Topic 9.9 Notes – Cell Potential and Free Energy

1. Cell Potential and What It Means

Cell potential (E°cell) is the voltage produced by a redox reaction in an electrochemical cell under standard conditions (1 M, 1 atm, 298 K).

• Units: volts (V), which equal J/C
• It measures the driving force for electron flow
• Positive voltage means electrons flow spontaneously through the wire

Quick galvanic refresher:

• Anode = oxidation
• Cathode = reduction
• Electrons flow anode → cathode
• “An Ox, Red Cat”

Here’s the standard Zn-Cu galvanic cell you’ve seen before:

Zn-Cu galvanic cell (voltaic cell)

What the sign tells you

• E°cell > 0 → reaction is thermodynamically favored (spontaneous)
• E°cell < 0 → reaction is unfavored (needs external energy, electrolytic)
• E°cell = 0 → system at equilibrium

In the Zn-Cu cell above, electrons flow from the zinc anode to the copper cathode because the overall E°cell is positive.

A positive voltage means the reaction can do electrical work on the surroundings.

2. Standard Reduction Potentials and Calculating E°cell

All tabulated values are standard reduction potentials (E°red).

The Standard Reduction Potential Table

Every half-reaction is written as a reduction and measured relative to the:

$$\ce{2H^{+} + 2e^{-} -> H2(g)} \quad E^\circ = 0.00\text{ V}$$

That’s the Standard Hydrogen Electrode (SHE).

Here’s how to interpret the numbers:

The species with the higher (more positive) reduction potential gets reduced.

Identifying Anode and Cathode

When given two half-reactions:

1. Pick the one with the more positive E°red → that’s the cathode (reduction).
2. The other must run in reverse → that’s the anode (oxidation).

The reaction that “wants” electrons more strongly wins the reduction spot.

Calculating Standard Cell Potential

$$E^\circ_{cell} = E^\circ_{cathode} - E^\circ_{anode}$$

Important rules students mess up:

• Use values exactly as written in the table.
• Do not multiply E° values when balancing electrons.
• If you reverse a half-reaction, change the sign of E°.
• Coefficients affect n, not E°.

Quick Example

Suppose:

$$\ce{Fe^{3+} + e^{-} -> Fe^{2+}} \quad E^\circ = +0.77\text{ V}$$ $$\ce{Sn^{2+} + 2e^{-} -> Sn(s)} \quad E^\circ = -0.14\text{ V}$$

Fe³⁺ has the higher reduction potential → cathode.

$$E^\circ_{cell} = 0.77 - (-0.14) = 0.91\text{ V}$$

Positive. The reaction is thermodynamically favored.

3. From Cell Potential to Spontaneity and ΔG°

Voltage is directly tied to free energy:

$$\Delta G^\circ = -nF E^\circ_{cell}$$

Where:

• n = moles of electrons transferred
• F = 96,485 C/mol e⁻
• E°cell in volts
• ΔG° in joules

This equation explains the sign relationship:

If voltage is positive, free energy decreases. That’s why the reaction runs.

Determining n (Common AP Trap)

• n comes from the balanced overall reaction
• It is the total electrons transferred
• You must balance electrons before finding n

If one half-reaction transfers 1 e⁻ and the other 2 e⁻, you scale them to match. That changes n, but never the E° values.

On FRQs, students often multiply E° after scaling. That always loses points.

4. Big-Picture Connections

Electrochemistry is thermodynamics in action.

• Galvanic cell → chemical energy → electrical energy
• Electrolytic cell → electrical energy forces a nonspontaneous reaction

If you can:

• Identify oxidation and reduction
• Calculate E°cell correctly
• Determine its sign
• Connect that sign to ΔG°

then you can explain whether a cell is thermodynamically favored in any AP-style question.