Electrochemistry · Lesson 2 of 13
Electrode Potentials and the Hydrogen Reference
“Measure relative reduction tendencies, calculate standard cell potentials and reason about oxidising and reducing strength.”
• Explain why electrode potentials need a reference electrode. • Describe the standard hydrogen electrode and standard-state conventions. • Calculate a cell potential using tabulated reduction potentials. • Use potentials to predict displacement and redox feasibility while stating limitations.
A potential develops at a metal–solution interface
When a metal contacts a solution containing its ions, atoms may leave the surface as ions while ions may gain electrons and join the metal. Charge separation across this interface produces an electrode potential. At equilibrium there can be microscopic exchange in both directions without net reaction. The potential describes the interface relative to a reference; an isolated half-cell does not provide a directly measurable absolute potential in a simple two-terminal experiment.
A voltmeter compares two electrodes. To assign values to individual couples, choose one reproducible reference. Standard reduction potentials describe the reaction as reduction, for example Cu²⁺ + 2e⁻ → Cu. A more positive value means a greater thermodynamic tendency for that reduction relative to the reference under the stated standard conditions. It does not by itself measure the rate.
The standard hydrogen electrode
The standard hydrogen electrode uses platinum coated with finely divided platinum, hydrogen gas at standard pressure 1 bar, and aqueous hydrogen ions of unit activity. Platinum conducts electrons and catalyses the interconversion but is not consumed. The reduction is 2H⁺(aq) + 2e⁻ ⇌ H₂(g). Its conventional standard potential is assigned 0 V at every temperature. Values quoted in a table must still specify temperature, commonly 298.15 K.
Activity is a dimensionless measure of effective chemical concentration. For an ideal dilute solution, an ion activity is approximated by its concentration divided by the standard concentration 1 mol L⁻¹. Thus a 1 M solution is a useful classroom approximation to unit activity, not an exact definition for every real solution. A gas activity is approximated by its pressure divided by 1 bar. Pure solids and pure liquids in their reference states have activity 1.
Problem
How can Mg²⁺/Mg be measured relative to the hydrogen reference?
- 1.Construct a magnesium half-cell under standard-state conditions and connect it to a standard hydrogen electrode through a compatible ionic junction and a high-resistance voltmeter.
- 2.Magnesium oxidises in spontaneous operation; hydrogen ions are reduced. For Mg|Mg²⁺||H⁺|H₂|Pt, E°cell = 0 − E°(Mg²⁺/Mg).
- 3.A positive measured emf of about 2.37 V therefore corresponds to E°(Mg²⁺/Mg) ≈ −2.37 V. The sign belongs to the magnesium reduction half-reaction, not to an unsigned voltmeter magnitude.
Using an electrode-potential table
| Reduction couple or half-reaction | E° / V, approximately |
|---|---|
| F₂(g) + 2e⁻ → 2F⁻ | +2.87 |
| Co³⁺ + e⁻ → Co²⁺ | +1.81 |
| H₂O₂ + 2H⁺ + 2e⁻ → 2H₂O | +1.78 |
| MnO₄⁻ + 8H⁺ + 5e⁻ → Mn²⁺ + 4H₂O | +1.51 |
| Au³⁺ + 3e⁻ → Au(s) | +1.50 |
| Cl₂(g) + 2e⁻ → 2Cl⁻ | +1.36 |
| Cr₂O₇²⁻ + 14H⁺ + 6e⁻ → 2Cr³⁺ + 7H₂O | +1.33 |
