1. Physical Transformations of Pure Substances
Chapter 4

2. Stabilities of Phase
A phase of a substance is a form of matter that is uniform throughout in chemical composition and physical state.
A phase transition is the spontaneous conversion of one phase into another.
Phase transitions occur at a characteristic temperature and pressure.

3. Stabilities of Phase
At 1 atm, < 0 °C, ice is the stable phase of H2O, but > 0 °C, liquid water is the stable phase.
The transition temperature, Ttrs, is the temperature at which two phases are in equilibrium.
So what happens to Gibbs energy?

4. Stabilities of Phase
At 1 atm, < 0 °C, ice is the stable phase of H2O, but > 0 °C, liquid water is the stable phase.
The transition temperature, Ttrs, is the temperature at which two phases are in equilibrium.
So what happens to Gibbs energy?
< 0 °C Gibbs energy decreases as liquid  solid.
> 0 °C Gibbs energy decreases as solid  liquid.

5. Stabilities of Phase
Thermodynamics does not provide information regarding the rate of phase change.
Diamond  graphite
Thermodynamically unstable phases that persist due to slow kinetics are called metastable phases.

6. Phase Diagrams
Phase boundaries show the values of p and T at which two phases coexist in equilibrium.

7. Vapor Pressure
The pressure of a vapor in equilibrium with a liquid is called the vapor pressure.
The pressure of a vapor in equilibrium with a solid is called the sublimation vapor pressure.

8. Boiling Point
Liquid can vaporize from a liquid surface below it’s boiling point – as we learnt from the Drinking Bird.
In an open vessel, the temperature at which the vapor pressure equals the external pressure, is called the boiling temperature.
At 1 atm, it’s called the normal boiling temperature, Tb.
At 1 bar, it’s called the standard boiling point.
Normal point of H2O is °C; it’s standard boiling point is 99.6 °C.

9. Critical Point In a closed rigid vessel, boiling does not occur.
As the temperature is raised the density of vapor increases and the density of the liquid decreases.
When the density of the vapor and liquid phases are equal the surface between the two phases disappears.
The temperature at which this occurs is called the critical temperature, Tc.
The vapor pressure at the critical temperature is called the critical pressure, pc.

10. Critical Point

11. Melting and Freezing
The temperature at which, under a specified pressure, the liquid and solid phases of a substance coexist in equilibrium is called them melting temperature.
The freezing temperature is the same as the melting point.
At 1 atm, the freezing temperature is called the normal freezing point, Tf.
At 1 bar, it’s called the standard freezing point.
The difference is negligible in most cases.
The normal freezing point is also called the normal melting point.

12. Triple Point
There is a set of conditions under which three different phases of a substance (typically solid, liquid and vapor) all simultaneously coexist in equilibrium.
This point is called the triple point.
For any pure substance the triple point occurs only at single definite pressure and temperature.
The triple point of water lies at K and 611 Pa.

13. Triple Point
The triple point marks the lowest pressure at which a liquid phase can exist.

14. Carbon Dioxide

15. Water

16. Helium
Helium-4 isotope

17. Thermodynamics of Phase Transitions
The molar Gibbs energy, Gm, is also called chemical potential, m. Phase transitions will be investigated primarily considering the change in m.
Thermodynamic definition of equilibrium: At equilibrium the chemical potential of a substance is the same throughout the sample, regardless of how many phases are present.

18. Thermodynamics of Phase Transitions

19. Thermodynamics of Phase Transitions
At low temperatures, and provided the pressure is not too low, the solid phase of a substance has the lowest chemical potential and is therefore the most stable.
Chemical potentials change with temperature: this explains why different phases exist.

20. Temperature Dependence of Phase Transitions
As temperature increases, chemical potential decreases.

21. Melting and Applied Pressure
Molar volume of solid is smaller than that of the liquid.

22. Melting and Applied Pressure
Molar volume of solid is greater than that of the liquid.

23. Melting and Applied Pressure

24. Melting and Applied Pressure
Calculate the effect on the chemical potentials of ice and water of increasing pressure from 1.00 to 2.00 bar at 0 °C. The density of ice is g cm-3 and that of liquid water is g cm-3.

25. Melting and Applied Pressure
Calculate the effect on the chemical potentials of ice and water of increasing pressure from 1.00 to 2.00 bar at 0 °C. The density of ice is g cm-3 and that of liquid water is g cm-3.

26. Vapor Pressure and Applied Pressure
When pressure is applied to a condensed phase, its vapor pressure rises.
This is interpreted as molecules get squeezed out of the condensed phase and escape as a gas.

27. Vapor Pressure and Applied Pressure
Pressurizing gas may dissolve in liquid
Gas solvation

28. Location of Phase Boundaries
Locations of phase boundaries – pressures and temperatures - can be located precisely by making use of the fact that at when two phases are in equilibrium, their chemical potentials must be equal

29. Location of Phase Boundaries

30. Location of Phase Boundaries

31. Solid-liquid boundary
Enthalpies of fusion are positive,
Delta V is small and usually positive.

32. Solid-liquid boundary

33. Solid-liquid boundary

34. Solid-liquid boundary

35. Liquid-vapor boundary
Enthalpy positive
Delta v is large so dp/dT not as large as solid-vapor

36. Liquid-vapor boundary

37. Liquid-vapor boundary

38. Liquid-vapor boundary

39. Liquid-vapor boundary

40. Solid-gas boundary