Cell Potentials

Cell potentials let you predict which electrode in an electrochemical cell gets oxidized and which gets reduced, using experimentally measured reduction potentials — the relative tendency of a chemical species to gain electrons. Those tendencies are measured against the reduction of the hydrogen ion (H⁺), which is used as an arbitrary zero reference point.

Key Takeaways

• Reduction potential measures a species' tendency to gain electrons, defined relative to the standard hydrogen electrode (SHE), which is set at 0 V.

• Standard reduction potential (E°red) is measured at standard conditions (25°C, 1 atm, 1 M); more positive E°red means a greater tendency to be reduced, less positive/more negative means a greater tendency to be oxidized.

• In a galvanic cell, the more-positive-E°red electrode is the cathode and the less-positive-E°red electrode is the anode (spontaneous, ΔG < 0); in an electrolytic cell, an external power source forces those roles to reverse (nonspontaneous, ΔG > 0).

• Oxidation potential = reverse the reduction half-reaction and flip the sign of the reduction potential.

• E°cell = E°cathode − E°anode, using each electrode's standard reduction potential — and standard potentials are never multiplied by the number of electrons transferred, since potential is an intensive property.

• Worked example: for the Daniell cell, E°cell = (+0.34 V) − (−0.76 V) = +1.10 V, matching its known emf and confirming spontaneity.

Reduction Potentials and the Standard Hydrogen Electrode

A reduction potential, measured in volts (V), describes a species' tendency to gain electrons and be reduced. It's defined relative to the standard hydrogen electrode (SHE), which by convention is assigned a potential of exactly 0 V.

Every species has its own intrinsic reduction potential:

• A more positive reduction potential means a greater tendency to be reduced (to gain electrons).

• A less positive (or more negative) reduction potential means a greater tendency to be oxidized (to lose electrons).

The SHE itself is a hydrogen electrode operating under standard conditions, and every other half-cell's reduction potential is reported as a voltage difference relative to it.

Standard Reduction Potential (E°red)

The standard reduction potential (E°red) is a reduction potential measured under standard conditions: 25°C (298 K), 1 atm pressure, and 1 M concentration for all reactants and products. Standardizing these conditions is what makes it possible to directly compare the reactivities of different half-cells and predict the direction of electron flow between them.

• A more positive E°red — the species is more easily reduced.

• A less positive (or more negative) E°red — the species is more easily oxidized.

Finding the Anode and Cathode from Reduction Potentials

Reduction potentials tell you exactly which electrode becomes the anode and which becomes the cathode — but the rule flips depending on whether the reaction is spontaneous or forced.

In a galvanic cell (spontaneous reaction):

• The electrode with the more positive reduction potential acts as the cathode, where reduction occurs.

• The electrode with the less positive reduction potential acts as the anode, where oxidation occurs.

• Because the species with the stronger natural pull on electrons is the one that actually gains them, the reaction proceeds on its own — it's spontaneous, and ΔG is negative.

In an electrolytic cell (nonspontaneous reaction, requires an external power source):

• The external power source forces the electrode with the more positive reduction potential to act as the anode (oxidation) instead.

• The electrode with the less positive reduction potential is forced to act as the cathode (reduction).

• Because this pushes electrons against the species' natural tendencies, the reaction is nonspontaneous, and ΔG is positive.

In both cases, the same reduction-potential values are doing the predicting — what changes is whether the cell is left to follow those tendencies (galvanic) or forced against them (electrolytic).

Oxidation Potential

Reduction and oxidation are opposite processes, so an oxidation potential is just a reduction potential viewed backward. To get one:

• 1. Reverse the reduction half-reaction (flip reactants and products).

• 2. Change the sign of the reduction potential.

For example, if a reduction half-reaction has E°red = +0.34 V, the reverse (oxidation) half-reaction has an oxidation potential of −0.34 V.

Calculating Cell Potential (E°cell)

The electromotive force (emf) of a reaction under standard conditions — also written E°cell — is the difference in potential between the cell's two half-cells. It's calculated directly from the two half-cells' standard reduction potentials:

E°cell = E°cathode − E°anode

To use this formula: take the standard reduction potential of whichever electrode is the cathode, and subtract the standard reduction potential of whichever electrode is the anode. Both values are looked up (or given) as reduction potentials — you don't need to convert the anode's value to an oxidation potential first, since the subtraction already accounts for that reversal.