| O₂(g) + 4H⁺ + 4e⁻ → 2H₂O | +1.23 |
| MnO₂(s) + 4H⁺ + 2e⁻ → Mn²⁺ + 2H₂O | +1.23 |
| Br₂(aq) + 2e⁻ → 2Br⁻ | +1.09 |
| Br₂(l) + 2e⁻ → 2Br⁻ | +1.065 |
| NO₃⁻ + 4H⁺ + 3e⁻ → NO(g) + 2H₂O | +0.97 |
| 2Hg²⁺ + 2e⁻ → Hg₂²⁺ | +0.92 |
| Ag⁺ + e⁻ → Ag(s) | +0.80 |
| Ag₂O(s) + H₂O + 2e⁻ → 2Ag(s) + 2OH⁻ | +0.342 |
| Fe³⁺ + e⁻ → Fe²⁺ | +0.77 |
| O₂(g) + 2H⁺ + 2e⁻ → H₂O₂ | +0.68 |
| I₂(s) + 2e⁻ → 2I⁻ | +0.54 |
| Cu⁺ + e⁻ → Cu(s) | +0.52 |
| Cu²⁺ + 2e⁻ → Cu(s) | +0.34 |
| AgCl(s) + e⁻ → Ag(s) + Cl⁻ | +0.22 |
| AgBr(s) + e⁻ → Ag(s) + Br⁻ | +0.10 |
| 2H⁺ + 2e⁻ → H₂(g) | 0.00 |
| Pb²⁺ + 2e⁻ → Pb(s) | −0.13 |
| Sn²⁺ + 2e⁻ → Sn(s) | −0.14 |
| Ni²⁺ + 2e⁻ → Ni(s) | −0.25 |
| Fe²⁺ + 2e⁻ → Fe(s) | −0.44 |
| Cr³⁺ + 3e⁻ → Cr(s) | −0.74 |
| Zn²⁺ + 2e⁻ → Zn(s) | −0.76 |
| 2H₂O + 2e⁻ → H₂(g) + 2OH⁻ | −0.83 |
| Al³⁺ + 3e⁻ → Al(s) | −1.66 |
| Mg²⁺ + 2e⁻ → Mg(s) | −2.37 |
| Na⁺ + e⁻ → Na(s) | −2.71 |
| Ca²⁺ + 2e⁻ → Ca(s) | −2.87 |
| K⁺ + e⁻ → K(s) | −2.93 |
| Li⁺ + e⁻ → Li(s) | −3.05 |
The aqueous entries above use the named phases, standard activities and approximately 298 K. Hydrogen ions or hydroxide ions shown in a half-reaction are essential conditions, not decoration. For example, acidic permanganate reduction to Mn²⁺ is not the same half-reaction as permanganate reduction in a different medium. An inert platinum or gold surface can supply an electronic contact to dissolved couples such as Fe³⁺/Fe²⁺ or Br₂/Br⁻ when no conducting metal product is present.
Subtract potentials, but balance electrons
Problem
Use E°(Cu²⁺/Cu) = +0.34 V and E°(Zn²⁺/Zn) = −0.76 V.
- 1.Copper has the more positive reduction potential and acts as the cathode during standard spontaneous discharge.
- 2.E°cell = 0.34 − (−0.76) = +1.10 V. Subtracting a negative number adds its magnitude.
- 3.Both half-reactions transfer two electrons, giving Zn + Cu²⁺ → Zn²⁺ + Cu. The positive potential predicts a favourable forward reaction under standard conditions.
When electron counts differ, multiply the half-reaction equations to cancel electrons, but do not multiply their potentials. Potential is energy per unit charge, so scaling both energy and charge leaves the ratio unchanged. For Zn + 2Ag⁺ → Zn²⁺ + 2Ag, the electron count is two but E°cell is 0.80 − (−0.76) = 1.56 V, not 2(0.80) + 0.76.
Potential measurements can be used to infer pH, equilibrium constants, solubility equilibria and endpoints in potentiometric titrations. The common principle is that composition affects the reversible potential. The appropriate electrode equation and calibration must be established for each measurement; a bare voltage reading does not by itself identify an unknown ion.
Strength, displacement and reaction conditions
The oxidised species in a high-potential couple is a relatively strong oxidising agent because it accepts electrons readily. The reduced species in a very negative-potential couple is a relatively strong reducing agent. Among the listed couples fluorine is an exceptionally strong oxidant and lithium metal an exceptionally strong reductant in aqueous thermodynamic comparisons. This does not mean lithium can persist in water; it reacts with water. Reaction medium, competing chemistry and kinetics must be considered.
Problem
Predict whether a zinc pot is suitable for aqueous CuSO₄.
