Chemistry: Atoms First 2e · Electrochemistry
Electrode and Cell Potentials
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In 30 seconds
Every half-reaction has a built-in tendency to gain electrons — some species pull strongly (fluorine, oxygen), others hold loosely (lithium, zinc). Electrochemistry turns that tendency into a number: the standard reduction potential, E°, measured in volts (1 V = 1 J per coulomb of charge). Because a single half-reaction cannot be measured in isolation, potentials are defined relative to the standard hydrogen electrode (SHE) Reference electrode: Pt in 1 M H⁺ with H₂ at 1 atm, assigned 0.00 V. Full entry →, assigned exactly 0.00 V. Tables of standard reduction potentials then let you predict which reactions are spontaneous and compute any cell's voltage with one rule: E°cell = E°cathode − E°anode.
Why this matters
Cell potentials are the practical currency of electrochemistry. Battery makers use them to choose electrode pairs; corrosion engineers use them to pick sacrificial metals; analytical chemists use them to design sensors. Most importantly, the sign of E°cell tells you instantly whether a reaction is spontaneous — the chapter's single most useful prediction — and its magnitude feeds Topic 4's free-energy and equilibrium calculations. Reading a reduction-potential table correctly is tested on virtually every exam.
The college version
Core Concepts
Standard reduction potentials
A standard reduction potential is the voltage of a half-reaction written as a reduction (species + electrons → product) under standard conditions 1 M solutes, 1 atm gases, 25 °C (298 K). Full entry →: solutes at 1 M, gases at 1 atm, 25 °C (298 K). The more positive the potential, the stronger the pull on electrons — and the stronger the oxidizing agent (the species on the left). The more negative the potential, the stronger the reducing agent (the species on the right). Reversing a half-reaction flips the sign of its potential, but multiplying it never changes the potential — potentials are intensive.
The standard hydrogen electrode (SHE)
The SHE is the reference for all other potentials: a platinum electrode (inert — it only conducts electrons) immersed in 1 M H⁺ with H₂ gas bubbled over it at 1 atm. By convention:
2H+(aq, 1 M) + 2e- → H2(g, 1 atm) E°= 0.00 V
To measure any other couple's potential, build a cell with the SHE as one electrode and read the voltmeter: the measured voltage is that couple's reduction potential.
Computing the cell potential
For any galvanic cell, the standard cell potential is the cathode potential minus the anode potential:
E°cell = E°cathode - E°anode
where E°cathode is the reduction potential of the half-reaction that runs as a reduction and E°anode is the potential of the half-reaction that runs as an oxidation (use the table value as written — the minus sign handles the reversal). Identify the electrodes by comparing potentials: the more positive couple is reduced (cathode), the more negative oxidized (anode).
Predicting spontaneity
The sign of E°cell is the verdict: E°cell > 0 means the reaction is spontaneous (it can power a galvanic cell); E°cell < 0 means it is nonspontaneous as written (it requires an electrolytic cell and external energy). This is the electrochemical version of the Chapter 12 rule: spontaneous processes have negative ΔG°, linked to E° by ΔG° = −nFE° (Topic 4).
Relative strengths of oxidizing and reducing agents
Think of the potential table as a ladder. Species high on the ladder (positive E°, e.g., F₂, MnO₄⁻) are the strongest oxidizing agents — they grab electrons from anything below them. Species low on the ladder (negative E°, e.g., Li, Zn) are the strongest reducing agents — they readily give electrons away. A reaction is spontaneous when the reducing agent sits below the oxidizing agent: electrons flow "downhill" from the more negative couple to the more positive one.
How It Works / Step-by-Step Process
- Write the two half-reactions and look up their standard reduction potentials.
- Identify the cathode (more positive E°) and the anode (more negative E°).
- Apply E°cell = E°cathode − E°anode, substituting the table values with their units.
- Interpret: positive E°cell = spontaneous as written; negative = nonspontaneous.
- If needed, balance the overall equation (Topic 1); the potential is unchanged.
Common Confusions
| Do Not Confuse | With | Difference |
|---|---|---|
| E°cathode − E°anode | E°reduction + E°oxidation | Both give the same number, but the subtraction form uses table values directly; adding requires flipping the anode sign first. |
| Which couple is the cathode | Which couple is the anode | The more positive E° is reduced (cathode); the more negative E° is oxidized (anode). |
| Oxidizing agent | Reducing agent in the table | The oxidized form (left side) is the oxidizing agent; the reduced form (right side) is the reducing agent. |
| Standard conditions | Actual lab conditions | E° applies only at 1 M/1 atm/25 °C; real cells deviate (Topic 4's Nernst equation handles this). |
Eli explains
The same idea, in plain words
Explain it like I’m 10
Every kind of atom has its own "electron hunger." Some atoms, like fluorine, are super hungry; others, like lithium, are happy to let electrons go. The potential table is a hunger chart: the hungriest atoms are at the top. Electrons slide downhill, from an atom that doesn't want them to one that does — the farther the slide, the bigger the voltage.
