Nernst Equation: Electron Count n
Zn–Cu cell, known E° and [Zn²⁺]. Measure E at several [Cu²⁺], fit E versus ln Q, and recover n from the slope −RT/nF.
Goal
Determine n from E = E° − (RT/nF) ln Q. The slope of E versus ln Q is −RT/nF, so n = −RT/(F · slope).
Equipment
- Zn–Cu cell
- Known E°, [Zn²⁺], T
- Voltmeter
- [Cu²⁺] stock
Experiment
Theory
For Zn + Cu²⁺ → Zn²⁺ + Cu, Q = [Zn²⁺]/[Cu²⁺] and n = 2. T = 25 °C and E° are known. The bench hides E, Q and any ready-made Nernst value. This is not the membrane K⁺ lab (58 mV/decade).
Procedure
- [Zn²⁺], T and E° are fixed and known. You only change [Cu²⁺].
- Record. A voltmeter logs E with small noise. There is no live E or Q.
- The notebook computes Q = [Zn²⁺]/[Cu²⁺] and ln Q. Repeat for at least 6 copper concentrations from about 0.02 M to 2.0 M.
- Fit E versus ln Q; n = −RT/(F · slope). Compare with the reference.
Conclusion
The fitted n agrees with two electrons for the Zn–Cu cell. Main uncertainties: voltmeter noise and ideal activities.