Don't scale by moles of electrons transferred. It's tempting to multiply a standard potential by the number of electrons a half-reaction gains or loses, especially right after balancing that half-reaction — but doing so is a mistake. A standard reduction potential is an intensive property: it depends only on the chemical identity of the electrode and its solution, not on how much material is present or how the half-reaction happens to be balanced. The standard reduction potential of a given electrode won't change unless the chemical identity of that electrode changes.

Worked Example: E°cell for the Daniell Cell

The Daniell cell — zinc anode, copper cathode, covered in the previous article — is a good place to put the E°cell formula to work. Its two standard reduction potentials are well-established values:

• Cu²⁺(aq) + 2e⁻ → Cu(s), E°red = +0.34 V

• Zn²⁺(aq) + 2e⁻ → Zn(s), E°red = −0.76 V

Copper's reduction potential (+0.34 V) is more positive than zinc's (−0.76 V), so copper is the cathode and zinc is the anode — matching how the Daniell cell is actually built. Plugging into the formula:

E°cell = E°cathode − E°anode = (+0.34 V) − (−0.76 V) = +1.10 V

Notice that even though the balanced overall reaction transfers 2 moles of electrons (Zn loses 2, Cu²⁺ gains 2), the "2" never appears anywhere in this calculation — the potentials themselves are never multiplied by it. The result, +1.10 V, matches the Daniell cell's experimentally known emf of about 1.1 V, and the positive value confirms the reaction is spontaneous (ΔG < 0), consistent with a galvanic cell.

Common MCAT Mistakes

• Multiplying a standard reduction potential by the number of electrons transferred. E° is an intensive property — it depends only on the identity of the electrode and solution, not on how the half-reaction happens to be balanced. Never scale it by n.

• Assuming the more-positive-E°red electrode is always the cathode. That's only true in a galvanic cell. In an electrolytic cell, the external power source forces the more-positive-E°red electrode to become the anode instead.

• Forgetting to flip the sign when writing an oxidation potential. Converting a reduction potential to an oxidation potential requires two changes together: reversing the half-reaction and flipping the sign of the voltage — not just one or the other.

• Converting the anode's reduction potential to an oxidation potential before subtracting. E°cell = E°cathode − E°anode already uses both values as reduction potentials; the subtraction itself accounts for the reversal at the anode, so no extra sign-flip is needed.

MCAT-Style Concept Check

Question: Two half-reactions are given: Ag⁺(aq) + e⁻ → Ag(s), E°red = +0.80 V, and Fe²⁺(aq) + 2e⁻ → Fe(s), E°red = −0.44 V. When combined into a galvanic cell, what is E°cell?

• A) 0.36 V

• B) 0.80 V

• C) 1.24 V

• D) −1.24 V

Answer: C

Explanation: Silver's reduction potential (+0.80 V) is more positive than iron's (−0.44 V), so in a galvanic cell silver is the cathode and iron is the anode. E°cell = E°cathode − E°anode = (+0.80 V) − (−0.44 V) = +1.24 V. The difference in the number of electrons transferred by each half-reaction (1 for Ag, 2 for Fe) doesn't factor into the calculation, since standard potentials aren't scaled by electron count.

FAQ

What is the standard hydrogen electrode, and why is it set at 0 V?

The standard hydrogen electrode (SHE) is a hydrogen electrode operating under standard conditions, and by convention it's assigned a reduction potential of exactly 0 V. It serves as the universal reference point that every other half-cell's reduction potential is measured against.

How do you determine which electrode is the anode and which is the cathode from reduction potentials?

In a galvanic (spontaneous) cell, the electrode with the more positive reduction potential is the cathode, and the one with the less positive reduction potential is the anode. In an electrolytic (nonspontaneous) cell, an external power source forces those roles to reverse.

How do you convert a reduction potential into an oxidation potential?

Reverse the reduction half-reaction so it reads as oxidation, and flip the sign of the potential. A reduction potential of +0.34 V becomes an oxidation potential of −0.34 V for the reverse reaction.

Why isn't E°cell multiplied by the number of electrons transferred in the balanced reaction?

Standard reduction potential is an intensive property — it reflects the chemical identity of the electrode and solution, not the amount of material reacting. E°cell = E°cathode − E°anode uses the reduction potentials directly, regardless of how many electrons the balanced half-reactions happen to transfer.