F. Electrochemistry · ElectrochemistryStandard Reduction Potentials and the Standard Hydrogen Electrode
F3.4 F3.3 F2.1 F2.5About 70 minutes
Learning goals- I can explain what a cell potential (voltage) measures.
- I can describe the standard hydrogen electrode and explain why it is used as the reference half-cell.
- I can find a standard reduction potential from a measurement against the hydrogen electrode.
- I can use a table of standard reduction potentials to compare oxidizing and reducing agents.
Words to know
cell potential (Ecell)
The electric potential difference between the two electrodes of a cell, in volts (V). It measures how strongly electrons are pushed through the external circuit.
standard conditions
For electrochemistry: all dissolved species at 1.0 mol/L, all gases at 100 kPa, and a temperature of 25 °C (298 K).
standard hydrogen electrode (SHE)
The reference half-cell: a platinum electrode in 1.0 mol/L H⁺(aq) with H₂(g) at 100 kPa bubbling over it. Its reduction potential is defined as exactly 0 V.
standard reduction potential (E°)
The potential of a half-cell under standard conditions, measured against the SHE and written for the reduction half-reaction.
reference electrode
A half-cell with a stable, known potential against which other half-cells are measured.
How hard is the push?
A zinc–copper cell makes about 1.1 V. An alkaline AA battery makes about 1.5 V; a lithium-ion phone cell, about 3.7 V. Why do different pairs of metals give different voltages, and can we predict the voltage before building a cell?
In Grade 11 Physics (SPH3U, Electricity and Magnetism) you met potential difference: the energy given to each coulomb of charge, measured in volts (1 V = 1 J/C). In a galvanic cell, the potential difference between the electrodes is called the cell potential, Ecell. It comes from the difference between how strongly the two half-cells attract electrons. The bigger the difference, the harder electrons are pushed from anode to cathode, and the higher the voltage.
The problem: you can only measure differences
A voltmeter needs two connections. It measures the difference between two electrodes, never the potential of one half-cell alone. It is like measuring heights: you can only say how tall a mountain is compared with something else, so we agree on a zero, sea level.
For half-cells, chemists chose the standard hydrogen electrode (SHE) as "sea level" and defined its potential as exactly 0 V.
Measuring a standard reduction potential
To find the potential of another half-cell, build a galvanic cell with that half-cell and an SHE, under standard conditions (1.0 mol/L solutions, gases at 100 kPa, 25 °C), and read the voltmeter.
- Copper: Cu(s) | Cu²⁺(aq) connected to the SHE gives 0.34 V, and the copper electrode is the cathode (positive). Copper ions take electrons more readily than H⁺. So E°(Cu²⁺/Cu) = +0.34 V.
- Zinc: Zn(s) | Zn²⁺(aq) connected to the SHE gives 0.76 V, but now zinc is the anode (negative). Zinc ions take electrons less readily than H⁺. So E°(Zn²⁺/Zn) = −0.76 V.
The rule: the size of E° is the voltmeter reading, and the sign is + if the half-cell is the cathode against the SHE and − if it is the anode.
Every value is written for the reduction half-reaction. That is why the list is called a table of standard reduction potentials.
