Thermodynamics and the Phase Rule GLY 4200 Fall, 2017

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

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

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)

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

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)

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?

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.

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.

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.

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

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

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

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.html

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

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

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

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

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