Ch.20 - Electrochemistry

Problem 52b

Chapter 20, Problem 52b

For each of the following reactions, write a balanced equation, calculate the standard emf, calculate ∆G° at 298 K, and calculate the equilibrium constant K at 298 K. (b) In acidic solution, copper(I) ion is oxidized to copper(II) ion by nitrate ion.

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Write the unbalanced chemical equation for the reaction: Cu^+ + NO_3^- -> Cu^{2+} + NO_2

Balance the chemical equation by ensuring the number of atoms and charges are equal on both sides. Consider the acidic solution, which allows you to add H^+ and H_2O as needed.

Use the standard reduction potentials from a table to find the half-reactions and their standard potentials. Calculate the standard emf (E°) for the reaction using E° = E°(cathode) - E°(anode).

Calculate the standard Gibbs free energy change (∆G°) using the formula ∆G° = -nFE°, where n is the number of moles of electrons transferred and F is the Faraday constant (96485 C/mol).

Calculate the equilibrium constant (K) at 298 K using the relationship ∆G° = -RTlnK, where R is the universal 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.

Balancing Chemical Equations

Balancing chemical equations involves ensuring that the number of atoms for each element is the same on both the reactant and product sides. This is crucial for accurately representing the conservation of mass in a chemical reaction. In the context of the given reaction, it requires identifying the oxidation states of copper and nitrate ions and adjusting coefficients to achieve balance.

Standard Electrode Potential (emf)

The standard electrode potential (emf) is a measure of the tendency of a chemical species to be reduced, expressed in volts. It is determined under standard conditions (1 M concentration, 1 atm pressure, and 25°C). Calculating the standard emf for the reaction involves using standard reduction potentials from tables and applying the Nernst equation to find the overall cell potential.

Gibbs Free Energy and Equilibrium Constant

Gibbs free energy (∆G°) is a thermodynamic quantity that indicates the spontaneity of a reaction at constant temperature and pressure. The relationship between ∆G° and the equilibrium constant (K) is given by the equation ∆G° = -RT ln(K), where R is the gas constant and T is the temperature in Kelvin. This relationship allows for the calculation of K from ∆G° and vice versa, providing insight into the position of equilibrium for the reaction.

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Related Practice

Textbook Question

Given the following reduction half-reactions:

Fe³⁺(aq) + e^- → Fe²⁺(aq) E°_red = +0.77 V

S₂O₆^2-(aq) + 4 H⁺(aq) + 2 e^- → 2 H₂SO₃(aq) E°_red = +0.60 V

N₂O(g) + 2 H⁺(aq) + 2 e^- → N₂(g) + H₂O(l) E°_red = -1.77 V

VO²⁺(aq) + 2 H⁺(aq) + e^- → VO²⁺ + H₂O(l) E°_red = +1.00 V

(b) Calculate ∆G° for each reaction at 298 K.

Textbook Question

Given the following reduction half-reactions:

Fe³⁺(aq) + e^- → Fe²⁺(aq) E°_red = +0.77 V

S₂O₆^2-(aq) + 4 H⁺(aq) + 2 e^- → 2 H₂SO₃(aq) E°_red = +0.60 V

N₂O(g) + 2 H⁺(aq) + 2 e^- → N₂(g) + H₂O(l) E°_red = -1.77 V

VO²⁺(aq) + 2 H⁺(aq) + e^- → VO²⁺ + H₂O(l) E°_red = +1.00 V

Textbook Question

For each of the following reactions, write a balanced equation, calculate the standard emf, calculate ∆G° at 298 K, and calculate the equilibrium constant K at 298 K. (a) Aqueous iodide ion is oxidized to I21s2 by Hg22+1aq2.

Textbook Question

For each of the following reactions, write a balanced equation, calculate the standard emf, calculate ∆G° at 298 K, and calculate the equilibrium constant K at 298 K. (c) In basic solution, Cr1OH231s2 is oxidized to CrO42-1aq2 by ClO-1aq2.