Electrolysis Calculations

Back to moles! Here are some things to know:

One faraday means one mole of electrons passing around the circuit.
One faraday = 96000 coulombs.
Charge (coulombs) = Current (amps) x Time (seconds)

Example: What mass of copper is deposited on the cathode during the electrolysis of copper (II) sulphate solution if 0.15A flows for 10mins?

The electrode equation is:

Cu²⁺ + 2e^– -> Cu

Calculate the coulombs involved:

10mins x 60 = 600 seconds

Charge = 0.15 x 600 = 90 coulombs

The equation says that 1 mole of copper ions + 2 moles of electrons give 1 mole of copper atoms

1 mole of electrons = 96000 coulombs

2 moles of electrons = 192 000 coulombs

2 moles of electrons (192 000 coulombs) give 1 mole of copper (RFM = 64g), so 90 coulombs give:

(90/192 000) x 64g = 0.03g

(Coulombs worked out/coulombs of electrons) x RFM of element = Mass of element deposited

When involving gases…

Example: During the electrolysis of dilute sulphuric acid, hydrogen is released at the cathode and oxygen at the anode. Calculate the volumes of hydrogen and oxygen produced if 1.0A flows for 20mins

The electrode equations are:

2H⁺+ 2e^– -> H₂

4OH^– -> 2H₂O + O₂ + 4e^–

Assume the molar volume of gas to be 24000 cm³

For hydrogen:

2H⁺+ 2e^– -> H₂

2 hydrogen ions + 2 moles of electrons give 1 mole of hydrogen molecule

20mins x 60 = 1200 seconds

1200 x 1A = 1200 coulombs

2 x 96 000 coulombs (2 moles of electrons) = 192 000 coulombs

1 mole of hydrogen gas = 24000 cm³

192 000 coulombs give 1 mole of hydrogen gas (or 24000 cm³ of hydrogen gas)

So 1200 coulombs give: (1200/192 000) x 24000 = 150 cm³ of hydrogen produced

For oxygen:

4OH^– -> 2H₂O + O₂ + 4e^–

20mins x 60 = 1200 seconds

1200 x 1A = 1200 coulombs

4 moles of hydroxide ions give 2 moles of water + 1 mole of oxygen gas + 4 moles of electrons (4 x 96000 = 384 000 coulombs)

1 mole of oxygen gas = 24000 cm³

384 000 coulombs give 1 mole of oxygen gas (or 24000 cm³ of oxygen gas)

So 1200 coulombs give: (1200/384 000) x 24000 = 75 cm³ of oxygen produced

The equation:

(Calculated coulombs/moles of electrons) x (mole of gas x 24000) = amount of gas produced in cm³