Textbook Question
Calculate ∆G°rxn and K for each reaction. b. The reaction of Cr3+(aq) and Cr(s) to form Cr2+(aq). [The electrode potential of Cr2+(aq) to Cr(s) is -0.91 V.]
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Ch.19 - Electrochemistry
Tro4th EditionChemistry: A Molecular ApproachISBN: 9780134112831
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Table of contents
- Ch.1 - Matter, Measurement & Problem Solving107
- Ch.2 - Atoms & Elements100
- Ch.3 - Molecules, Compounds & Chemical Equations127
- Ch.4 - Chemical Quantities & Aqueous Reactions114
- Ch.5 - Gases103
- Ch.6 - Thermochemistry92
- Ch.7 - Quantum-Mechanical Model of the Atom50
- Ch.8 - Periodic Properties of the Elements89
- Ch.9 - Chemical Bonding I: The Lewis Model84
- Ch.10 - Chemical Bonding II: Molecular Shapes & Valence Bond Theory74
- Ch.11 - Liquids, Solids & Intermolecular Forces60
- Ch.12 - Solids and Modern Material50
- Ch.13 - Solutions90
- Ch.14 - Chemical Kinetics111
- Ch.15 - Chemical Equilibrium65
- Ch.16 - Acids and Bases135
- Ch.17 - Aqueous Ionic Equilibrium145
- Ch.18 - Free Energy and Thermodynamics92
- Ch.19 - Electrochemistry100
- Ch.20 - Radioactivity and Nuclear Chemistry68
- Ch.21 - Organic Chemistry121
Chapter 19, Problem 122a
Calculate ∆G°rxn and K for each reaction. a. The reaction of Cr2+(aq) with Cr2O72–(aq) in acid solution to form Cr3+(aq).
Verified step by step guidance1
Identify the half-reactions involved in the overall reaction. For the reduction of dichromate ion, Cr2O7^2-(aq), to Cr3+(aq) and the oxidation of Cr2+(aq) to Cr3+(aq) in acidic solution.
Balance the half-reactions for mass and charge. In acidic solution, use H+ and H2O to balance oxygen and hydrogen atoms respectively. Electrons should be added to balance the charges on both sides of each half-reaction.
Combine the half-reactions to get the overall balanced chemical equation. Ensure that the number of electrons lost in the oxidation half-reaction equals the number of electrons gained in the reduction half-reaction.
Use the standard reduction potentials for each half-reaction to calculate the standard Gibbs free energy change (∆Gr°xn) for the reaction. Use the formula ∆Gr°xn = -nFE°cell, where n is the number of moles of electrons transferred, F is the Faraday constant (96485 C/mol), and E°cell is the standard cell potential.
Calculate the equilibrium constant (K) for the reaction using the relationship between Gibbs free energy and the equilibrium constant, K = e^(-∆Gr°xn/RT), where R is the gas constant (8.314 J/mol·K) and T is the temperature in Kelvin.
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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Gibbs Free Energy (∆G)
Gibbs Free Energy (∆G) is a thermodynamic potential that measures the maximum reversible work obtainable from a thermodynamic system at constant temperature and pressure. The change in Gibbs Free Energy (∆Gr°xn) for a reaction indicates whether the reaction is spontaneous (negative ∆G) or non-spontaneous (positive ∆G). It is calculated using the standard free energies of formation of the reactants and products.
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Gibbs Free Energy of Reactions
Equilibrium Constant (K)
The equilibrium constant (K) is a dimensionless value that expresses the ratio of the concentrations of products to reactants at equilibrium for a given reaction at a specific temperature. It is related to the Gibbs Free Energy change by the equation ∆Gr° = -RT ln(K), where R is the universal gas constant and T is the temperature in Kelvin. A larger K value indicates a greater tendency for the reaction to favor products.
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Redox Reactions
Redox reactions involve the transfer of electrons between species, resulting in changes in oxidation states. In the given reaction, Cr2+(aq) is oxidized to Cr3+(aq) while Cr2O7^2-(aq) is reduced. Understanding the half-reactions and the roles of oxidizing and reducing agents is crucial for calculating ∆Gr°xn and K, as these values depend on the electron transfer processes occurring in the reaction.