Phase equilibrium occurs when the chemical potential of each component is the same in every phase present. In this chapter, we use that criterion to develop the Gibbs Phase Rule, the Clapeyron and Clausius–Clapeyron equations, and the interpretation of phase diagrams for both pure substances and mixtures. Applications include vapor–liquid equilibrium, distillation, azeotropes, eutectic systems, and the use of cooling curves to determine phase boundaries.
Learn how thermodynamics defines equilibrium between phases. You will see why the equality of chemical potential provides the fundamental criterion for phase equilibrium.
Derive and apply the Gibbs Phase Rule to determine how many variables may be changed independently in a system at equilibrium. This powerful relationship explains the significance of triple points and other phase boundaries.
Derive the Clapeyron equation from the thermodynamic criterion for phase equilibrium. Use it to understand how pressure and temperature are related along a phase boundary.
Use the Clapeyron equation to predict whether a phase boundary will have a positive or negative slope. Connect the behavior of phase diagrams to changes in entropy and molar volume during phase transitions.
Develop the Clausius–Clapeyron equation by applying reasonable approximations to the Clapeyron equation. Understand the assumptions that make the model useful for vaporization and sublimation processes.
Use the Clausius–Clapeyron equation to calculate vapor pressures at different temperatures or determine the enthalpy of a phase change from experimental data.
Interpret temperature-composition phase diagrams for binary mixtures. Identify the phases present in each region and determine how phase composition changes with temperature and overall composition.
Apply the lever rule to determine the relative amounts of material present in coexisting phases. This tool allows quantitative interpretation of two-phase regions in binary phase diagrams.
Use Raoult's Law and Henry's Law to relate liquid composition to vapor pressure and vapor composition. These relationships provide the foundation for understanding vapor-liquid phase diagrams.
Explain how differences in volatility allow mixtures to be separated by distillation. Understand why azeotropes limit the effectiveness of distillation and place fundamental constraints on purification.
Learn how cooling curves reveal phase transitions through changes in cooling behavior. Use these measurements to understand how phase boundaries can be determined experimentally.