Electrochemistry Formulas: Key Notes

1. Cell Potential Calculation

• Standard Cell Potential Formula:

  E°cell = E°cathode - E°anode
  

• Explanation:
  • Cathode: Location of reduction (gains electrons)
  • Anode: Location of oxidation (loses electrons)
  • Standard reduction potentials must be reversed (change sign) for oxidation reactions at the anode.
• Example:
  • Copper(II) reduction:
    Cu²⁺ + 2e⁻ → Cu(s) E° = +0.34 V (reduction at cathode)
  • Zinc oxidation (reverse of standard reduction):
    Zn(s) → Zn²⁺ + 2e⁻ E° = +0.76 V (oxidation at anode, when reversed from -0.76 V)

2. Oxidation & Reduction

• Oxidation: Loss of electrons (at the anode)
• Reduction: Gain of electrons (at the cathode)

3. Gibbs Free Energy and Cell Potential

• Formula:

  ΔG° = -nFE°cell
  

  • ΔG°: Standard Gibbs free energy change
  • n: Number of electrons exchanged in balanced reaction
  • F: Faraday’s constant = 96,485 C/mol e⁻
  • E°cell: Standard cell potential (in volts)

4. Relationship with Equilibrium Constant (K)

• Formula Linking ΔG° and K:

  ΔG° = -RT ln K
  

• Formula Linking E°cell and K:

  E°cell = (RT / nF) * ln K
  

  • R: Universal gas constant = 8.3145 J/mol·K
  • T: Temperature in Kelvin

5. Calculating K from Cell Potential

• Formula:

  K = exp(nFE°cell / RT)
  

6. Nernst Equation

• Non-Standard Cell Potential (at 25°C):

  Ecell = E°cell - 0.0591/n * log(Q)
  

• General Nernst Equation (any temperature):

  Ecell = E°cell - (RT / nF) * ln(Q)
  

  • Q: Reaction quotient (products/reactants, solids ignored, similar to K)

7. Reaction Quotient, Q

• For reaction: Zn(s) + Cu²⁺(aq) → Zn²⁺(aq) + Cu(s)

  Q = [Zn²⁺] / [Cu²⁺]
  

8. Electroplating & Electrical Quantities

• Faraday's Constant (F): 96,485 C/mol e⁻
• Charge Calculation:

  Q = I × t
  

  • Q: Charge (Coulombs)
  • I: Current (Amperes)
  • t: Time (Seconds)
• Voltage and Work:

  Work = Q × Voltage
  

  • 1 Volt = 1 Joule / 1 Coulomb

9. Voltage (Electric Potential Difference)

• Voltage between two points (A & B): Difference in their electric potentials.
  • Example: If potential at A = 25 V, at B = 10 V, then V_AB = 15 V.

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Summary Table

| Formula | Description | |------------------------------------------------|-------------------------------------------------| | E°cell = E°cathode - E°anode | Standard cell potential | | ΔG° = -nFE°cell | Gibbs free energy from cell potential | | ΔG° = -RT ln K | Gibbs free energy from equilibrium constant | | E°cell = (RT / nF) × ln K | Cell potential in terms of K | | K = exp(nFE°cell / RT) | Find K from cell potential | | Ecell = E°cell - 0.0591/n * log(Q) | Nernst at 25°C | | Ecell = E°cell - (RT / nF) × ln(Q) | General Nernst | | Q = I × t | Charge from current and time | | Work = Q × V | Work from charge and voltage |

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Recommended Resources

• For additional formulas and example problems, check the referenced links and videos in the description.

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Note: These are the key formulas and principles required for typical electrochemistry problems and calculations in academic contexts.