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8: Phase Equilibrium

Last updated

Apr 13, 2022
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- 7.S: Mixtures and Solutions (Summary)
- 8.1: Prelude to Phase Equilibrium

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8.1: Prelude to Phase Equilibrium
The text describes the basic classification of matter into solid, liquid, and gas phases based on shape and volume characteristics. It notes that while this categorization is elementary, further exploration reveals that solids and liquids are not entirely incompressible. The chapter aims to use thermodynamic principles to delve deeper into understanding phase boundaries and their properties.
8.2: Single Component Phase Diagrams
Phase stability is determined by the chemical potential, where the most stable phase has the lowest chemical potential at certain conditions. Phase diagrams can represent this, with phase boundaries found by observing cooling rates. During a phase change, temperature pauses until heat extraction completes, revealing boundary points. Similar data can be collected through controlled heating, such as scanning calorimetry, identifying phase change temperatures by temperature measurement pauses.
8.3: Criterion for Phase Equilibrium
The thermodynamic criterion for phase equilibrium is based on the chemical potentials of components in a system. A single-component system reaches equilibrium when the chemical potential is the same across phases, preventing mass migration. The Gibbs phase rule describes the system's degrees of freedom, balancing compositional and phase variables. For a single component, the maximum phases at equilibrium is three, defining a "triple point.
8.4: The Clapeyron Equation
The page discusses the thermodynamic criterion for equilibrium between two phases, using the Clapeyron equation to describe the relationship between pressure and temperature changes. It explains how the chemical potentials of phases must be equal in equilibrium and derives the Clapeyron equation, which relates the change in pressure to the change in temperature and the differences in molar volume and entropy.
8.5: The Clausius-Clapeyron Equation
The page discusses the derivation and application of the Clausius-Clapeyron equation for phase equilibria involving gas phases, focusing on vaporization. It explains the equation's construction, assumptions (e.g., treating vapor as an ideal gas), and integration. An example problem uses known temperature and vapor pressure conditions to find the enthalpy of vaporization ( $\Delta H_{vap}$ ).
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
The document discusses the volatility of liquids and how they transition to the vapor phase at increased temperatures. It describes Raoult???s Law, which predicts the total vapor pressure above a mixture of two volatile liquids, highlighting that the vapor phase composition differs from the liquid phase. Additionally, it explores phase diagrams at constant pressure and illustrates how distillation can purify a more volatile liquid from a mixture by collecting and re-evaporating vapor fractions.
8.8: Non-ideality - Henry's Law and Azeotropes
The page discusses the behaviors of ideal solutions of volatile compounds that obey Raoult's Law and how Henry's Law can describe deviations. It features an example calculating the Henry's Law constant for the solubility of CO2 in water. The page also covers azeotropes, explaining their characteristics and phase diagrams, which represent maximum and minimum boiling points. It includes examples and solutions to illustrate these concepts and their implications in phases and compositions.
8.9: Solid-Liquid Systems - Eutectic Points
The page explains phase diagrams for two-component systems with eutectic points. It describes the behavior of solid and liquid phases, detailing scenarios including immiscible solids and liquid phases, formation of third compounds, and incongruent melting, where stable compounds decompose upon melting. Example systems like tin-lead, zinc-magnesium, and sodium-potassium are discussed, illustrating different behaviors of solid-liquid equilibria and chemical reactions forming new compounds.
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)
The page outlines learning objectives for a chapter on thermodynamics, including understanding chemical potential for equilibrium, deriving and interpreting the Gibbs Phase Rule and Clapeyron equation, and using the Clausius-Clapeyron equation for calculations. It also covers phase diagrams, Raoult???s and Henry???s Laws, and distillation processes. Vocabulary terms such as azeotrope and eutectic point are introduced.

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