Final answer:
To calculate the potential for the Cu²⁺ / Cu⁺ electrode at 25°C with the given ion concentrations, use the Nernst equation with Q set to 3, but the standard electrode potential E° must be known to complete the calculation.
Step-by-step explanation:
To calculate the potential for the Cu²⁺ / Cu⁺ electrode at 25°c when the concentration of Cu⁺ ions is three times that of Cu²⁺ ions, we can use the Nernst equation:
E = E° - (RT/nF) * ln(Q)
Where:
- E = Electrode potential
- E° = Standard electrode potential
- R = Universal gas constant (8.314 J/(mol·K))
- T = Temperature in Kelvin (298 K for 25°C)
- n = Number of moles of electrons transferred in the reaction (n=1 for this half-reaction)
- F = Faraday's constant (96485 C/mol)
- Q = Reaction quotient = [Cu⁺]/[Cu²⁺]
Given that the concentration of Cu⁺ is three times that of Cu²⁺:
Q = [Cu⁺]/[Cu²⁺] = 3[Cu²⁺]/[Cu²⁺] = 3
We do not have the value for E° for the Cu²⁺/Cu⁺ couple, but if we did, we would proceed as follows:
Substitute R, T, n, F, and Q into the Nernst equation and solve for E:
E = E° - (8.314 * 298 / (1 * 96485)) * ln(3)
After calculating ln(3) and multiplying by the constants, we can subtract this value from the standard electrode potential to find the electrode potential E.