AP Chemistry: Electrolysis and Faraday’s Laws

AP Chemistry – Electrolysis and Faraday’s Laws

AP Chemistry: Electrolysis and Faraday’s Laws – Exam-Ready Study Guide

What This Is

Electrolysis is the process of using electricity to drive a nonspontaneous chemical reaction (usually decomposition). Faraday’s Laws quantify how much substance is produced or consumed at an electrode based on the charge passed through the system. This topic matters on the AP exam because it bridges thermodynamics (ΔG > 0 for nonspontaneous reactions), redox chemistry, and stoichiometry—often appearing in FRQs as calculations or experimental design questions. Real-world example: Electroplating (e.g., coating jewelry with gold) relies on electrolysis; the Statue of Liberty’s copper exterior was originally shiny but oxidized over time—electrolysis could theoretically reverse this corrosion.

Key Terms & Concepts

• Electrolysis: A nonspontaneous redox reaction driven by an external electrical current. Occurs in an electrolytic cell (vs. a galvanic/voltaic cell, which is spontaneous).
• Electrolytic cell: Contains two electrodes (anode = oxidation, cathode = reduction), an electrolyte, and an external power source (battery).
• Faraday’s First Law: The mass of a substance produced or consumed at an electrode is directly proportional to the charge (Q) passed through the cell.
• Formula: m = (Q · M) / (n · F)
  • m = mass (g)
  • Q = charge (Coulombs, C)
  • M = molar mass (g/mol)
  • n = moles of electrons transferred (from half-reaction)
  • F = Faraday’s constant (96,485 C/mol e⁻)
• Faraday’s Second Law: The masses of different substances produced by the same charge are proportional to their equivalent weights (molar mass / n).
• Current (I): Charge per time (I = Q/t), measured in Amperes (A = C/s).
• Coulomb (C): Unit of charge; 1 C = 1 A · 1 s.
• Overpotential: Extra voltage needed beyond the theoretical value to drive a reaction (due to kinetic barriers; not tested quantitatively on AP but may appear in qualitative questions).
• Inert electrode: Doesn’t participate in the reaction (e.g., Pt, graphite); used when the electrode material isn’t part of the redox process.
• Active electrode: Participates in the reaction (e.g., Cu in Cu²⁺ + 2e⁻ → Cu).
• Standard reduction potential (E°): Used to predict which half-reaction occurs at each electrode (but electrolysis overrides spontaneity—the power source forces the reaction).
• Electroplating: Coating an object with a metal layer via electrolysis (e.g., silver-plating utensils).

Step-by-Step: Solving Electrolysis Problems

Problem type: "How much metal is plated if X amps flow for Y minutes?"

1. Write the half-reaction for the electrode of interest (e.g., Ag⁺ + e⁻ → Ag).
2. Calculate total charge (Q):
3. Use Q = I · t (convert time to seconds if in minutes/hours).
4. Convert charge to moles of electrons:
5. Use moles e⁻ = Q / F (Faraday’s constant = 96,485 C/mol e⁻).
6. Use stoichiometry to find moles of product:
7. Relate moles of e⁻ to moles of substance (e.g., 1 mol Ag⁺ requires 1 mol e⁻).
8. Convert moles to mass:
9. Use m = n · M (molar mass).
10. Check units and sig figs (AP graders deduct for missing units!).

Example:
How much copper is plated if 2.5 A flows for 30 minutes in a Cu²⁺ solution? 1. Half-reaction: Cu²⁺ + 2e⁻ → Cu.
2. Q = (2.5 A)(30 min × 60 s/min) = 4,500 C.
3. Moles e⁻ = 4,500 C / 96,485 C/mol = 0.0466 mol e⁻.
4. Moles Cu = 0.0466 mol e⁻ × (1 mol Cu / 2 mol e⁻) = 0.0233 mol Cu.
5. Mass Cu = 0.0233 mol × 63.55 g/mol = 1.48 g Cu.

Common Mistakes

• Mistake: Forgetting to convert time to seconds in Q = I · t.

• Correction: Always use seconds for time (e.g., 30 min = 1,800 s). AP loves to test unit conversions!

• Mistake: Mixing up anode/cathode in electrolytic vs. galvanic cells.

• Correction:

  
  
  • Electrolytic cell: Anode = positive (oxidation), cathode = negative (reduction).
  • Galvanic cell: Anode = negative, cathode = positive.
  • Why? The power source forces electrons to flow opposite to spontaneity.

• Mistake: Using the wrong n (moles of e⁻) in Faraday’s Law.

• Correction: Check the half-reaction! For Al³⁺ + 3e⁻ → Al, n = 3.

