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?

Verified step by step guidance

1. 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).
2. 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).
3. 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.
4. 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.
5. 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.

Key Concepts

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.

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.

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.