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26: Chemical Equilibrium

Last updated

Apr 16, 2022
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- 25.8: Homework Problems
- 26.1: Equilibrium Results when Gibbs Energy is Minimized

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26.1: Equilibrium Results when Gibbs Energy is Minimized
This page emphasizes the significance of chemical reactions in solutions, particularly in water, focusing on the extent of reaction ( $ξ$ ) and its measurement through the indirect quantity $q$ . It outlines the relationship between Gibbs free energy and $ξ$ , highlighting that equilibrium is achieved when Gibbs energy is minimized. Additionally, it discusses gas reactions, introduces the reaction quotient $Q$ , and addresses varying standard potentials within thermodynamics.
26.2: An Equilibrium Constant is a Function of Temperature Only
This page explains the relationship between Gibbs energy and equilibrium constants using the Van't Hoff equation, which connects temperature, equilibrium constant $K$ , and reaction enthalpy $\Delta_rH$ . It discusses how pressure and temperature changes affect equilibrium positions per Le Chatelier's Principle and clarifies the relationship between concentration and pressure in ideal gases, including the influence of activity coefficients in non-ideal solutions.
26.3: Standard Gibbs Energies of Formation Can Be Used to Calculate Equilibrium Constants
This page discusses the thermodynamic equilibrium constant $K$ and its connection to the standard molar Gibbs energy change $\Delta_r G^\circ$ , including calculation methods using standard molar Gibbs energies of formation. It provides equations relating Gibbs energy, enthalpy, and entropy, emphasizing differences in entropy between ions and neutral substances.
26.4: Gibbs Energy of a Reaction vs. Extent of Reaction is a Minimum at Equilibrium
This page explains the extent of reaction ( $\xi$ ), which quantifies the progress of a chemical reaction. It covers the changes in Gibbs free energy relative to $\xi$ , conditions for spontaneity and equilibrium, and the relationship between chemical potentials of reactants and products.
26.5: Reaction Quotient and Equilibrium Constant Ratio Determines Reaction Direction
This page explains the Gibbs free energy function's role in predicting spontaneous chemical reactions. It connects the reaction quotient $Q$ , standard free energy change $Δ_rG^o$ , and equilibrium constant $K$ . A negative $Δ_rG$ indicates a forward reaction, while a positive value suggests a reverse direction. $Q$ changes with concentrations, contrasting with the constant $K$ .
26.6: The Sign of ΔG and not ΔG° Determines the Direction of Reaction Spontaneity
This page explains the difference between Gibbs energy of reaction ( $\Delta_rG$ ) and standard state Gibbs energy of reaction ( $\Delta_rG^\circ$ ). It notes that $\Delta_rG^\circ$ indicates that the formation of ammonia from nitrogen and hydrogen is favored under standard conditions. The Gibbs energy changes with composition and becomes zero at equilibrium when the reaction quotient matches the equilibrium constant.
26.7: The van 't Hoff Equation
This page explains the Gibbs-Helmholtz equation's significance in analyzing how the equilibrium constant $K$ varies with temperature in chemical reactions, emphasizing the connection to the reaction's enthalpy $ΔH^o$ .
26.8: Equilibrium Constants in Terms of Partition Functions
This page discusses a gas phase chemical reaction's equilibrium properties, focusing on the equilibrium constant (K_c) and chemical potential. It details the calculation of K_c for the formation of HCl from H₂ and Cl₂ using molecular partition functions, including contributions from various states. At 650 K, the reaction is spontaneous with a K_c of about 2.26 x 10^11, attributed to strong H—Cl bond formation despite breaking H—H and Cl—Cl bonds.
26.9: Molecular Partition Functions and Related Thermodynamic Data Are Extensively Tabulated
This page discusses the complexity of real molecules and the need for detailed calculations that can impact efficiency. To simplify access to thermodynamic data, numerical tables like the JANAF tables compile experimental and theoretical properties, including heat capacity, entropy, Gibbs energy, and enthalpy for various substances.
26.10: Real Gases Are Expressed in Terms of Partial Fugacities
This page discusses the limitations of the ideal gas relationship for chemical potential $\mu$ in real gases, necessitating the introduction of fugacity as a correction factor. The fugacity modifies the chemical potential expression to better reflect non-ideal behavior. It introduces the fugacity coefficient $\gamma$ , which connects fugacity to pressure.
26.11: Thermodynamic Equilibrium Constants Are Expressed in Terms of Activities
This page covers the extension of concentration principles to both ideal and non-ideal liquid solutions, emphasizing the use of activity in equilibrium expressions. It underscores the role of the standard state in defining activities for pure solids or liquids. The text concludes that reactions with only pure condensed phases cannot reach equilibrium unless ΔrGo=0, typically at melting points.
26.12: Activities are Important for Ionic Species
This page discusses the differences between weak and strong electrolytes, highlighting that strong electrolytes can be analyzed with Debye-Hückel theory at low concentrations, while weak electrolytes like acetic acid involve equilibrium, complicating analysis. It covers the calculation of equilibrium constants with activity coefficients and iterative methods for estimating ionic activity.
26.13: Homework Problems
This page discusses Werner Heisenberg's uncertainty principle from the mid-1920s, highlighting the inverse relationship between the precision of measuring an electron's position and momentum. It emphasizes the wave nature of particles that limits exact localization and compares the uncertainties in position between a baseball and an electron to illustrate the differences in quantum and classical behaviors.

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