| Reduction half-reaction | E° (V) |
|---|
| F₂(g) + 2e⁻ ⇌ 2F⁻(aq) | +2.87 |
| PbO₂(s) + SO₄²⁻(aq) + 4H⁺(aq) + 2e⁻ ⇌ PbSO₄(s) + 2H₂O(l) | +1.69 |
| MnO₄⁻(aq) + 8H⁺(aq) + 5e⁻ ⇌ Mn²⁺(aq) + 4H₂O(l) | +1.51 |
| Au³⁺(aq) + 3e⁻ ⇌ Au(s) | +1.50 |
| Cl₂(g) + 2e⁻ ⇌ 2Cl⁻(aq) | +1.36 |
| O₂(g) + 4H⁺(aq) + 4e⁻ ⇌ 2H₂O(l) | +1.23 |
| Br₂(l) + 2e⁻ ⇌ 2Br⁻(aq) | +1.07 |
| NO₃⁻(aq) + 4H⁺(aq) + 3e⁻ ⇌ NO(g) + 2H₂O(l) | +0.96 |
| Ag⁺(aq) + e⁻ ⇌ Ag(s) | +0.80 |
| Fe³⁺(aq) + e⁻ ⇌ Fe²⁺(aq) | +0.77 |
| I₂(s) + 2e⁻ ⇌ 2I⁻(aq) | +0.54 |
| O₂(g) + 2H₂O(l) + 4e⁻ ⇌ 4OH⁻(aq) | +0.40 |
| Cu²⁺(aq) + 2e⁻ ⇌ Cu(s) | +0.34 |
| 2H⁺(aq) + 2e⁻ ⇌ H₂(g) | 0.00 |
| Pb²⁺(aq) + 2e⁻ ⇌ Pb(s) | −0.13 |
| Sn²⁺(aq) + 2e⁻ ⇌ Sn(s) | −0.14 |
| Ni²⁺(aq) + 2e⁻ ⇌ Ni(s) | −0.26 |
| PbSO₄(s) + 2e⁻ ⇌ Pb(s) + SO₄²⁻(aq) | −0.36 |
| Cd²⁺(aq) + 2e⁻ ⇌ Cd(s) | −0.40 |
| Fe²⁺(aq) + 2e⁻ ⇌ Fe(s) | −0.45 |
| Zn²⁺(aq) + 2e⁻ ⇌ Zn(s) | −0.76 |
| 2H₂O(l) + 2e⁻ ⇌ H₂(g) + 2OH⁻(aq) | −0.83 |
| Al³⁺(aq) + 3e⁻ ⇌ Al(s) | −1.66 |
| Mg²⁺(aq) + 2e⁻ ⇌ Mg(s) | −2.37 |
| Na⁺(aq) + e⁻ ⇌ Na(s) | −2.71 |
| Ca²⁺(aq) + 2e⁻ ⇌ Ca(s) | −2.87 |
| K⁺(aq) + e⁻ ⇌ K(s) | −2.93 |
| Li⁺(aq) + e⁻ ⇌ Li(s) | −3.04 |
E° does not change when you multiply
Ag⁺ + e⁻ → Ag has E° = +0.80 V. So does 2Ag⁺ + 2e⁻ → 2Ag. A potential is energy per coulomb, so doubling the amount doubles the energy and the charge, and their ratio stays the same. Never multiply E° by a coefficient.
Worked exampleExample 1: Finding E° from a measurement
A nickel half-cell (Ni in 1.0 mol/L Ni²⁺) is connected to an SHE at 25 °C. The voltmeter reads 0.26 V, and electrons flow from the nickel to the platinum. Find E° for Ni²⁺/Ni.
- Electrons leave the nickel, so nickel is being oxidized: nickel is the anode.
- The SHE is the cathode: hydrogen ions take electrons more readily than nickel ions.
- The size of E° is the reading, 0.26 V; the sign is negative because nickel is the anode against the SHE.
Worked exampleExample 2: Ranking agents with E° values
Use the table to rank Cl₂, Ag⁺, Zn²⁺ and Cu²⁺ from strongest to weakest oxidizing agent. Then rank Zn, Cu, Ag and Cl⁻ as reducing agents.
- Oxidizing agents: the more positive the E°, the stronger. Cl₂ (+1.36) > Ag⁺ (+0.80) > Cu²⁺ (+0.34) > Zn²⁺ (−0.76).
- Reducing agents are the products of those half-reactions. The more negative the E°, the stronger the reducing agent: Zn (−0.76) > Cu (+0.34) > Ag (+0.80) > Cl⁻ (+1.36).
OA: Cl₂ > Ag⁺ > Cu²⁺ > Zn²⁺. RA: Zn > Cu > Ag > Cl⁻. The two orders are exact reverses, as expected.
Worked exampleExample 3: Interpreting a sign
E°(Mg²⁺/Mg) = −2.37 V. What does the negative sign tell you about magnesium and acids?
