24: Solutions I - Volatile Solutes
- Page ID
- 11820
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\(\newcommand{\avec}{\mathbf a}\) \(\newcommand{\bvec}{\mathbf b}\) \(\newcommand{\cvec}{\mathbf c}\) \(\newcommand{\dvec}{\mathbf d}\) \(\newcommand{\dtil}{\widetilde{\mathbf d}}\) \(\newcommand{\evec}{\mathbf e}\) \(\newcommand{\fvec}{\mathbf f}\) \(\newcommand{\nvec}{\mathbf n}\) \(\newcommand{\pvec}{\mathbf p}\) \(\newcommand{\qvec}{\mathbf q}\) \(\newcommand{\svec}{\mathbf s}\) \(\newcommand{\tvec}{\mathbf t}\) \(\newcommand{\uvec}{\mathbf u}\) \(\newcommand{\vvec}{\mathbf v}\) \(\newcommand{\wvec}{\mathbf w}\) \(\newcommand{\xvec}{\mathbf x}\) \(\newcommand{\yvec}{\mathbf y}\) \(\newcommand{\zvec}{\mathbf z}\) \(\newcommand{\rvec}{\mathbf r}\) \(\newcommand{\mvec}{\mathbf m}\) \(\newcommand{\zerovec}{\mathbf 0}\) \(\newcommand{\onevec}{\mathbf 1}\) \(\newcommand{\real}{\mathbb R}\) \(\newcommand{\twovec}[2]{\left[\begin{array}{r}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\ctwovec}[2]{\left[\begin{array}{c}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\threevec}[3]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\cthreevec}[3]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\fourvec}[4]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\cfourvec}[4]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\fivevec}[5]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\cfivevec}[5]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\mattwo}[4]{\left[\begin{array}{rr}#1 \amp #2 \\ #3 \amp #4 \\ \end{array}\right]}\) \(\newcommand{\laspan}[1]{\text{Span}\{#1\}}\) \(\newcommand{\bcal}{\cal B}\) \(\newcommand{\ccal}{\cal C}\) \(\newcommand{\scal}{\cal S}\) \(\newcommand{\wcal}{\cal W}\) \(\newcommand{\ecal}{\cal E}\) \(\newcommand{\coords}[2]{\left\{#1\right\}_{#2}}\) \(\newcommand{\gray}[1]{\color{gray}{#1}}\) \(\newcommand{\lgray}[1]{\color{lightgray}{#1}}\) \(\newcommand{\rank}{\operatorname{rank}}\) \(\newcommand{\row}{\text{Row}}\) \(\newcommand{\col}{\text{Col}}\) \(\renewcommand{\row}{\text{Row}}\) \(\newcommand{\nul}{\text{Nul}}\) \(\newcommand{\var}{\text{Var}}\) \(\newcommand{\corr}{\text{corr}}\) \(\newcommand{\len}[1]{\left|#1\right|}\) \(\newcommand{\bbar}{\overline{\bvec}}\) \(\newcommand{\bhat}{\widehat{\bvec}}\) \(\newcommand{\bperp}{\bvec^\perp}\) \(\newcommand{\xhat}{\widehat{\xvec}}\) \(\newcommand{\vhat}{\widehat{\vvec}}\) \(\newcommand{\uhat}{\widehat{\uvec}}\) \(\newcommand{\what}{\widehat{\wvec}}\) \(\newcommand{\Sighat}{\widehat{\Sigma}}\) \(\newcommand{\lt}{<}\) \(\newcommand{\gt}{>}\) \(\newcommand{\amp}{&}\) \(\definecolor{fillinmathshade}{gray}{0.9}\)- 24.1: A Mixture is a Combination of Two or More Substances
- This page covers the thermodynamics of two-component mixtures, detailing aspects like volume changes, Gibbs free energy, and partial molar volumes. It highlights Dalton's Law for gases, varying behaviors of liquid mixtures, and solid miscibility. Additionally, it examines a binary mixture of toluene and benzene, discussing vapor-liquid equilibrium, phase diagrams, the Lever Rule, and the distillation process for component separation.
- 24.2: The Gibbs-Duhem Equation Relates Chemical Potential and Composition at Equilibrium
- This page discusses the Gibbs-Duhem relationship, which states that at equilibrium, chemical potential changes in a mixture at constant temperature and pressure are linked to the system's composition. Derived from Gibbs free energy, it shows the interrelation of chemical potentials in binary systems and their dependence on concentration, relating to Raoult's law. Ultimately, the relationship emphasizes the thermodynamic consistency necessary for equilibrium in multi-component systems.
- 24.3: Chemical Potential of Each Component Has the Same Value in Each Phase in Which the Component Appears
- This page explains the partial molar Gibbs function, also known as chemical potential, and its role in determining how the Gibbs function changes with mixture composition. It notes that systems minimize Gibbs function to reach equilibrium through chemical potential, which can be derived from key thermodynamic functions (U, H, A, G).
- 24.4: Ideal Solutions obey Raoult's Law
- This page explains that volatile liquids vaporize at higher temperatures, with their behavior described by Raoult’s Law, predicting vapor pressure and composition favoring volatile compounds. Phase diagrams illustrate temperature and composition relationships. Distillation is used to purify volatile components. Ideal solutions show decreased Gibbs free energy during mixing, confirming spontaneity, with negligible enthalpy changes.
- 24.5: Most Solutions are Not Ideal
- This page explores the link between partial pressures and mole fractions in mixtures, detailing Raoult's law for ideal solutions and Henry's law for dilute solutions. It notes that as a component's mole fraction nears 1, Raoult's law becomes applicable, while at low concentrations, Henry's law is relevant.
- 24.6: Vapor Pressures of Volatile Binary Solutions
- This page discusses various laws and concepts relevant to solutions: Raoult’s Law applies to ideal volatile solutions, while Henry's Law addresses gas solubility deviations. Azeotropes feature constant vapor-liquid ratios, complicating distillation. The Gibbs-Duhem relation illustrates component interactions in non-ideal solutions, linking Raoult's and Henry's Laws. Additionally, Margules functions approximate non-ideality across compositions, needing experimental data for precision.
- 24.7: Activities of Nonideal Solutions
- This page explores the concept of activity in solutions to explain deviations from ideal behavior, using activity coefficients to link real solute concentrations to chemical potential. It addresses ionic solutes through the mean activity coefficient with a geometric average, applying the Debye-Hückel law for calculations from experimental data. The chapter contrasts Raoult’s and Henry's laws, highlighting the importance of varying concentration units for solutes, especially non-volatile ones.
- 24.8: Activities are Calculated with Respect to Standard States
- This page discusses thermodynamic activity (\(a\)), which reflects the effective concentration of a species in a mixture and is dimensionless. It relates to fugacity for gases and concentration for solutions. In ideal gas systems, activity simplifies to \(a_i = \frac{P_i}{P^{\circ}}\), while in solutions, it includes activity coefficients. For solids or liquids, the activity is defined as \(a_i = 1\).
- 24.9: Gibbs Energy of Mixing of Binary Solutions in Terms of the Activity Coefficient
- This page outlines activity and activity coefficients in non-ideal solutions, detailing their connection to mole fractions and Gibbs free energy changes. It discusses azeotropes, eutectics, and the impact of pressure on boiling points, emphasizing that lower pressures can lead to early boiling of mixtures. As temperature increases, mutual solubility improves until reaching the eutectic point, where distinct boiling behaviors occur.