Galvanic Cells and Thermodynamic Applications

Cell Potential and Free Energy

$\Delta G° = -nFE°_{cell}$

$E°_{cell} = E°_{cathode} - E°_{anode}$

A positive $E°_{cell}$ indicates a spontaneous reaction.

Standard Reduction Potentials

More positive $E°$ → stronger oxidizing agent (more easily reduced) More negative $E°$ → stronger reducing agent (more easily oxidized)

Nernst Equation

$E = E° - \frac{RT}{nF}\ln Q = E° - \frac{0.0592}{n}\log Q \quad \text{(at 25°C)}$

At equilibrium: $E = 0$, $Q = K$: $E° = \frac{0.0592}{n}\log K$

Connecting the Big Three

$\Delta G° = -RT\ln K = -nFE°$

$\ln K = \frac{nFE°}{RT}$

Practical Applications

Batteries

• Primary: Non-rechargeable (alkaline, lithium)
• Secondary: Rechargeable (Li-ion, lead-acid)
• Fuel cells: Continuous fuel supply (hydrogen fuel cell)

Corrosion

Iron rusting: electrochemical process where Fe is oxidized $\text{Fe}(s) \to \text{Fe}^{2+}(aq) + 2e^-$

Prevention: galvanizing (zinc coating), cathodic protection, painting

Electrolysis

Using electrical energy to drive a non-spontaneous reaction $\Delta G > 0 \quad (\text{requires external energy})$

Faraday's Laws: $\text{moles} = \frac{It}{nF}$

where $I$ = current (A), $t$ = time (s)

AP Chemistry Tip: Be comfortable converting between $\Delta G°$, $K$, and $E°$. These three quantities are all interconnected and describe the same thermodynamic reality.