Copper electrolysis: Faraday's law and where the missing mass went
Two clean copper plates, each of mass 5.000 g, are weighed and connected as the two electrodes in 0.50 mol/L CuSO₄(aq). A steady current of 0.500 A is passed for 30.0 min; the current is monitored throughout and stays constant. Afterwards the cathode has gained 0.280 g and the anode has lost 0.315 g, and fine copper particles are visible at the bottom of the beaker. M(Cu) = 63.5 g/mol, F = 9.65 × 10⁴ C/mol. The student who ran the experiment concludes that "the cathode result must be wrong, because charge is conserved, so the two mass changes should be identical". The teacher replies that the missing mass is in the beaker, not in the wires.
1. Calculate the mass of copper that Faraday's law predicts for the cathode and comment on the current efficiency of the deposition.
Read the worked answer
Charge passed:
Q = It = 0.500 × (30.0 × 60) = 0.500 × 1800 = 900 C
Moles of electrons:
n(e⁻) = Q/F = 900 / 9.65 × 10⁴ = 9.33 × 10⁻³ mol
Cu²⁺ + 2e⁻ → Cu, so n(Cu) = 9.33 × 10⁻³ / 2 = 4.66 × 10⁻³ mol
m(Cu) = 4.66 × 10⁻³ × 63.5 ≈ 0.296 g
The cathode actually gained 0.280 g, so the apparent Faraday efficiency is 0.280/0.296 ≈ 94.6 %.
The calculation assumes (i) no side reaction at the cathode, (ii) current uniform over the plate area, and (iii) all deposited copper adhering firmly. Since the current was constant and monitored, an error in Q is unlikely; the shortfall is on the electrode side, so a claim of "about 5 % current efficiency loss" is premature until the third assumption is checked - which the beaker contents will tell us.
2. Explain why the anode lost more mass than the cathode gained, and judge which electrode's mass change is the more reliable measure of the charge passed.
Read the worked answer
With copper electrodes in CuSO₄ the anode reaction is Cu → Cu²⁺ + 2e⁻, so the anode should lose exactly the 0.296 g the cathode gains. The anode lost 0.315 g - about 6 % more.
Two processes explain this without any violation of charge conservation:
- Mechanical loss. In a real cell the anode surface becomes roughened and dislodges fine copper particles (visible as sludge in the beaker). Those particles were weighed as part of the anode but never entered solution as Cu²⁺, so they inflate the apparent mass loss without carrying any charge.
- Cathode loss. Symmetrically, if the deposit is spongy or dendritic, some copper can spall off the cathode. That lowers the measured cathode gain without reducing the charge transferred, and it is the same sludge the student can see.
So the gap could be entirely mechanical and not an efficiency loss at all.
Judgement: on these data, the cathode is the more reliable measure, because the deposit is formed cleanly from solution and its mass is less exposed to the roughening problem - but only marginally. Neither electrode's mass change is trustworthy for measuring charge, because both are affected by the same sludge. The reliable quantity in this experiment is the current × time, which is why it was monitored.
3. The student claims the data show that the current efficiency of copper deposition is below 100 %. Evaluate this conclusion and say what further measurement would settle it.
Read the worked answer
The conclusion is not yet supported, because the data are equally consistent with two different pictures:
- Picture A (real efficiency loss): a side reaction such as reduction of dissolved oxygen or of water consumes part of the 900 C, so less copper is deposited. Efficiency ≈ 94.6 %.
- Picture B (100 % efficiency, mechanical loss): all 900 C deposits 0.296 g of copper, but roughly 0.016 g spalls off the cathode and 0.019 g of loose metal falls from the anode, leaving the observed masses. Efficiency = 100 %, and the imbalance is a weighing artefact.
Both explain 0.280 g and 0.315 g. Distinguishing them requires measuring the copper that ended up in the beaker: filter, wash, dry and weigh the sludge. If its mass is close to (0.315 − 0.280) g, Picture B is favoured. Alternatively, repeat with a lower current density or a copper-plated cathode of smoother finish, where spalling is suppressed; if the cathode gain then rises towards 0.296 g, Picture A is rejected.
This is the standard trap: a numerical discrepancy is not evidence for the hypothesis you happen to have in mind until competing explanations have been eliminated.