Understanding Electrolysis
Electrolysis occurs when an electric current passes through a conductive liquid (an electrolyte) containing dissolved ions. The current drives electrons through the circuit, causing oxidation at one electrode (the anode) and reduction at the other (the cathode). This reverses reactions that would normally proceed spontaneously in the opposite direction.
The fundamental unit of charge is the coulomb (C), where one coulomb represents the charge carried by approximately 6.24 × 1018 electrons. When you apply a known current for a measured time, you can calculate the total charge delivered:
- Current is measured in amperes (A), representing charge flow per second
- Time must be consistent (seconds, minutes, or hours)
- Charge (Q) is their product: current multiplied by time
The key insight is that the mass of substance liberated or deposited depends only on the total charge passed and the chemical identity of the electrode material.
Faraday's Law of Electrolysis
Faraday's first law states that the mass deposited or dissolved at an electrode is directly proportional to the charge flowing through the electrolyte. The proportionality constant, known as the electrochemical equivalent, links the charge to mass change.
m = Z × Q
Q = I × t
m— Mass deposited or dissolved at electrode, in kilograms (kg)Z— Electrochemical equivalent (kg per coulomb), specific to each elementQ— Total charge passed through the electrolyte, in coulombs (C)I— Electrical current, in amperes (A)t— Duration of electrolysis, in seconds (s)
The Electrochemical Equivalent Z
The electrochemical equivalent Z is a material-specific constant that describes how much mass transfers per unit of charge. Its value depends on the atomic or molecular weight and the number of electrons involved in the redox reaction.
For common elements used in electroplating and industrial processes:
- Copper (Cu): approximately 3.3 × 10−4 kg/C
- Silver (Ag): approximately 1.1 × 10−4 kg/C
- Zinc (Zn): approximately 3.4 × 10−4 kg/C
- Hydrogen (H₂): approximately 1.0 × 10−5 kg/C
- Oxygen (O₂): approximately 8.3 × 10−6 kg/C
Tables of Z values are widely available in chemistry references. You can also calculate Z if you know the atomic mass and electron stoichiometry of the reaction.
Water Electrolysis Example
Water electrolysis splits H₂O into hydrogen gas at the cathode and oxygen gas at the anode. This process requires careful attention to which gas you are calculating, since hydrogen and oxygen have different electrochemical equivalents.
Suppose you electrolyse water at 2 amperes for 30 minutes (1800 seconds). The charge delivered is:
- Q = 2 A × 1800 s = 3600 C
For hydrogen gas production (Z ≈ 1.04 × 10−5 kg/C):
- mH₂ = 1.04 × 10−5 kg/C × 3600 C ≈ 0.037 kg = 37 grams
For oxygen gas production (Z ≈ 8.29 × 10−6 kg/C):
- mO₂ = 8.29 × 10−6 kg/C × 3600 C ≈ 0.030 kg = 30 grams
The ratio of hydrogen to oxygen produced by mass is approximately 1:8, reflecting their different atomic masses and electron transfer stoichiometry.
Common Pitfalls in Electrolysis Calculations
Avoid these frequent mistakes when applying Faraday's law to your electrolysis problems.
- Confusing current with charge — Current (amperes) and charge (coulombs) are not interchangeable. You must multiply current by time in seconds to get total charge. A 1-amp current for 60 seconds delivers 60 coulombs, not 1 coulomb.
- Using incorrect Z values — Electrochemical equivalents vary with oxidation state and reaction conditions. Always verify the Z value for the specific ion or compound you are electrolyzing. A table for Cu²⁺ is different from one for Cu⁺, for example.
- Unit inconsistencies — Ensure time is in seconds before calculating charge. If your current is in milliamperes or your time is in hours, convert first. Mismatched units will give you answers that are orders of magnitude wrong.
- Forgetting multi-electron transfers — Some ions require multiple electrons per atom to be reduced. The electrochemical constant accounts for this, but if you are deriving Z from atomic mass, you must divide by the number of electrons transferred in the half-reaction.