Electrolysis Quantity Calculations

Electrolysis quantity calculations link the amount of substance deposited or released at an electrode to the number of moles of electrons transferred. At IGCSE level, these calculations use half-equations and stoichiometric ratios rather than Faraday’s constant directly.

The method

1. Write the half-equation for the reaction at the relevant electrode.
2. Identify the mole ratio between electrons and the product.
3. If given the moles of electrons, use the ratio to find moles of product.
4. Convert moles of product to mass (using Mr) or volume (using molar volume for gases).

The formula

From the half-equation, identify:

• How many moles of electrons produce how many moles of product

moles of product = moles of electrons / electrons per mole of product

Then:

• mass = moles x Mr
• volume of gas = moles x 24 dm3 (at RTP)

Worked examples

Example 1: Mass of copper deposited

Question: During the electrolysis of copper(II) sulfate solution, 0.1 mol of electrons was transferred. Calculate the mass of copper deposited. (Ar: Cu = 64)

Working:

• Half-equation: Cu2+ + 2e- -> Cu
• 2 moles of electrons produce 1 mole of Cu
• Moles of Cu = 0.1 / 2 = 0.05 mol
• Mass of Cu = 0.05 x 64 = 3.2 g

Answer: 3.2 g

Examiner note: The half-equation shows Cu2+ needs 2 electrons. This 2:1 ratio is the key step.

Example 2: Volume of chlorine gas produced

Question: During the electrolysis of concentrated sodium chloride solution, 0.04 mol of electrons was transferred at the anode. Calculate the volume of chlorine gas produced at RTP. (Ar: Cl = 35.5)

Working:

• Half-equation: 2Cl- -> Cl2 + 2e-
• 2 moles of electrons produce 1 mole of Cl2
• Moles of Cl2 = 0.04 / 2 = 0.02 mol
• Volume of Cl2 = 0.02 x 24 = 0.48 dm3 (or 480 cm3)

Answer: 0.48 dm3

Examiner note: Chlorine is produced as Cl2 molecules, not individual Cl atoms. The half-equation makes this clear.

Example 3: Mass of silver deposited

Question: 0.06 mol of electrons was passed through silver nitrate solution. Calculate the mass of silver deposited. (Ar: Ag = 108)

Working:

• Half-equation: Ag+ + e- -> Ag
• 1 mole of electrons produces 1 mole of Ag
• Moles of Ag = 0.06 mol
• Mass of Ag = 0.06 x 108 = 6.48 g

Answer: 6.48 g

Examiner note: Silver is Ag+ (charge 1+), so the electron-to-metal ratio is 1:1. This is simpler than Cu2+ examples.

Example 4: Volume of oxygen produced

Question: During the electrolysis of dilute sulfuric acid, 0.2 mol of electrons was transferred at the anode. Calculate the volume of oxygen gas produced at RTP.

Working:

• Half-equation: 4OH- -> 2H2O + O2 + 4e-
• 4 moles of electrons produce 1 mole of O2
• Moles of O2 = 0.2 / 4 = 0.05 mol
• Volume of O2 = 0.05 x 24 = 1.2 dm3

Answer: 1.2 dm3

Examiner note: Oxygen requires 4 electrons per molecule. This is because each oxygen atom needs 2 electrons, and O2 has 2 oxygen atoms.

Example 5: Comparing products at cathode and anode

Question: During the electrolysis of dilute sulfuric acid, 0.2 mol of electrons was transferred. Calculate the volumes of hydrogen (at the cathode) and oxygen (at the anode) produced at RTP.

Working:

• Cathode: 2H+ + 2e- -> H2
  • Moles of H2 = 0.2 / 2 = 0.1 mol
  • Volume of H2 = 0.1 x 24 = 2.4 dm3
• Anode: 4OH- -> 2H2O + O2 + 4e-
  • Moles of O2 = 0.2 / 4 = 0.05 mol
  • Volume of O2 = 0.05 x 24 = 1.2 dm3
• Volume ratio H2 : O2 = 2.4 : 1.2 = 2 : 1

Answer: H2 = 2.4 dm3, O2 = 1.2 dm3 (ratio 2:1)

Examiner note: The 2:1 ratio of hydrogen to oxygen matches the formula of water (H2O). This is a commonly tested relationship.

Common mistakes

1. Using the wrong number of electrons. Always write the half-equation first. The charge on the ion determines how many electrons are involved: Cu2+ needs 2e-, Al3+ needs 3e-, Ag+ needs 1e-.
2. Forgetting that gases form molecules. Chlorine is Cl2 (not Cl), oxygen is O2 (not O), hydrogen is H2 (not H). The half-equation accounts for this.
3. Confusing anode and cathode products. Metals and hydrogen form at the cathode (reduction). Non-metals form at the anode (oxidation).
4. Not converting moles to the required quantity. The question may ask for mass (use Mr) or volume (use molar volume). Check what is being asked.

When this appears

Electrolysis calculations are Extended tier content and appear on Paper 4. They build on moles from mass and gas volume calculations. See the electrochemistry topic for the underlying theory.