- Negative E° means Mg²⁺ is a weaker oxidizing agent than H⁺, so Mg is a stronger reducing agent than H₂.
- So H⁺ (above) can oxidize Mg (below): the reaction Mg + 2H⁺ → Mg²⁺ + H₂ is spontaneous.
Magnesium reacts with acids to produce hydrogen gas. Any metal with a negative E° reacts with 1.0 mol/L acid (in principle; some are slowed by oxide layers).
Reference electrodes in real life
The SHE is the official zero, but hydrogen gas and platinum black are awkward in daily use. Real instruments use more convenient reference electrodes whose potentials are known relative to the SHE, such as the silver/silver chloride electrode. A pH meter, which you may use in the sibling unit Acid-Base and Solubility Equilibria, contains a reference electrode of this kind: it measures a potential that depends on [H⁺].
Just for funThe SHE is the only half-cell whose potential is exactly zero... because chemists voted it so. It's the electrochemistry version of declaring your own height to be the official unit of tall.
Hands-on activityMake copper your "standard electrode"
You need: a lemon (or a glass of salt water), a piece of bare copper wire, and as many of these as you can find: a strip of aluminium foil, a galvanized (zinc-coated) nail or screw, a plain steel nail, and a stainless-steel spoon. You also need a digital multimeter. A grown-up should cut slits in the lemon with a knife.
- Roll the lemon on the table to release juice. A grown-up cuts two small slits about 3 cm apart.
- Push the copper wire into one slit. It is your reference electrode for the whole activity, the way the SHE is the reference for chemists.
- Push one test metal into the other slit. Connect the red lead to the copper and the black lead to the test metal. Record the voltage. Clean the slit with a paper towel between metals.
- Rank the metals by voltage. A bigger positive reading means the test metal is a stronger reducing agent compared with copper.
- Compare your ranking with the table. Zinc (from the galvanized coating) and aluminium should give the biggest readings, then steel (iron). Stainless steel, which is protected by a thin oxide film, is likely to give a small reading.
What to look for: your values will not match the table differences exactly. Lemon juice is not 1.0 mol/L of any metal ion, aluminium carries an oxide layer, and the meter draws a little current. That is exactly why the standard conditions are defined so carefully. Do not eat the lemon afterwards.
Your turn
1What is the standard reduction potential of the SHE, and why?
0.00 V, by definition. It is the agreed reference point, because only differences in potential can be measured.
2State the three standard conditions for E° values.
Dissolved species at 1.0 mol/L, gases at 100 kPa, temperature 25 °C (298 K).
3A Pb²⁺/Pb half-cell is the anode when connected to an SHE, and the voltmeter reads 0.13 V. What is E°(Pb²⁺/Pb)?
−0.13 V (anode against the SHE → negative).
4A Ag⁺/Ag half-cell is the cathode when connected to an SHE, and the voltmeter reads 0.80 V. What is E°(Ag⁺/Ag)?
+0.80 V (cathode against the SHE → positive).
5Which is the strongest oxidizing agent in the table, and which is the strongest reducing agent?
Strongest OA: F₂(g) (+2.87 V). Strongest RA: Li(s) (−3.04 V).
6What is E° for 2Ag⁺(aq) + 2e⁻ → 2Ag(s)?
+0.80 V. E° does not change when a half-reaction is multiplied.
7Why is platinum used in the SHE?
Platinum is inert: it conducts electrons and provides a surface for the H⁺/H₂ reaction without reacting itself.
More practice: warm-up
1What does a positive E° tell you about the oxidizing agent compared with H⁺?
It is a stronger oxidizing agent than H⁺.
4What unit is cell potential measured in?
5Which is the stronger reducing agent, Mg or Al?
Mg (−2.37 V is more negative than −1.66 V).
More practice: on your own
1A student connects a Cd²⁺/Cd half-cell to an SHE under standard conditions. Electrons flow from the cadmium electrode to the platinum, and the meter reads 0.40 V. Find E°, and say whether cadmium reacts with 1.0 mol/L HCl.
