Cell potentials, predictions and a voltmeter that reads low
A student is given these standard electrode potentials: Zn²⁺/Zn = −0.76 V, Fe²⁺/Fe = −0.44 V, Cu²⁺/Cu = +0.34 V, Ag⁺/Ag = +0.80 V. She builds a cell from a zinc strip in 0.10 mol dm⁻³ zinc sulfate and a copper strip in 0.10 mol dm⁻³ copper sulfate, joined by a salt bridge, and connects a high-resistance voltmeter. It reads 1.04 V, whereas the textbook value for the standard Zn/Cu cell is 1.10 V. She then places a clean copper strip in silver nitrate solution and a grey, shiny deposit forms. Finally she puts an iron nail in zinc sulfate solution and, after a week, sees no visible change. She concludes that silver is a stronger oxidising agent than copper(II), that iron cannot displace zinc, and that her voltmeter reading shows the textbook value is wrong.
1. Calculate E° for the zinc/copper cell, write the two electrode reactions and the cell diagram, and evaluate her claim that the reading of 1.04 V shows the textbook value is wrong.
Read the worked answer
The more negative potential is oxidised: Zn → Zn²⁺ + 2e⁻ (anode, −0.76 V). The more positive is reduced: Cu²⁺ + 2e⁻ → Cu (cathode, +0.34 V).
E°cell = E°(cathode) − E°(anode) = +0.34 − (−0.76) = +1.10 V
Cell diagram: Zn(s) | Zn²⁺(aq) || Cu²⁺(aq) | Cu(s)
A positive E°cell means the reaction Zn + Cu²⁺ → Zn²⁺ + Cu is feasible, as observed.
Her claim is not justified. A difference of 0.06 V is normal for a school cell:
- both solutions are 0.10 mol dm⁻³, so the concentration terms largely cancel and do not explain a change in the predicted direction;
- standard potentials refer to 1 mol dm⁻³ (unit activity) at 298 K, with pure metals and no junction; her solutions are more dilute, at room temperature, and joined by a salt bridge that contributes a liquid-junction potential;
- oxide films or impurities on the metal surfaces change the effective potential;
- a real voltmeter draws a small current, so the cell is not measured at zero current.
Judgement: 1.04 V is a measurement of the same cell under non-standard conditions, not evidence against the standard value. An E° is a defined reference quantity, not a prediction of exactly what any particular cell will read.
2. Use the E° values to explain the silver nitrate observation and the iron nail observation, giving an equation for the reaction that does occur.
Read the worked answer
Copper in silver nitrate: possible reaction Cu + 2Ag⁺ → Cu²⁺ + 2Ag E°cell = E°(Ag⁺/Ag) − E°(Cu²⁺/Cu) = +0.80 − (+0.34) = +0.46 V Positive, so the reaction is feasible; silver is reduced and deposited as a grey, shiny solid while the solution becomes blue from Cu²⁺. This supports her conclusion that Ag⁺ is a stronger oxidising agent than Cu²⁺ - the higher (more positive) the E°, the greater the tendency to be reduced.
Iron in zinc sulfate: possible reaction Fe + Zn²⁺ → Fe²⁺ + Zn E°cell = E°(Zn²⁺/Zn) − E°(Fe²⁺/Fe) = −0.76 − (−0.44) = −0.32 V Negative, so the reaction is not feasible; the position of equilibrium lies far to the left and no visible change is expected. This is consistent with zinc being the stronger reducing agent of the two.
Her second conclusion is therefore correct in outcome, but it should be stated as 'iron cannot reduce Zn²⁺ under these conditions', which is what the negative E° shows - not as a general claim about iron's reactivity.
3. She now wants to silver-plate a copper spoon using a silver nitrate solution and a silver electrode. State how the cell should be connected and explain what happens at each electrode. Predict what happens to the voltage of her zinc/copper cell if it is left connected for several hours.
Read the worked answer
Electroplating: the copper spoon must be the cathode, connected to the negative terminal of the power supply, because reduction happens at the cathode and the object to be plated must receive the Ag⁺ ions: Ag⁺ + e⁻ → Ag, giving a coating of silver on the spoon.
The silver electrode is the anode, connected to the positive terminal: Ag → Ag⁺ + e⁻. Silver dissolves from the anode and plates onto the spoon; the silver nitrate solution acts as the electrolyte and its concentration stays roughly constant because the same number of silver atoms dissolve as are deposited.
Leaving the zinc/copper cell connected: the voltage falls. As the cell discharges, Zn²⁺ concentration rises and Cu²⁺ concentration falls, so the reaction quotient increases and the cell potential decreases; eventually the copper ion concentration becomes so low (and the zinc electrode so corroded) that the cell can no longer drive current. Polarisation and the build-up of ions at the electrodes also reduce the reading. This is why the cell must be measured with a high-resistance voltmeter, drawing negligible current, if a potential close to E°cell is to be recorded.