Checking Copper Electroplating Against Faraday's Laws
In a school laboratory, students electroplate copper onto a copper cathode from copper(II) sulfate solution. In run A they pass a current of 0.50 A for 40.0 min and find the cathode gains 0.38 g. In run B they use 1.00 A for 20.0 min, so the same total charge passes, but the cathode gains only 0.28 g. The power supply is marked as calibrated, and the balance reads to 0.01 g. The students use the same electrodes, solution and temperature in both runs. They know that copper(II) ions are reduced at the cathode, but they wonder whether the second result means that copper has a charge of +1 in this solution. The teacher asks them to calculate the expected mass from Faraday's laws, compare the two runs, and decide what the evidence supports. Use F = 96,500 C mol⁻¹ and A_r(Cu) = 63.5.
1. Calculate the expected mass for run A and the percentage of the expected mass actually obtained.
Read the worked answer
Q = It = 0.50 × 40.0 × 60 = 1200 C. Moles of electrons = 1200/96500 = 1.244 × 10⁻² mol. Cu²⁺ + 2e⁻ → Cu, so n(Cu) = 1.244 × 10⁻²/2 = 6.218 × 10⁻³ mol. Expected mass = 6.218 × 10⁻³ × 63.5 = 0.395 g.
Measured 0.38 g gives 0.38/0.395 = 0.962, about 96%. With a balance reading to 0.01 g, the measured value is 0.38 ± 0.005 g, i.e. 95–97% of expected. This is close enough to support the Cu²⁺ model, though a small side reaction or measurement error is possible.
2. Run B passes the same charge but gives 0.28 g. Calculate the apparent current efficiency and give two plausible explanations. Describe one measurement that would distinguish them.
Read the worked answer
Run B: Q = 1.00 × 20.0 × 60 = 1200 C, so the same expected mass, 0.395 g. Measured 0.28 g gives 0.28/0.395 = 0.709, about 71% current efficiency.
Two plausible explanations: (i) at the higher current density, a side reaction such as hydrogen evolution consumes electrons at the cathode; (ii) poor stirring or a low Cu²⁺ concentration near the cathode causes mass-transport limitation, again allowing side reactions. A less likely but possible explanation is that the power supply's 1.00 A setting is inaccurate or the time was mis-measured. To distinguish, look for gas bubbles at the cathode, stir vigorously and repeat at 1.00 A, or use a coulometer/independent ammeter to record the actual charge. If stirring restores the mass to about 0.395 g, transport was the problem; if not, side reaction or current calibration is implicated.
3. The students suggest that if copper were +1, run B's low mass would be explained. Evaluate this suggestion.
Read the worked answer
If copper were Cu⁺, the reduction would be Cu⁺ + e⁻ → Cu. Then n(Cu) = n(e) = 1.244 × 10⁻² mol, and the expected mass would be 1.244 × 10⁻² × 63.5 = 0.790 g, about twice the Cu²⁺ prediction. The observed 0.28 g is much lower, not higher, so the +1 hypothesis cannot explain run B.
The low mass indicates that fewer electrons went to copper deposition, i.e. lower current efficiency, not a lower charge on copper. Run A's 96% agreement with the Cu²⁺ prediction further supports Cu²⁺. The second run is evidence about the plating conditions, not about copper's oxidation state.