substances: μ = G m

7. Thermodynamic Criteria for Phase Equilibrium - At equilibrium, the Chemical Potential of a substance is the same throughout the sample, regardless of the amount of phases. μ1μ1 μ2μ2 At Equilibrium

8. Gibbs Phase Rule J.W. Gibbs presented an elegant rule that basically specifies that the number of phases in equilibrium is constrained by the number of components and the number of intensive variables. C = number of Components present P = max. number of Phases in Equilibrium F = max. number of intensive variables One-component Phase diagram F = 3 - P

9. Phase Diagram for Carbon Dioxide

10. Phase Diagram for Water Ice- I

11. Phase Diagram for Helium

12. Location of Phase boundaries Clapeyon Equation

13. Clausius-Clapeyron equation for variation of vapor pressure and temperature Clausius-Clapeyron Eq.

14. Problem 4.1- How many phases are present in each of the points marked in figure.

15. Problem 4.4 What is the maximum number of phases that can be in mutual equilibrium in a 4-component system.

16. Problem 4.12 When benzene freezes at 5.5*C and its density changes from.879 g/cm3 to.891 g/cm3. Its Enthalpy of fusion is 10.59 kJ/mol. Estimate the freezing point of benzene at 1000 atm.