Electrochemistry Formulas
Reference for electrochemistry formulas: cell potential, Nernst equation, Gibbs free energy, and Faraday's laws for electrolysis and battery design.
The Formulas
Cell Potential: E°cell = E°cathode - E°anode
Gibbs Energy: ΔG° = -nFE°cell
Nernst Equation: E = E° - (RT / nF) × ln(Q)
Faraday's Law: m = (M × I × t) / (n × F)
Gibbs Energy: ΔG° = -nFE°cell
Nernst Equation: E = E° - (RT / nF) × ln(Q)
Faraday's Law: m = (M × I × t) / (n × F)
Electrochemistry connects electrical energy with chemical reactions. These formulas are essential for understanding batteries, corrosion, electrolysis, and fuel cells.
Variables
| Symbol | Meaning | Unit |
|---|---|---|
| E°cell | Standard cell potential | Volts (V) |
| ΔG° | Standard Gibbs free energy change | Joules (J) |
| n | Moles of electrons transferred | mol |
| F | Faraday's constant (96,485 C/mol) | C/mol |
| R | Gas constant (8.314 J/mol·K) | J/(mol·K) |
| T | Temperature | Kelvin (K) |
| Q | Reaction quotient | (unitless) |
| m | Mass deposited at electrode | grams (g) |
| M | Molar mass | g/mol |
| I | Current | Amperes (A) |
| t | Time | Seconds (s) |
Example 1
A zinc-copper cell: E°(Cu²⁺/Cu) = +0.34 V, E°(Zn²⁺/Zn) = -0.76 V
E°cell = E°cathode - E°anode = 0.34 - (-0.76)
= 1.10 V
Example 2
How much copper is deposited by 2 A for 1 hour? (Cu²⁺ + 2e⁻ → Cu, M = 63.55)
t = 3600 s, n = 2, F = 96,485
m = (63.55 × 2 × 3600) / (2 × 96,485)
= 2.37 g of copper
When to Use Them
Use electrochemistry formulas when:
- Calculating battery voltage and capacity
- Designing electrolysis processes (electroplating, metal refining)
- Predicting whether an electrochemical reaction is spontaneous
- Analyzing corrosion rates and prevention strategies
Key Notes
- Cell potential: E°_cell = E°_cathode − E°_anode: The standard electrode potentials are always tabulated as reduction potentials. Subtract the anode value (where oxidation occurs) from the cathode value. A positive E°_cell means the reaction is spontaneous.
- Gibbs energy connection: ΔG° = −nFE°: n is moles of electrons transferred; F = 96,485 C/mol (Faraday's constant). Positive E° → negative ΔG° → spontaneous. This links thermodynamics directly to electrochemistry.
- Faraday's law of electrolysis: Moles of substance deposited = Q / (nF) where Q is total charge in coulombs. To deposit 1 mol of copper (n=2), you need 2 × 96,485 = 192,970 coulombs of charge.
- Non-standard conditions — Nernst equation: E = E° − (RT/nF) ln Q. At 25°C: E = E° − (0.05916/n) log Q. Concentrations change the actual cell voltage from the standard value.
- Applications: Electrochemistry underpins rechargeable batteries (Li-ion, lead-acid), fuel cells, electroplating (chrome, gold), chlorine production (electrolysis of brine), and corrosion protection (sacrificial anodes, cathodic protection).