8.S: Phase Equilibrium (Summary)
- Page ID
- 84540
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\(\newcommand{\avec}{\mathbf a}\) \(\newcommand{\bvec}{\mathbf b}\) \(\newcommand{\cvec}{\mathbf c}\) \(\newcommand{\dvec}{\mathbf d}\) \(\newcommand{\dtil}{\widetilde{\mathbf d}}\) \(\newcommand{\evec}{\mathbf e}\) \(\newcommand{\fvec}{\mathbf f}\) \(\newcommand{\nvec}{\mathbf n}\) \(\newcommand{\pvec}{\mathbf p}\) \(\newcommand{\qvec}{\mathbf q}\) \(\newcommand{\svec}{\mathbf s}\) \(\newcommand{\tvec}{\mathbf t}\) \(\newcommand{\uvec}{\mathbf u}\) \(\newcommand{\vvec}{\mathbf v}\) \(\newcommand{\wvec}{\mathbf w}\) \(\newcommand{\xvec}{\mathbf x}\) \(\newcommand{\yvec}{\mathbf y}\) \(\newcommand{\zvec}{\mathbf z}\) \(\newcommand{\rvec}{\mathbf r}\) \(\newcommand{\mvec}{\mathbf m}\) \(\newcommand{\zerovec}{\mathbf 0}\) \(\newcommand{\onevec}{\mathbf 1}\) \(\newcommand{\real}{\mathbb R}\) \(\newcommand{\twovec}[2]{\left[\begin{array}{r}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\ctwovec}[2]{\left[\begin{array}{c}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\threevec}[3]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\cthreevec}[3]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\fourvec}[4]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\cfourvec}[4]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\fivevec}[5]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\cfivevec}[5]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\mattwo}[4]{\left[\begin{array}{rr}#1 \amp #2 \\ #3 \amp #4 \\ \end{array}\right]}\) \(\newcommand{\laspan}[1]{\text{Span}\{#1\}}\) \(\newcommand{\bcal}{\cal B}\) \(\newcommand{\ccal}{\cal C}\) \(\newcommand{\scal}{\cal S}\) \(\newcommand{\wcal}{\cal W}\) \(\newcommand{\ecal}{\cal E}\) \(\newcommand{\coords}[2]{\left\{#1\right\}_{#2}}\) \(\newcommand{\gray}[1]{\color{gray}{#1}}\) \(\newcommand{\lgray}[1]{\color{lightgray}{#1}}\) \(\newcommand{\rank}{\operatorname{rank}}\) \(\newcommand{\row}{\text{Row}}\) \(\newcommand{\col}{\text{Col}}\) \(\renewcommand{\row}{\text{Row}}\) \(\newcommand{\nul}{\text{Nul}}\) \(\newcommand{\var}{\text{Var}}\) \(\newcommand{\corr}{\text{corr}}\) \(\newcommand{\len}[1]{\left|#1\right|}\) \(\newcommand{\bbar}{\overline{\bvec}}\) \(\newcommand{\bhat}{\widehat{\bvec}}\) \(\newcommand{\bperp}{\bvec^\perp}\) \(\newcommand{\xhat}{\widehat{\xvec}}\) \(\newcommand{\vhat}{\widehat{\vvec}}\) \(\newcommand{\uhat}{\widehat{\uvec}}\) \(\newcommand{\what}{\widehat{\wvec}}\) \(\newcommand{\Sighat}{\widehat{\Sigma}}\) \(\newcommand{\lt}{<}\) \(\newcommand{\gt}{>}\) \(\newcommand{\amp}{&}\) \(\definecolor{fillinmathshade}{gray}{0.9}\)Learning Objectives
After mastering the material in this chapter, one will be able to
- State the thermodynamic criterion for equilibrium in terms of chemical potential.
- Derive and interpret the Gibbs Phase Rule.
- Derive the Clapeyron equation from the thermodynamic criterion for equilibrium.
- Interpret the slope of phase boundaries on a pressure-temperature phase diagram in terms of the relevant changes in entropy and molar volume for the given phase change.
- Derive the Clausius-Clapeyron equation, stating all of the necessary approximations.
- Use the Clausius-Clapeyron equation to calculate the vapor pressure of a substance or the enthalpy of a phase change from pressure-temperature data.
- Interpret phase diagrams for binary mixtures, identifying the phases and components present in each region.
- Perform calculations using Raoult’s Law and Henry’s Law to relate vapor pressure to composition in the liquid phase.
- Describe the distillation process, explaining how the composition of liquid and vapor phases can differ, and how azeotrope composition place bottlenecks in the distillation process.
- Describe how cooling curves are used to derive phase diagrams by locating phase boundaries.
Vocabulary and Concepts
- azeotrope
- Clapeyron equation
- Clausius-Clapeyron equation
- compositional degrees of freedom
- cooling curve
- distillation
- eutectic halt
- eutectic point
- Gibbs phase rule
- Henry’s Law
- incongruent melting
- lever rule
- lower critical temperature
- phase diagram
- platinum resistance thermometer
- Raoult’s law
- scanning calorimetry
- thermodynamic constraints
- triple point
- upper critical temperature
- volatile liquid
References
- Ferloni, P., & Spinolo, G. (1974). Int. DATA Ser., Sel. Data Mixtures, Ser. A, 70.
- Ghosh, P., Mezbahul-Islam, M., & Medraj, M. (2011). Critical assessment and thermodynamic modeling of Mg–Zn, Mg–Sn, Sn–Zn and Mg–Sn–Zn systems. Calphad, 36, 28-43.
- Nave, R. (n.d.). Saturated Vapor Pressure, Density for Water. (Georgia State University, Department of Physics and Astronomy) Retrieved April 7, 2016, from HyperPhysics: http://hyperphysics.phy-astr.gsu.edu...ic/watvap.html
- Rossen, G. L., & Bleiswijk, H. v. (1912). Über das Zustandsdiagramm der Kalium-Natriumlegierungen. Zeitschrift für anorganische Chemie, 74(1), 152-156.
- Strouse, G. F. (2008, January). Standard Platinum Resistance Thermometer Calibrations from the Ar TP to the Ag FP. National Institute of Standards and Technology Special Publication 250-81.