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Ch.19 - Electrochemistry
All textbooksMcMurry 8th EditionCh.19 - ElectrochemistryProblem 104
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Chapter 19, Problem 104

Standard reduction potentials for the Pb2+/Pb and Cd2+/Cd half-reactions are -0.13 V and -0.40 V, respectively. At what relative concentrations of Pb2+ and Cd2+ will these half-reactions have the same reduction potential?

Verified step by step guidance
1
Step 1: Understand that the problem involves finding the relative concentrations of Pb2+ and Cd2+ where their reduction potentials are equal. This involves using the Nernst equation, which relates the reduction potential of a half-cell to the standard reduction potential and the concentrations of the involved species.
Step 2: Write the Nernst equation for each half-reaction. For the Pb2+/Pb half-reaction, the equation is: E = E° - (RT/nF) * ln([Pb]/[Pb2+]). For the Cd2+/Cd half-reaction, the equation is: E = E° - (RT/nF) * ln([Cd]/[Cd2+]).
Step 3: Set the two Nernst equations equal to each other since we want the reduction potentials to be the same: E°(Pb) - (RT/nF) * ln([Pb]/[Pb2+]) = E°(Cd) - (RT/nF) * ln([Cd]/[Cd2+]).
Step 4: Substitute the given standard reduction potentials into the equation: -0.13 V - (RT/nF) * ln([Pb]/[Pb2+]) = -0.40 V - (RT/nF) * ln([Cd]/[Cd2+]).
Step 5: Solve the equation for the ratio of concentrations [Pb2+]/[Cd2+]. This involves algebraic manipulation to isolate the concentration terms and solve for the desired ratio.
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