Chemistry 2e · Electrochemistry
Electrode and Cell Potentials
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In 30 seconds
Every galvanic cell produces a measurable cell potential (voltage) — the "push" that drives electrons through the external circuit. That voltage comes from the difference in the tendencies of the two half-reactions to gain electrons. Each half-reaction has a characteristic electrode potential The tendency of a half-reaction to gain electrons, measured against the SHE. Full entry →, and the cell potential is the difference between the two electrode potentials.
Because an individual half-reaction's potential cannot be measured in isolation, chemists defined a reference: the standard hydrogen electrode (SHE) Reference electrode: 2H+ + 2e- → H2, assigned E°= 0.00 V. Full entry →, assigned a potential of exactly 0.00 V. Every other half-reaction is measured against it under standard conditions (1 M concentrations for solutions, 1 atm for gases, usually 25 °C), producing a table of standard reduction potentials, E°. With that table, the potential of any cell — and therefore whether it is spontaneous — can be computed from
E°cell = E°cathode - E°anode
A positive E°cell means the reaction is spontaneous as written; a negative value means the reverse is favored. This topic explains the table, how to read it, and how to use it to predict cell voltage and spontaneity — the quantitative heart of electrochemistry.
Why this matters
- Quantitative prediction: Instead of building a cell to see if it works, you can compute its voltage and spontaneity from a table in minutes.
- Comparing oxidizing/reducing strength: The table ranks species: the most positive reduction potentials are the strongest oxidizing agents; the most negative are the strongest reducing agents.
- Battery design: Engineers select electrode pairs with large, opposite potentials to maximize voltage (e.g., lithium–ion cells exploit lithium's very negative potential).
- Corrosion and protection: Knowing potentials explains why one metal corrodes preferentially when in contact with another (galvanic corrosion) and why sacrificial anodes protect steel.
- Biological and environmental systems: Redox potentials govern electron-transfer chains in respiration and photosynthesis, and drive the chemistry of groundwater, soils, and wastewater treatment.
- Exams: Expect to compute E°cell, identify the stronger oxidizing/reducing agent, and decide spontaneity from the sign of E°cell.
The college version
Core Concepts
Electrode potential: what it measures
An electrode potential measures the tendency of a half-reaction to occur as a reduction (gain of electrons) relative to the SHE. Half-reactions are always tabulated as reductions:
Ox + ne- → Red
A more positive E° means the oxidized form is a stronger oxidizing agent (it wants electrons more). A more negative E° means the reduced form is a stronger reducing agent (it wants to give electrons away).
The standard hydrogen electrode
The SHE consists of H2 gas (1 atm) bubbling over a platinum electrode in 1 M H+ solution:
2H+(aq, 1 M) + 2e- → H2(g, 1 atm) E°= 0.00 V
Platinum is an inert conductor; it does not react. By convention, this half-reaction defines the zero of the potential scale. All tabulated E° values are measured against it under standard conditions: 1 M solutions, 1 atm gases, 25 °C.
Reading the table of standard reduction potentials
- All values are written as reductions. When a half-reaction is reversed (used as oxidation), the sign of E° flips, but the magnitude does not change — and it never gets multiplied by a stoichiometric coefficient, because potential is an intensive property.
- Example entries: Cu2+ + 2e- → Cu, E°= +0.34 V; Zn2+ + 2e- → Zn, E°= -0.76 V.
Computing the cell potential
For a cell made of two half-cells, with the reduction written for the cathode and oxidation for the anode:
E°cell = E°cathode - E°anode
Using tabulated reduction potentials for both, the subtraction automatically handles the sign flip for the anode. A positive result means the reaction is spontaneous as written; negative means the reverse reaction is spontaneous.
Potential, spontaneity, and free energy
The cell potential connects directly to free energy (detailed in the next topic):
ΔG°= -nFE°cell
where n is the number of moles of electrons transferred per mole of reaction and F is the Faraday constant, F = 96,485 C/mol e-. A positive E°cell gives a negative ΔG° — spontaneous. This is why a battery's voltage and its thermodynamic favorability are the same fact viewed twice.
How It Works / Step-by-Step Process
- Write both half-reactions as reductions and look up their E° values.
- Identify which half-reaction will be the cathode (the one with the more positive E°, i.e., the stronger oxidizing agent) and which the anode.
- Compute E°cell = E°cathode - E°anode.
- If positive, the cell reaction as written is spontaneous; if negative, the reverse is spontaneous (swap anode/cathode).
- Balance the electrons if you need the full reaction — but never rescale the E° values.
- Optionally convert to free energy with ΔG°= -nFE°cell.
