Quantitative Electrolysis (Faraday's Laws)

Core Concept

Electrolysis obeys exact stoichiometry through electric charge. The charge passed is Q = I × t (current × time, in coulombs). Dividing by the Faraday constant F = 96,485 C/mol e⁻ gives the moles of electrons transferred, and the half-reaction stoichiometry (e.g., Ag⁺ + e⁻ → Ag uses 1 e⁻ per Ag; Cu²⁺ + 2 e⁻ → Cu uses 2) converts moles of electrons to moles of product — and, via molar mass, to grams. These relationships (Faraday's laws) let you predict exactly how much metal plates out, how long to run a current, or what current is needed.

Key Ideas

• Q = I × t. Charge (coulombs) = current (amperes) × time (seconds). 1 A = 1 C/s.
• Faraday constant. One mole of electrons carries 96,485 coulombs.
• n(e⁻) = Q / F. The central conversion from charge to chemical amount.
• Stoichiometry from the half-reaction. Moles of product = moles of electrons ÷ (electrons per product ion).
• Time in seconds. Convert minutes/hours to seconds before multiplying by current.

Equations and Variables

Q = I × t ; n(e⁻) = Q / F

How It Works

1. Compute Q = I × t (with t in seconds).
2. Convert to moles of electrons: n(e⁻) = Q / F.
3. Use the balanced half-reaction to find moles of product per mole of electrons.
4. Multiply by molar mass for grams (or use ideal-gas/volume conversions for gases).
5. Rearrange to solve for time or current if mass is the given quantity.

Worked Example

How many grams of silver plate out when a current of 1.50 A passes through AgNO₃ solution for 25.0 minutes?

• t = 25.0 min × 60 s/min = 1500 s.
• Q = I × t = 1.50 A × 1500 s = 2250 C.
• n(e⁻) = Q / F = 2250 C ÷ 96,485 C/mol = 0.02332 mol e⁻.
• Half-reaction: Ag⁺ + e⁻ → Ag, so 1 mol e⁻ deposits 1 mol Ag.
• n(Ag) = 0.02332 mol; mass = 0.02332 mol × 107.87 g/mol = 2.52 g Ag.

Reverse problem: to deposit 2.52 g Ag in 25 min requires I = (n·F)/t = (0.02332 × 96,485)/1500 = 1.50 A — the same numbers, run backward.

How it works

1. Compute Q = I × t (with t in seconds).
2. Convert to moles of electrons: n(e⁻) = Q / F.
3. Use the balanced half-reaction to find moles of product per mole of electrons.
4. Multiply by molar mass for grams (or use ideal-gas/volume conversions for gases).
5. Rearrange to solve for time or current if mass is the given quantity.

Common confusions

• "Use time in minutes." — Wrong. Q = I × t requires seconds; convert minutes/hours first.
• "F is the gas constant." — Wrong. F = 96,485 C/mol e⁻ (Faraday); R = 8.314 J/(mol·K) (gas).
• "Forgetting the electron stoichiometry." — Wrong. Cu²⁺ needs 2 e⁻ per Cu, Al³⁺ needs 3; the mass per electron differs.
• "Current in milliamps is fine as-is." — Wrong. Convert mA to A (1 A = 1000 mA) before multiplying.
• "Q/F gives moles of product directly." — Wrong. It gives moles of electrons; divide by the half-reaction electron count for moles of product.

Quick review

• Q = I × t (seconds).
• n(e⁻) = Q / F, F = 96,485 C/mol e⁻.
• Moles of product = n(e⁻) ÷ (electrons per formula unit).
• mass = moles × molar mass.
• Solve forward (mass) or backward (time/current) with the same equations.