• Mistake: Assuming the standard reduction potential (E°) determines the reaction in electrolysis.

• Correction: The power source overrides E°—the most easily oxidized/reduced species may not react if the voltage is too low. AP tests this qualitatively (e.g., "Why might Cl₂ form instead of O₂ at the anode?").

• Mistake: Ignoring overpotential in qualitative questions.

• Correction: If asked why a reaction occurs despite unfavorable E°, mention kinetic factors (e.g., O₂ has a high overpotential, so Cl₂ forms instead in brine electrolysis).

AP Exam Insights

1. FRQ Hotspot: Electrolysis calculations (Faraday’s Law) appear every 2–3 years in FRQs, often paired with:
2. Stoichiometry (e.g., "What volume of gas is produced at STP?").
3. Thermodynamics (e.g., "Is this reaction spontaneous? How does electrolysis change this?").

4. Experimental design (e.g., "Describe a procedure to plate copper onto a key").

5. Multiple-Choice Traps:

6. Unit errors: Questions give time in minutes but expect seconds.
7. Electrode confusion: "Which electrode gains mass?" (Answer: cathode, where reduction occurs).

8. Half-reaction mix-ups: "How many moles of e⁻ are needed to produce 1 mol of X?" (Check the balanced equation!)

9. Tricky Distinction:

10. Galvanic vs. Electrolytic Cells:
    | Feature | Galvanic Cell | Electrolytic Cell |
    |------------------|-----------------------------|------------------------------|
    | Spontaneity | Spontaneous (ΔG < 0) | Nonspontaneous (ΔG > 0) |
    | Anode | Negative (oxidation) | Positive (oxidation) |
    | Cathode | Positive (reduction) | Negative (reduction) |
    | Energy | Produces electricity | Requires electricity |

11. Qualitative Questions:

12. "Why does water sometimes oxidize instead of the anion?" → Overpotential (O₂ has a high overpotential, so Cl₂ forms in brine).
13. "What happens if the power source is removed?" → The reaction stops (no more driving force).

Quick Check Questions

1. Multiple Choice:
   A current of 5.0 A is passed through a solution of AgNO₃ for 1,930 seconds. What mass of silver is plated at the cathode?
   (A) 5.4 g
   (B) 10.8 g
   (C) 21.6 g
   (D) 43.2 g
   Answer: (B) 10.8 g.
   Explanation: Q = (5.0 A)(1,930 s) = 9,650 C; moles e⁻ = 9,650 / 96,485 = 0.1 mol; moles Ag = 0.1 mol (1:1 ratio); mass = 0.1 × 107.87 g/mol ≈ 10.8 g.

2. Short FRQ:
   An electrolytic cell is used to plate nickel onto a spoon. The half-reaction is Ni²⁺ + 2e⁻ → Ni.
   a) Identify the anode and cathode.
   b) If 0.50 A flows for 2.0 hours, what mass of nickel is plated?
   Answer:
   a) Anode = positive electrode (oxidation of Ni or inert material); cathode = spoon (reduction of Ni²⁺).
   b) Q = (0.50 A)(7,200 s) = 3,600 C; moles e⁻ = 3,600 / 96,485 ≈ 0.0373 mol; moles Ni = 0.0373 / 2 = 0.01865 mol; mass = 0.01865 × 58.69 g/mol ≈ 1.1 g Ni.

3. Multiple Choice:
   In the electrolysis of molten NaCl, which product forms at the anode?
   (A) Na
   (B) Cl₂
   (C) O₂
   (D) H₂
   Answer: (B) Cl₂.
   Explanation: Anode = oxidation; Cl⁻ is oxidized to Cl₂ (O₂ isn’t formed in molten NaCl—no water present).

Last-Minute Cram Sheet

1. Faraday’s Law: m = (Q · M) / (n · F) (Q = I · t).
2. Faraday’s constant (F): 96,485 C/mol e⁻ (≈ 96,500 for quick calculations).
3. 1 A · 1 s = 1 C (current × time = charge).
4. Anode = oxidation = positive in electrolytic cells; cathode = reduction = negative.
5. Electroplating: Metal ions (e.g., Ag⁺, Cu²⁺) are reduced at the cathode to coat an object.
6. Overpotential: Extra voltage needed to drive a reaction (e.g., O₂ has high overpotential, so Cl₂ forms in brine).
7. Inert electrodes: Pt, graphite (don’t react; used for gases like H₂/O₂).
8. Active electrodes: Cu, Ag (participate in the reaction).
9. ⚠️ Time must be in seconds for Q = I · t.
10. ⚠️ Check the half-reaction for n (moles of e⁻)—don’t assume n = 1!