Thermodynamics and the Phase Rule

1. 1 Thermodynamics and the Phase Rule GLY 4200 Fall, 2011

2. 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. 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. 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. 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. 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 (Cp)

7. 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. 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?

9. 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?

10. 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 The phase assemblage with the lowest G under a specific set of conditions is the most stable

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

12. 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. 13 Reaction Some change in the nature or types of phases in a system

14. 14 Josiah Willard Gibbs Josiah Willard Gibbs (1839 - 1903) 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: http://jwgibbs.cchem.berkeley.edu/jwgibbs_bio.htmlSource: http://jwgibbs.cchem.berkeley.edu/jwgibbs_bio.html

15. 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. 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. 17 3000K

18. 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. 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