17: Chemical Thermodynamics
- Page ID
- 7325
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\(\newcommand{\avec}{\mathbf a}\) \(\newcommand{\bvec}{\mathbf b}\) \(\newcommand{\cvec}{\mathbf c}\) \(\newcommand{\dvec}{\mathbf d}\) \(\newcommand{\dtil}{\widetilde{\mathbf d}}\) \(\newcommand{\evec}{\mathbf e}\) \(\newcommand{\fvec}{\mathbf f}\) \(\newcommand{\nvec}{\mathbf n}\) \(\newcommand{\pvec}{\mathbf p}\) \(\newcommand{\qvec}{\mathbf q}\) \(\newcommand{\svec}{\mathbf s}\) \(\newcommand{\tvec}{\mathbf t}\) \(\newcommand{\uvec}{\mathbf u}\) \(\newcommand{\vvec}{\mathbf v}\) \(\newcommand{\wvec}{\mathbf w}\) \(\newcommand{\xvec}{\mathbf x}\) \(\newcommand{\yvec}{\mathbf y}\) \(\newcommand{\zvec}{\mathbf z}\) \(\newcommand{\rvec}{\mathbf r}\) \(\newcommand{\mvec}{\mathbf m}\) \(\newcommand{\zerovec}{\mathbf 0}\) \(\newcommand{\onevec}{\mathbf 1}\) \(\newcommand{\real}{\mathbb R}\) \(\newcommand{\twovec}[2]{\left[\begin{array}{r}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\ctwovec}[2]{\left[\begin{array}{c}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\threevec}[3]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\cthreevec}[3]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\fourvec}[4]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\cfourvec}[4]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\fivevec}[5]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\cfivevec}[5]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\mattwo}[4]{\left[\begin{array}{rr}#1 \amp #2 \\ #3 \amp #4 \\ \end{array}\right]}\) \(\newcommand{\laspan}[1]{\text{Span}\{#1\}}\) \(\newcommand{\bcal}{\cal B}\) \(\newcommand{\ccal}{\cal C}\) \(\newcommand{\scal}{\cal S}\) \(\newcommand{\wcal}{\cal W}\) \(\newcommand{\ecal}{\cal E}\) \(\newcommand{\coords}[2]{\left\{#1\right\}_{#2}}\) \(\newcommand{\gray}[1]{\color{gray}{#1}}\) \(\newcommand{\lgray}[1]{\color{lightgray}{#1}}\) \(\newcommand{\rank}{\operatorname{rank}}\) \(\newcommand{\row}{\text{Row}}\) \(\newcommand{\col}{\text{Col}}\) \(\renewcommand{\row}{\text{Row}}\) \(\newcommand{\nul}{\text{Nul}}\) \(\newcommand{\var}{\text{Var}}\) \(\newcommand{\corr}{\text{corr}}\) \(\newcommand{\len}[1]{\left|#1\right|}\) \(\newcommand{\bbar}{\overline{\bvec}}\) \(\newcommand{\bhat}{\widehat{\bvec}}\) \(\newcommand{\bperp}{\bvec^\perp}\) \(\newcommand{\xhat}{\widehat{\xvec}}\) \(\newcommand{\vhat}{\widehat{\vvec}}\) \(\newcommand{\uhat}{\widehat{\uvec}}\) \(\newcommand{\what}{\widehat{\wvec}}\) \(\newcommand{\Sighat}{\widehat{\Sigma}}\) \(\newcommand{\lt}{<}\) \(\newcommand{\gt}{>}\) \(\newcommand{\amp}{&}\) \(\definecolor{fillinmathshade}{gray}{0.9}\)- 17.1: Equilibrium Constant
- This page covers chemical reactions, emphasizing a reversible reaction between reactants A and B and products C and D. It focuses on chemical equilibrium, where the rates of forward and backward reactions are equal, resulting in a stable ratio of reactants and products known as the equilibrium constant, which changes with temperature. The page also briefly addresses simpler reactions like dissociation and ionization, connecting their equilibrium constants to temperature and energy.
- 17.2: Heat of Reaction
- This page covers exothermic and endothermic reactions, defining them based on heat dynamics. It explains the heat of reaction with positive and negative values for endothermic and exothermic processes, respectively. It clarifies measurements at constant pressure (∆H) and constant volume (∆U), noting that ∆H is generally larger. The page stresses the significance of specifying conditions like temperature, pressure, and reactant states for accurate reporting of heats of reaction.
- 17.3: The Gibbs Phase Rule
- This page explains the Gibbs Phase Law, which connects the number of phases, components, and degrees of freedom in thermodynamic systems. Important concepts include the definitions of "phase" and "components." It illustrates the determination of degrees of freedom using the formula \(F = C - P + 2\) and highlights the law's relevance in practical contexts, particularly in binary and ternary alloys.
- 17.4: Chemical Potential
- This page explores the impact of heat and expansion on internal energy, enthalpy, Helmholtz function, and Gibbs function in closed systems, using differential calculus. It details how these thermodynamic functions change with the addition of matter, linked by the concept of chemical potential.
- 17.5: Partial and Mean Molar Quantities
- This page covers partial molar volumes, explaining their importance in component mixtures and introducing concepts like mole fraction and their effect on volume at constant conditions. It defines partial molar volumes and contrasts them with molar volumes, linking these quantities to Gibbs functions for understanding phase equilibrium. The page concludes with a focus on partial pressures in mixtures of ideal gases, including Dalton’s Law of Partial Pressures.
- 17.6: The Gibbs-Duhem Relation
- This page explains the connection between chemical potential, Gibbs function, and a mixture's composition at constant temperature and pressure. It introduces the relationship between chemical potential (µi) and partial molar Gibbs function (gi), as well as the Gibbs-Duhem relation that describes how chemical potentials change with composition.
- 17.7: Chemical Potential, Pressure, Fugacity
- This page covers the calculation of the Gibbs function change for ideal gases transitioning between states, detailing equations for Gibbs energy based on temperature and pressure. It introduces chemical potential in mixtures and establishes relationships through equations connecting Gibbs energy, partial pressures, and fugacity. The summary emphasizes key equations and the necessary adjustments for non-ideality in gas mixtures, focusing on the importance of temperature-dependent constants.
- 17.8: Entropy of Mixing, and Gibbs' Paradox
- This page explains entropy's role in thermodynamics, detailing its increase through heat and irreversible work. It discusses how heat flows from hot to cold, leading to greater disorder, and quantitatively analyzes gas mixing, concluding that entropy rises when different gases combine. Additionally, it addresses Gibbs’ Paradox and links the Gibbs function to chemical equilibrium, enhancing the comprehension of entropy's significance in thermodynamic processes.
- 17.9: Binary Alloys
- This page details the melting and solidification of tin (Sn) and lead (Pb) as an alloy, highlighting their liquid miscibility and differing crystallization upon cooling. It presents the melting points of pure Pb and Sn and features a graph of melting point versus composition. The solidification process is described, particularly at the eutectic point of 183 ºC with 26% Pb, where crystallization occurs for both metals.
- 17.10: Ternary Alloys
- This page discusses the phase equilibria of a Pb-Bi-Sn alloy through a triangular prism model. It utilizes eutectic diagrams to illustrate the sequential solidification of metals at varying temperatures, beginning with Pb, then Bi, and finally Sn. As the temperature drops, solidification patterns form from the corners of the triangle towards a central eutectic point, signifying complete solidification below a critical temperature, highlighting an important transition in the alloy's composition.