Thermodynamics and the Phase Rule

Thermodynamics and the Phase Rule GLY 4200 Fall, 2012

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? 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

Phase Rule • The Phase Rule (J. Willard Gibbs) f = c - p + 2 • System of c components and pphases 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

Thermodynamics and the Phase Rule