Textbook Question
Silver can be electroplated at the cathode of an electrolysis cell by the half-reaction: Ag+(aq) + e– → Ag(s) What mass of silver would plate onto the cathode if a current of 6.8 A flowed through the cell for 72 min?
Ch.20 - Electrochemistry
Chapter 20, Problem 103
Consider the reaction shown here occurring at 25 °C: A(s) + B2+(aq) → A2+(aq) + B(s). Given that ∆Gr°xn = -14.0 kJ, determine the value of Ec°ell and K for the reaction, and complete the following table for [B2+], [A2+], Q, Ecell, and ∆Grxn with initial values 1.00, 1, 1.0 * 10^-4, 3.54 * 10^-3, and 1.00 * 10^-4 respectively.
Verified step by step guidance1
Identify the relationship between the standard Gibbs free energy change (\( \Delta G^\circ_{rxn} \)) and the standard cell potential (\( E^\circ_{cell} \)) using the equation \( \Delta G^\circ_{rxn} = -nFE^\circ_{cell} \), where \( n \) is the number of moles of electrons transferred and \( F \) is the Faraday constant (approximately 96485 C/mol).
Determine the number of moles of electrons transferred (\( n \)) in the balanced redox reaction. In this case, it appears that 2 electrons are transferred as A is oxidized to A2+ and B2+ is reduced to B.
Rearrange the equation to solve for \( E^\circ_{cell} \): \( E^\circ_{cell} = -\frac{\Delta G^\circ_{rxn}}{nF} \). Substitute the given \( \Delta G^\circ_{rxn} = -14.0 \) kJ (convert to J by multiplying by 1000) and the calculated \( n \) value.
Use the Nernst equation to find the cell potential (\( E_{cell} \)) under non-standard conditions: \( E_{cell} = E^\circ_{cell} - \frac{RT}{nF} \ln Q \), where \( R \) is the gas constant (8.314 J/mol·K), \( T \) is the temperature in Kelvin (convert 25 °C to Kelvin), and \( Q \) is the reaction quotient.
Calculate the equilibrium constant (\( K \)) using the relationship \( \Delta G^\circ_{rxn} = -RT \ln K \). Rearrange to solve for \( K \): \( K = e^{-\frac{\Delta G^\circ_{rxn}}{RT}} \). Substitute the given \( \Delta G^\circ_{rxn} \) and calculate \( K \).
Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Gibbs Free Energy (∆Gr°)
Gibbs Free Energy (∆Gr°) is a thermodynamic potential that measures the maximum reversible work obtainable from a thermodynamic process at constant temperature and pressure. A negative value of ∆Gr° indicates that a reaction is spontaneous under standard conditions, while a positive value suggests non-spontaneity. In this context, the given ∆Gr°xn of -14.0 kJ indicates that the reaction favors the formation of products.
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01:51
Gibbs Free Energy of Reactions
Nernst Equation
The Nernst Equation relates the cell potential (Ecell) of an electrochemical reaction to the standard cell potential (Ec°ell) and the concentrations of the reactants and products. It is expressed as Ecell = Ec°ell - (RT/nF)ln(Q), where R is the gas constant, T is the temperature in Kelvin, n is the number of moles of electrons transferred, and F is Faraday's constant. This equation is crucial for calculating Ecell under non-standard conditions.
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01:17The Nernst Equation
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. It is derived from the standard Gibbs free energy change (∆Gr°) using the relationship ∆Gr° = -RTln(K). A larger K value indicates a greater tendency for the reaction to favor products, while a smaller K suggests a preference for reactants. Understanding K is essential for predicting the direction of the reaction under varying conditions.
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01:14Equilibrium Constant K
Related Practice
Textbook Question
A major source of sodium metal is the electrolysis of molten sodium chloride. What magnitude of current produces 1.0 kg of sodium metal in 1 hour?
Textbook Question
Consider the reaction shown here occurring at 25°C. Cr(s) + Cd2+(aq) → Cr2+(aq) + Cd(s) Determine E°cell, K, and ∆G°rxn for the reaction and complete the table.
[Cd2+] [Cr2+] Q Ecell 𝚫Grxn
1.00 1.00
1.00 1.00 × 10-5
1.00 × 10-5 1.00
4.18 × 10-4 1.00
Textbook Question
Consider the unbalanced redox reaction: Cr2O72-(aq) + Cu(s) → Cr3+(aq) + Cu2+(aq) Balance the equation and determine the volume of a 0.850 M K2Cr2O7 solution required to completely react with 5.25 g of Cu.