Worked example
Example 1: The Daniell cell
For the Zn/Cu cell (Zn anode, Cu cathode), the half-reactions and table values are:
Cu2+(aq) + 2e- → Cu(s) E°= +0.34 V
Zn2+(aq) + 2e- → Zn(s) E°= -0.76 V
Copper has the more positive potential, so it is the cathode and zinc the anode. Apply the formula before substituting:
E°cell = E°cathode - E°anode = +0.34 V - (-0.76 V) = +1.10 V
The positive value confirms the reaction is spontaneous, delivering 1.10 V under standard conditions.
Example 2: A lead–nickel cell
Which electrode is the anode in a Pb²⁺/Pb (E° = −0.13 V) vs. Ni²⁺/Ni (E° = −0.26 V) cell? Lead's potential is less negative, so Pb²⁺ is reduced (cathode) and Ni oxidized (anode):
E°cell = E°cathode - E°anode = -0.13 V - (-0.26 V) = +0.13 V
The cell is spontaneous, but only barely — 0.13 V. Note the stronger reducing agent: nickel (−0.26 V) is more negative than lead. The balanced cell reaction is Ni(s) + Pb²⁺(aq) → Ni²⁺(aq) + Pb(s).
Example 3: Will tin metal reduce iron(III)?
Predict whether Sn(s) will reduce Fe³⁺(aq) to Fe²⁺(aq) under standard conditions. The couples: Fe³⁺ + e⁻ → Fe²⁺ (E° = +0.77 V) and Sn²⁺ + 2e⁻ → Sn (E° = −0.14 V). Fe³⁺ has the more positive potential, so it is reduced (cathode), and Sn is oxidized (anode):
E°cell = +0.77 V - (-0.14 V) = +0.91 V
Positive, so the reaction is spontaneous: 2Fe³⁺(aq) + Sn(s) → 2Fe²⁺(aq) + Sn²⁺(aq) — two Fe³⁺ accept the two electrons each Sn atom gives up. Had E°cell come out negative, you would predict no reaction — a common exam format.
Key takeaways
- E° values are measured against the SHE (0.00 V) at 1 M/1 atm/25 °C.
- More positive E° = stronger oxidizing agent; more negative E° = stronger reducing agent.
- E°cell = E°cathode − E°anode; the more positive couple is the cathode (reduced), the more negative is the anode (oxidized).
- E°cell > 0 → spontaneous (galvanic cell); E°cell < 0 → nonspontaneous (electrolytic cell).
- Reversing a half-reaction flips the sign of E°; multiplying it does not change E° — E° is intensive.
- A more negative E° (more active metal) predicts which metal corrodes or dissolves first.
Check yourself
6 review questions from the chapter. Try each one, then open the answer.
Why must every reduction potential be measured relative to the SHE rather than absolutely?
Show answer
A single electrode's absolute potential cannot be measured — only differences can. The SHE provides a fixed, reproducible zero.
A cell uses the couples Fe³⁺/Fe²⁺ (+0.77 V) and Br₂/Br⁻ (+1.09 V). Which is the cathode, and what is E°cell?
Show answer
Br₂/Br⁻ (+1.09 V) is the cathode. E°cell = 1.09 V − 0.77 V = +0.32 V.
True or false: doubling the coefficients of a half-reaction doubles its E° value. Explain.
Show answer
False. E° is an intensive property; multiplying a half-reaction changes the number of electrons but not the potential per electron.
Which is the stronger reducing agent, Zn (−0.76 V) or Ni (−0.26 V)? Which is the stronger oxidizing agent, Cu²⁺ (+0.34 V) or Ag⁺ (+0.80 V)?
Show answer
Zn is the stronger reducing agent (more negative E°); Ag⁺ is the stronger oxidizing agent (more positive E°).
If E°cell for a reaction is −0.45 V, will the reaction proceed spontaneously as written?
Show answer
No. A negative E°cell means the reaction is nonspontaneous as written.
Why does a metal with a very negative E° (like sodium, −2.71 V) react vigorously with water rather than sitting quietly in it?
Show answer
Sodium's very negative E° makes it an extremely strong reducing agent: it readily gives up electrons, in this case to water, reducing H₂O to H₂ gas and OH⁻ (Topic 18 covers the reaction).
Study tools & related lessonsKey vocabulary · Related
Key vocabulary
- standard reduction potential (E°)
- Voltage of a half-reaction written as a reduction under standard conditions.
- standard hydrogen electrode (SHE)
- Reference electrode: Pt in 1 M H⁺ with H₂ at 1 atm, assigned 0.00 V.
- standard conditions
- 1 M solutes, 1 atm gases, 25 °C (298 K).
- oxidizing agent strength
- How strongly a species pulls electrons (high E°).
- reducing agent strength
- How readily a species gives up electrons (low E°).
- cell potential (E°cell)
- The voltage of a full cell: E°cathode − E°anode.
Sources & references
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