Ch.19 - Electrochemistry

Problem 157

Chapter 19, Problem 157

A concentration cell has the same half-reactions at the anode and cathode, but a voltage results from different concentrations in the two electrode compartments. (b) A similar cell has 0.10 M Cu2+ in both compartments. When a stoichiometric amount of ethylenediamine (NH2CH2CH2NH2) is added to one compartment, the measured cell potential is 0.179 V. Calculate the formation constant Kf for the complex ion Cu(NH2CH2CH2CH2)22+. Assume there is no volume change.

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Identify the half-reaction for the copper concentration cell: Cu^{2+} + 2e^- \rightarrow Cu.

Recognize that the cell potential is due to the formation of the complex ion Cu(NH_2CH_2CH_2NH_2)_2^{2+} in one compartment.

Use the Nernst equation to relate the cell potential (E) to the concentrations: E = E^0 - \frac{RT}{nF} \ln Q, where Q is the reaction quotient.

Since the standard cell potential (E^0) for a concentration cell is 0, simplify the Nernst equation to: E = -\frac{RT}{nF} \ln Q.

Relate the reaction quotient Q to the formation constant K_f: Q = \frac{1}{K_f}, and solve for K_f using the measured cell potential (0.179 V).

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Concentration Cells

Concentration cells are electrochemical cells where the same half-reaction occurs at both the anode and cathode, but the potential difference arises from differing concentrations of reactants. The Nernst equation is used to relate the cell potential to the concentrations of the reactants, indicating that a higher concentration of reactants at one electrode leads to a greater tendency for reduction, thus generating voltage.

Formation Constant (Kf)

The formation constant (Kf) quantifies the stability of a complex ion in solution, representing the equilibrium between the free metal ion and the ligand-bound complex. It is calculated from the concentrations of the reactants and products at equilibrium, providing insight into how favorably a metal ion forms a complex with ligands, such as ethylenediamine in this case.

Nernst Equation

The Nernst equation relates the cell potential to the concentrations of the reactants and products in an electrochemical reaction. It is expressed as E = E° - (RT/nF) ln(Q), where 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. This equation is crucial for calculating the potential of concentration cells and understanding how changes in concentration affect cell voltage.

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Textbook Question

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Open Question

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Textbook Question

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