AP Chemistry 9.6: Electrochemical Cells, Cell Potential, and the Nernst Equation

Electrochemistry connects:

• redox reactions ↔ electrical energy
• Recall:

loss of electrons

gain of electrons

• Remember:
• OIL RIG

Electrochemical cells separate oxidation and reduction into different locations.

• There are two major types:

Uses a thermodynamically favored redox reaction to produce electrical energy.

Uses external electrical energy to drive a thermodynamically unfavored reaction.

This never changes:

oxidation occurs

reduction occurs

• Remember:
• AN OX
• Anode = Oxidation
• RED CAT
• Reduction = Cathode
• These rules work for both galvanic and electrolytic cells.

Electrons move through the external wire:

• anode → cathode
• Why?
• Electrons are produced by oxidation at the anode.
• They are consumed by reduction at the cathode.

Consider:

• Zn(s) + Cu²⁺(aq) → Zn²⁺(aq) + Cu(s)
• Half-reactions:

Zn → Zn²⁺ + 2e⁻

• Oxidation.

Cu²⁺ + 2e⁻ → Cu

• Reduction.
• Electrons travel:
• Zn electrode → Cu electrode

In the zinc-copper example:

At the Zn anode:

• Zn(s) → Zn²⁺
• Zn atoms leave the electrode.
• Therefore:
• Zn electrode mass decreases

At the Cu cathode:

• Cu²⁺ → Cu(s)
• Cu is deposited.
• Therefore:
• Cu electrode mass increases

A salt bridge allows ions to move between the half-cells.

• Its job is to:
• maintain electrical neutrality
• Without ion movement, charge would quickly build up and electron flow would stop.

At the anode, positive ions are often produced.

• Anions from the salt bridge migrate toward the anode compartment.

At the cathode, positive ions are often consumed.

• Cations from the salt bridge migrate toward the cathode compartment.

For a galvanic cell:

• anode = negative
• cathode = positive

For an electrolytic cell:

• anode = positive
• cathode = negative

Do not memorize the electrode sign as part of the definition.

Instead always remember:

• anode = oxidation
• cathode = reduction
• Those never change.

Electrical potential is represented by:

• E
• Under standard conditions:
• E°cell
• Measured in:
• volts (V)

A positive standard cell potential indicates that the reaction as written is thermodynamically favored under standard conditions.

Tables usually list reactions as reductions.

The more positive the reduction potential:

• the greater the tendency for that species to be reduced

The half-reaction with the more positive reduction potential usually serves as the cathode reaction in a spontaneous galvanic cell.

Using reduction potentials:

• E°cell = E°cathode − E°anode

Both values are taken from the table as reduction potentials.

Suppose:

• Cu²⁺ + 2e⁻ → Cu
• E° = +0.34 V
• and:
• Zn²⁺ + 2e⁻ → Zn
• E° = −0.76 V
• Cu is reduced at the cathode.
• Zn is oxidized at the anode.
• Therefore:
• E°cell = 0.34 − (−0.76)
• = 1.10 V

If you multiply a half-reaction by 2 to balance electrons:

• do NOT multiply E° by 2

Cell potential is an intensive property.

• This is a very common AP Chemistry mistake.

The major equation is:

• ΔG° = −nFE°
• where:
• n = moles of electrons transferred
• F = Faraday constant
• E° = standard cell potential

Faraday constant:

• F ≈ 96,485 C/mol e⁻

If:

• E° > 0
• then:
• ΔG° < 0
• Reaction is thermodynamically favored.
• If:
• E° < 0
• then:
• ΔG° > 0
• Reaction is thermodynamically unfavored.

At equilibrium:

• E = 0
• and:
• ΔG = 0

Combine:

• ΔG° = −RT ln K
• and:
• ΔG° = −nFE°
• So:
• nFE° = RT ln K
• This creates another important connection.

Then:

• K > 1
• Products favored.

Then:

• K < 1
• Reactants favored.

You should recognize:

ΔG° < 0

• E°cell > 0
• K > 1

ΔG° > 0

• E°cell < 0
• K < 1
• This relationship is extremely important.

Electrochemical cells do not always operate under standard conditions.

• Actual cell potential depends on concentrations or partial pressures.
• This is described by the:
• Nernst equation
• At 25°C:
• E = E° − (0.0592 V / n) log Q
• where:
• E = current cell potential
• E° = standard cell potential
• n = electrons transferred
• Q = reaction quotient

For a spontaneous cell reaction, as products build up:

• Q increases

As Q moves toward K:

• E decreases

Eventually at equilibrium:

• Q = K
• and:
• E = 0
• The battery can no longer produce net electrical work.

At standard conditions:

• Q = 1
• Since:
• log 1 = 0
• the Nernst equation becomes:
• E = E°