1. Thermodynamics and the Phase Rule
GLY 4200
Fall, 2012

2. Thermodynamic Background
System: The portion of the universe that is being studied
Surroundings: The part of the universe not included in the system

3. Free Energy Any change in the system involves a transfer of energy
All chemical systems tend naturally toward states of minimum Gibbs free energy

4. Gibbs Free Energy G = H - TS Where: G = Gibbs Free Energy
H = Enthalpy (heat content)
T = Temperature in Kelvin
S = Entropy (a measure of randomness)

5. Alternative Equation
For other temperatures and pressures we can use the equation: dG = VdP – SdT
where V = volume and S = entropy (both molar)
This equation can be used to calculate G for any phase at any T and P by integrating
GT2P2 - GT1P1 = ∫P1P2VdP - ∫T1T2SdT

6. Using Thermodynamics
G is a measure of relative chemical stability for a phase
We can determine G for any phase by measuring H and S for the reaction creating the phase from the elements (SiO2 from silicon and oxygen, for example)
We can then determine G at any T and P mathematically
How do V and S vary with P and T?
dV/dP is the coefficient of isothermal compressibility
dS/dT is the heat capacity at constant pressure (Cp)

7. Applying Thermodynamics
If we know G for various phases, we can determine which is most stable
With appropriate reactions comparing two or more phases, we can answer questions like:
Why is melt more stable than solids at high T?
Which polymorphic phase will be stable under given conditions?
What will be the effect of increased P on melting?

8. High Pressure
High pressure favors low volume, so which phase should be stable at high P?
Hint: Does the liquid or solid have the larger volume?
Figure 5-2. Schematic P-T phase diagram of a melting reaction. Winter (2001) An Introduction to Igneous and Metamorphic Petrology. Prentice Hall.

9. High Temperature
High temperature favors randomness, so which phase should be stable at higher T?
Hint: Does liquid or solid have a higher entropy?
Figure 5-2. Schematic P-T phase diagram of a melting reaction. Winter (2001) An Introduction to Igneous and Metamorphic Petrology. Prentice Hall.

10. Stability
Does the liquid or solid have the lowest G at point A? at point B?
The phase assemblage with the lowest G under a specific set of conditions is the most stable
Figure 5-2. Schematic P-T phase diagram of a melting reaction. Winter (2001) An Introduction to Igneous and Metamorphic Petrology. Prentice Hall.

11. Intensive Property
An intensive property does not depend on the amount of material present
Examples: Temperature, density, electric or magnetic field strength

12. Phase
Phase: Any homogeneous region, characterized by certain intensive properties, and separated from other phases by discontinuities in one or more of those intensive properties
Solid, often a mineral
Liquid
Vapor
Note: # of regions is not important, just the # of kinds of regions

13. Reaction
Some change in the nature or types of phases in a system

14. Josiah Willard Gibbs
Josiah Willard Gibbs ( ) has been reckoned as one of the greatest American scientists of the 19th century
He provided a sound thermodynamic foundation to much of Physical Chemistry
Yale educated, he was awarded the first Doctor of Engineering in the U.S., and was appointed Professor of Mathematical Physics at Yale in 1871
Source:

15. Phase Rule The Phase Rule (J. Willard Gibbs) f = c - p + 2
System of c components and p phases has variance “f”, the degrees of freedom
f = # degrees of freedom = The number of intensive parameters that must be specified in order to completely determine the system
Intensive variables are pressure, temperature, and composition, that can be changed independently without loss of a phase

16. Phase Rule 2 p =number of phases
phases are mechanically separable constituents
c = minimum number of components, which are chemical constituents that must be specified in order to define all phases

17. 3000K
H2O ↔ H2 + ½O2
Two components are present - since the other can be made from whichever of the two have been chosen
Thus, a stoichiometric relationship between substances reduces the number of components necessary

18. Alternative Definition of Number of Components
The minimum number of pure chemical substances that are required for arbitrary amounts of all phases of the system

19. Extended Phase Rule f = c - p + x
Where x is the number of intensive variables, pressure, temperature, composition, and possibly magnetic and electric fields, that can be changed independently without loss of a phase