Multiple Choice
Calculate the ΔE°cell for the following concentration cell: Cu(s) | Cu2+(aq, 0.049M) || Cu2+(aq, 0.231M) | Cu(s). Cu2+(aq) + 2e- → Cu(s), E° = 0.340V.
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20. Electrochemistry
Cell Potential: The Nernst Equation
Multiple Choice
What is the emf of this cell when [Fe²⁺] = 1.5 M, [Fe³⁺] = 1.4 × 10⁻² M, P(O₂) = 0.56 atm, and the pH of the solution in the cathode compartment is 3.5, given that the standard cell potential (E°) is 1.23 V?
A
1.05 V
B
1.15 V
C
1.23 V
D
1.30 V
Verified step by step guidance1
Identify the half-reactions involved in the cell. For this problem, the half-reactions are: Fe³⁺ + e⁻ → Fe²⁺ and O₂ + 4H⁺ + 4e⁻ → 2H₂O.
Write the Nernst equation for the cell: E = E° - (RT/nF) * ln(Q), where E is the cell potential, E° is the standard cell potential, R is the gas constant, T is the temperature in Kelvin, n is the number of moles of electrons transferred, F is Faraday's constant, and Q is the reaction quotient.
Calculate the reaction quotient (Q) using the concentrations and partial pressures given: Q = ([Fe²⁺]/[Fe³⁺]) * (1/(P(O₂) * [H⁺]⁴)). Substitute the given values: [Fe²⁺] = 1.5 M, [Fe³⁺] = 1.4 × 10⁻² M, P(O₂) = 0.56 atm, and [H⁺] = 10^(-pH) = 10^(-3.5).
Substitute the values into the Nernst equation. Use the standard cell potential E° = 1.23 V, and calculate the temperature in Kelvin if not given (assume 298 K if not specified). Use n = 4 for the number of electrons transferred in the balanced overall reaction.
Solve the Nernst equation to find the emf of the cell. This will involve calculating the logarithmic term and adjusting the standard potential by this value to find the actual cell potential under the given conditions.
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