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Ch.20 - Electrochemistry
Chapter 20, Problem 78b

A voltaic cell consists of a Pb/Pb2+ half-cell and a Cu/Cu2+ half-cell at 25°C. The initial concentrations of Pb2+ and Cu2+ are 0.0500 M and 1.50 M, respectively. b. What is the cell potential when the concentration of Cu2+ has fallen to 0.200 M?

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Identify the half-reactions for the Pb and Cu electrodes. For the Pb electrode, the half-reaction is Pb^2+ + 2e^- \rightarrow Pb(s). For the Cu electrode, the half-reaction is Cu^2+ + 2e^- \rightarrow Cu(s).
Write the overall cell reaction by combining the two half-reactions. The electrons should cancel out, resulting in: Pb(s) + Cu^2+ \rightarrow Pb^2+ + Cu(s).
Use the Nernst equation to calculate the cell potential. The Nernst equation is E = E^0 - \frac{RT}{nF} \ln Q, where E^0 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 the Faraday constant, and Q is the reaction quotient.
Calculate the standard cell potential, E^0, using the standard reduction potentials of the half-reactions. E^0 = E^0_{Cu} - E^0_{Pb}, where E^0_{Cu} and E^0_{Pb} are the standard reduction potentials for copper and lead, respectively.
Determine the reaction quotient, Q, using the initial and final concentrations given. Q = \frac{[Pb^2+]}{[Cu^2+]}, where [Pb^2+] and [Cu^2+] are the concentrations of Pb^2+ and Cu^2+ at the specified point in the reaction.

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Key Concepts

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

Electrochemical Cells

Electrochemical cells, such as voltaic cells, convert chemical energy into electrical energy through redox reactions. In a voltaic cell, oxidation occurs at the anode and reduction at the cathode, creating a flow of electrons that generates an electric current. Understanding the roles of the half-cells and the overall cell reaction is crucial for analyzing cell potential.
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Nernst Equation

The Nernst equation relates the cell potential to the concentrations of the reactants and products in a redox reaction. It allows for the calculation of the cell potential under non-standard conditions, taking into account temperature and concentration changes. This equation is essential for determining how changes in ion concentration affect the overall voltage of the cell.
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Standard Electrode Potentials

Standard electrode potentials are measured voltages for half-reactions under standard conditions (1 M concentration, 1 atm pressure, and 25°C). These values are used to predict the direction of electron flow and the feasibility of redox reactions. Knowing the standard potentials for the Pb and Cu half-reactions is necessary to calculate the initial cell potential and apply the Nernst equation for concentration changes.
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Related Practice
Textbook Question

A voltaic cell consists of a Zn/Zn2+ half-cell and a Ni/Ni2+ half-cell at 25 °C. The initial concentrations of Ni2+ and Zn2+ are 1.50 M and 0.100 M, respectively. b. What is the cell potential when the concentration of Ni2+ has fallen to 0.500 M?

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Textbook Question

A voltaic cell consists of a Zn/Zn2+ half-cell and a Ni/Ni2+ half-cell at 25 °C. The initial concentrations of Ni2+ and Zn2+ are 1.50 M and 0.100 M, respectively. c. What are the concentrations of Ni2+ and Zn2+ when the cell potential falls to 0.45 V?

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Textbook Question

A voltaic cell consists of a Pb/Pb2+ half-cell and a Cu/Cu2+ half-cell at 25°C. The initial concentrations of Pb2+ and Cu2+ are 0.0500 M and 1.50 M, respectively. a. What is the initial cell potential?

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Textbook Question

A voltaic cell consists of a Pb/Pb2+ half-cell and a Cu/Cu2+ half-cell at 25°C. The initial concentrations of Pb2+ and Cu2+ are 0.0500 M and 1.50 M, respectively. c. What are the concentrations of Pb2+ and Cu2+ when the cell potential falls to 0.35 V?

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Textbook Question

Make a sketch of a concentration cell employing two Zn/Zn2+ half-cells. The concentration of Zn2+ in one of the half-cells is 2.0 M and the concentration in the other half-cell is 1.0×10–3 M. Label the anode and the cathode and indicate the half-reaction occuring at each electrode. Also indicate the direction of electron flow.

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Textbook Question

Consider the concentration cell: b. Indicate the direction of electron flow.

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