Electrons leave cadmium, so Cd is the anode: E° = −0.40 V. Since E° is negative, H⁺ is the stronger oxidizing agent and cadmium does react with acid: Cd + 2H⁺ → Cd²⁺ + H₂.
2Rank as oxidizing agents, strongest first: Fe³⁺, I₂, Br₂, Fe²⁺.
Br₂ (+1.07) > Fe³⁺ (+0.77) > I₂ (+0.54) > Fe²⁺ (−0.45). (Fe²⁺ as an oxidizing agent is in the Fe²⁺/Fe row.)
3Explain, using an analogy, why there is no way to measure the potential of a single half-cell by itself.
A voltmeter measures a difference between two points, like measuring height relative to sea level. With one half-cell there is nothing to compare it with, so we choose a reference (the SHE) and give it the value 0.
4Using E° values, predict whether silver reacts with 1.0 mol/L HCl. Explain.
E°(Ag⁺/Ag) = +0.80 V is above the SHE (0.00 V), so H⁺ is the weaker oxidizing agent and cannot oxidize silver. No reaction.
5If chemists had instead chosen the Cu²⁺/Cu half-cell as the zero, what would E° for Zn²⁺/Zn and for the SHE be?
Every value would drop by 0.34 V. Zn²⁺/Zn: −0.76 − 0.34 = −1.10 V; SHE: 0.00 − 0.34 = −0.34 V. Differences between half-cells (and so all cell voltages) would not change.
Challenge
1A metal M forms M²⁺. An M half-cell connected to a Cu half-cell (standard conditions) gives 0.60 V, with M as the anode. Find E°(M²⁺/M). Which metal in the table might M be?
E°cell = E°(Cu) − E°(M), so 0.60 = 0.34 − E°(M), and E°(M) = −0.26 V. That matches nickel.
2A Zn | Zn²⁺ half-cell is measured against a Ag/AgCl reference electrode, whose potential is +0.22 V relative to the SHE. What will the voltmeter read?
The difference between the half-cells: 0.22 − (−0.76) = 0.98 V, with zinc as the anode.
3The value of E° for O₂ + 4H⁺ + 4e⁻ → 2H₂O is +1.23 V, but for O₂ + 2H₂O + 4e⁻ → 4OH⁻ it is +0.40 V. Both describe oxygen being reduced. Explain the difference.
The standard conditions are different. The first has [H⁺] = 1.0 mol/L (pH 0); the second has [OH⁻] = 1.0 mol/L (pH 14). Oxygen is a stronger oxidizing agent in acid than in base, so its potential depends on pH. (This is why corrosion and fuel cells behave differently in acidic and basic conditions.)
Quiz
1. The standard hydrogen electrode has a reduction potential of 0.00 V because:
2. Which set lists standard conditions for E° values?
3. A half-cell is the anode when connected to the SHE, and the voltmeter reads 1.66 V. Its E° is:
4. Which is the strongest oxidizing agent?
5. What is E° for 3Cu²⁺(aq) + 6e⁻ → 3Cu(s)?
6. A metal with a negative standard reduction potential will:
Big idea (F3.4, F3.3): a voltmeter can only measure the difference between two half-cells, so chemists defined the standard hydrogen electrode as 0 V. Every other half-cell's standard reduction potential is measured against it: positive means a stronger oxidizing agent than H⁺, negative means weaker.
How to help: Use the sea-level analogy. Ask your teen: "Why can't we know a single half-cell's potential? What did chemists do about it?" Then quiz a few values from the table and ask which species is the stronger oxidizing agent.
Common difficulties:
- Multiplying E° by coefficients. E° never changes with coefficients.
- Getting the sign backwards: a half-cell that is the cathode against the SHE has a positive E°.
- Reading the reducing-agent strength from the wrong end. The most negative E° has the strongest reducing agent (on the right side).
Safety: a grown-up should cut the lemon. Don't eat a lemon that has had metal in it.