Common Confusions
| Do Not Confuse | With | Difference |
|---|---|---|
| E°cell sign | Spontaneity of any direction | The sign applies to the reaction as written: positive = forward spontaneous, negative = reverse spontaneous. |
| Multiplying E° by coefficients | Rescaling cell potential | E° is intensive — doubling a half-reaction does not double its potential. |
| More negative E° | "Stronger oxidizing agent" | More negative = stronger reducing agent; more positive = stronger oxidizing agent. |
| SHE potential | "Hydrogen is unreactive" | SHE is a defined reference (0.00 V), not a statement about hydrogen's chemistry. |
| E°cell = E°cat + E°an (both as written) | Subtraction formula | Using tabulated reduction values for both requires subtraction; adding applies only if the anode value is already sign-flipped. |
Eli explains
The same idea, in plain words
Explain it like I’m 10
Think of each half-reaction as a hill with a height. The standard hydrogen electrode is the "sea level" hill, set to zero. Every other reaction gets a height measured from sea level — some want electrons a lot (tall hills), some barely at all (valleys). The cell's voltage is just the difference in height between the two hills. If the downhill direction matches the way the reaction is written, the cell runs by itself.
Worked example
Example 1: The Daniell cell potential
For the cell Zn(s) | Zn2+(aq) | | Cu2+(aq) | Cu(s), look up E°(Cu2+/Cu) = +0.34 V and E°(Zn2+/Zn) = -0.76 V.
Formula:
E°cell = E°cathode - E°anode
Substitution (Cu²⁺ is the cathode since it has the more positive potential):
E°cell = (+0.34 V) - (-0.76 V) = +1.10 V
Positive E°cell confirms the spontaneous direction: zinc is oxidized and copper(II) is reduced. The 1.10 V matches the measured voltage of a standard Daniell cell.
Example 2: Predicting spontaneity from the table
Will Ni2+ oxidize metallic Al? Use E°(Ni2+/Ni) = -0.26 V and E°(Al3+/Al) = -1.66 V.
If Ni2+ is reduced (cathode) and Al oxidized (anode):
E°cell = E°(Ni2+/Ni) - E°(Al3+/Al) = (-0.26 V) - (-1.66 V) = +1.40 V
Positive — the reaction is spontaneous: Ni2+(aq) + Al(s) → Ni(s) + Al3+(aq) proceeds, plating nickel onto aluminum and dissolving the aluminum. Aluminum's very negative potential makes it a strong reducing agent.
Example 3: Stronger oxidizing agent
Between Cu2+ and Fe2+, which is the stronger oxidizing agent? Compare E°(Cu2+/Cu) = +0.34 V with E°(Fe2+/Fe) = -0.44 V. The more positive potential belongs to Cu2+/Cu, so Cu2+ is the stronger oxidizing agent: it will accept electrons from anything Fe²⁺ could donate, and can even oxidize solid Fe. This ranking is exactly how you decide which of two species wins electrons in a spontaneous reaction.
Key takeaways
- Standard conditions: 1 M solutions, 1 atm gases, 25 °C; SHE defines E°= 0.00 V.
- Half-reactions are tabulated as reductions; reversing a half-reaction flips the sign of E° but not its magnitude.
- E°cell = E°cathode - E°anode; positive = spontaneous, negative = nonspontaneous (reverse favored).
- More positive E° = stronger oxidizing agent; more negative E° = stronger reducing agent.
- E° is intensive: never multiply it by stoichiometric coefficients when balancing half-reactions.
- ΔG°= -nFE°cell links voltage to free energy; F = 96,485 C/mol e-.
Check yourself
5 review questions from the chapter. Try each one, then open the answer.
What are the three standard conditions for tabulated E° values, and what is the reference electrode?
Show answer
1 M concentrations for dissolved species, 1 atm for gases, and 25 °C; the standard hydrogen electrode (SHE), E°= 0.00 V.
Compute E°cell for Fe2+/Fe (-0.44 V) and Ag+/Ag (+0.80 V), and state whether the reaction is spontaneous.
Show answer
E°cell = (+0.80) - (-0.44) = +1.24 V; positive, so Ag+ reduced and Fe oxidized is spontaneous.
Why is E° not multiplied by stoichiometric coefficients when balancing half-reactions?
Show answer
Potential is an intensive property — it measures tendency per reaction, independent of how much material reacts; only the electron count (n) scales with stoichiometry.
Which is the stronger reducing agent: Zn or Cu? Explain using potentials.
Show answer
Zn: its potential is more negative (-0.76 V vs +0.34 V), so Zn's reduced form more readily gives up electrons.
If E°cell = +1.10 V and n = 2, what is ΔG° for the Daniell cell?
Show answer
ΔG°= -nFE°cell = -(2)(96,485 C/mol)(1.10 V) = -2.12 × 105 J/mol ≈ -212 kJ/mol.
Study tools & related lessonsKey vocabulary · Related
Key vocabulary
- electrode potential
- The tendency of a half-reaction to gain electrons, measured against the SHE.
- standard reduction potential, E°
- Electrode potential measured under standard conditions, with the half-reaction written as a reduction.
- standard hydrogen electrode (SHE)
- Reference electrode: 2H+ + 2e- → H2, assigned E°= 0.00 V.
- cell potential, E°cell
- Difference between cathode and anode reduction potentials.
- Faraday constant, F
- Charge of one mole of electrons, 96,485 C/mol.
- oxidizing agent strength
- Ranked by E°: larger (more positive) E° = stronger oxidizer.
Sources & references
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