- 1.Test Zn + Cu²⁺ → Zn²⁺ + Cu. E°cell = 1.10 V is positive, so the displacement is thermodynamically favoured under standard conditions.
- 2.The zinc container would dissolve while copper deposits. It is therefore chemically unsuitable for storage.
- 3.A positive E° establishes the standard thermodynamic direction. Concentrations and surface films can change actual behaviour, but they do not make zinc a sensible inert container for copper sulphate.
For a metal reacting with a non-oxidising acid, compare its reduction potential with H⁺/H₂. Zinc can reduce H⁺ while copper cannot do so favourably under standard conditions. Copper can still dissolve in an oxidising acid such as nitric acid because nitrate, rather than H⁺ alone, accepts electrons. A protective oxide film can also slow a favourable reaction, as happens with aluminium.
Problem
Identify three species able to oxidise Fe²⁺ to Fe³⁺ under suitable standard conditions.
- 1.Fe³⁺ + e⁻ → Fe²⁺ has E° = 0.77 V. Reverse this half-reaction for Fe²⁺ oxidation.
- 2.Choose a reduction couple above 0.77 V: Cl₂/Cl⁻, acidic MnO₄⁻/Mn²⁺ and acidic Cr₂O₇²⁻/Cr³⁺ qualify.
- 3.For chlorine, 2Fe²⁺ + Cl₂ → 2Fe³⁺ + 2Cl⁻ has E°cell = 1.36 − 0.77 = 0.59 V. Acidic conditions are required for the specified permanganate and dichromate half-reactions.
Quick Quiz
Quiz
What is the conventional standard potential of the standard hydrogen electrode?
Its standard potential is assigned zero; other electrode values are relative to it.
Which quantity is not multiplied when a balanced half-reaction is doubled?
Potential is intensive: energy and charge scale together, leaving their ratio unchanged.
Using +0.80 V for Ag⁺/Ag and −0.76 V for Zn²⁺/Zn, what is E° for Zn + 2Ag⁺ → Zn²⁺ + 2Ag?
Subtract reduction potentials: 0.80 − (−0.76) = 1.56 V. Do not double the silver potential.
Which is the stronger reducing metal under standard aqueous comparisons: Cu or Zn?
The more negative Zn²⁺/Zn reduction potential means zinc metal more readily acts as the reductant.
What is the most accurate meaning of unit activity for an aqueous ion?
Activity accounts for non-ideal interactions. Concentration divided by 1 M approximates it in an ideal solution.
Practice Problems
- Order Mg, Al, Zn, Fe and Cu by their tendency to displace the ions of metals below them, using standard potentials.
- Arrange Ag, Hg, Cr, Mg and K in increasing reducing power using the supplied reduction potentials Ag⁺/Ag = +0.80 V, Hg₂²⁺/2Hg = +0.797 V, Cr³⁺/Cr = −0.74 V, Mg²⁺/Mg = −2.37 V and K⁺/K = −2.93 V.
- Predict Fe³⁺ + I⁻ and Fe³⁺ + Br⁻ reactions using Fe³⁺/Fe²⁺ = 0.77 V, I₂/I⁻ = 0.54 V and Br₂/Br⁻ = 1.09 V.
- Predict whether Ag⁺ oxidises Cu, Fe³⁺ oxidises Ag, and Br₂ oxidises Fe²⁺.
- Why can copper resist a non-oxidising acid yet dissolve in nitric acid?
1. Read increasingly negative reduction potentials as increasingly strong metal reducing ability. 2. The order is Mg > Al > Zn > Fe > Cu. A metal toward the left can thermodynamically reduce appropriate ions toward the right under standard conditions. 3. Passivation and competing water reactions can prevent a simple visible displacement, so the ranking is a thermodynamic comparison.
Key Takeaways
• Electrode potentials are measured relative to a reference half-cell. • The standard hydrogen electrode has assigned standard potential 0 V. • Standard states use activities; concentration is an approximation. • Calculate E°cell by subtracting the anode reduction potential from the cathode value. • Balance electron counts without multiplying electrode potentials. • A more positive reduction potential indicates stronger oxidising tendency of the oxidised form. • A positive E° predicts standard thermodynamic feasibility, not reaction speed.