# 8: Phase Equilibrium

• 8.1: Prelude to Phase Equilibrium
From the very elementary stages of our journey to describe the physical nature of matter, we learn to classify mater into three (or more) phases: solid, liquid, and gas. This is a fairly easy classification system that can be based on such simple ideas as shape and volume.
• 8.2: Single Component Phase Diagrams
The stability of phases can be predicted by the chemical potential, in that the most stable form of the substance will have the minimum chemical potential at the given temperature and pressure.
• 8.3: Criterion for Phase Equilibrium
The thermodynamic criterion for phase equilibrium is simple. It is based upon the chemical potentials of the components in a system. For simplicity, consider a system with only one component. For the overall system to be in equilibrium, the chemical potential of the compound in each phase present must be the same.
• 8.4: The Clapeyron Equation
Based on the thermodynamic criterion for equilibrium, it is possible to draw some conclusions about the state variables p and T and how they are related along phase boundaries. This results in the Clapeyron equation.
• 8.5: The Clausius-Clapeyron Equation
The Clapeyron equation can be developed further for phase equilibria involving the gas phase as one of the phases. This is the case for either sublimation (solid → gas) or vaporization (liquid → gas).
• 8.6: Phase Diagrams for Binary Mixtures
As suggested by the Gibbs Phase Rule, the most important variables describing a mixture are pressure, temperature and composition. In the case of single component systems, composition is not important so only pressure and temperature are typically depicted on a phase diagram. However, for mixtures with two components, the composition is of vital important, so there is generally a choice that must be made as to whether the other variable to be depicted is temperature or pressure.
• 8.7: Liquid-Vapor Systems - Raoult’s Law
Liquids tend to be volatile, and as such will enter the vapor phase when the temperature is increased to a high enough value (provided they do not decompose first!) A volatile liquid is one that has an appreciable vapor pressure at the specified temperature. An ideal mixture continuing at least one volatile liquid can be described using Raoult’s Law.
• 8.8: Non-ideality - Henry's Law and Azeotropes
The proceeding discussion was based on the behaviors of ideal solutions of volatile compounds, and for which both compounds follow Raoult’s Law. Henry’s Law can be used to describe these deviations.
• 8.9: Solid-Liquid Systems - Eutectic Points
Phase diagrams are often complex with multiple phases that exhibit  differing non-ideal behavior like minimum boiling azeotropes, eutectic points (omposition for which the mixture of the two solids has the lowest melting point), incongruent melting where the stable compound formed by two solids is only stable in the solid phase and will decompose upon melting.
• 8.10: Cooling Curves
The method that is used to map the phase boundaries on a phase diagram is to measure the rate of cooling for a sample of known composition. The rate of cooling will change as the sample (or some portion of it) begins to undergo a phase change. These “breaks” will appear as changes in slope in the temperature-time curve.
• 8.E: Phase Equilibrium (Exercises)
Exercises for Chapter 8 "Phase Equilibrium" in Fleming's Physical Chemistry Textmap.
• 8.S: Phase Equilibrium (Summary)
Summary for Chapter 8 "Phase Equilibrium" in Fleming's Physical Chemistry Textmap.