5.4.1 Electrolysis: Calculations

• Faraday’s constant can be used to calculate:
  • The mass of a substance deposited at an electrode
  • The volume of gas liberated at an electrode

Calculating the mass of a substance deposited at an electrode

• To calculate the mass of a substance deposited at the electrode, you need to be able to:
  • Write the half-equation at the electrode
  • Determine the number of coulombs needed to form one mole of substance at the specific electrode using Faraday’s constant
  • Calculate the charge transferred during electrolysis
  • Use simple proportion and the relative atomic mass of the substance to find its mass

Worked example: Calculating the mass of a substance deposited at an electrode

Answer

The magnesium (Mg²⁺) ion is a positively charged cation that will move towards the cathode.

• Step 1: Write the half-equation at the cathode

Mg²⁺(aq)          +          2e^-       →         Mg(s)

1 mol                           2 mol               1 mol

• Step 2: Determine the number of coulombs required to deposit one mole of magnesium at the cathode

For every one mole of electrons, the number of coulombs needed is 96 500 C mol^-1

In this case, there are two moles of electrons required

So, the number of coulombs needed is:

F = 2 x 96 500

F = 193 000 C mol^-1

• Step 3: Calculate the charge transferred during the electrolysis

Q = I x t

Q = 2.20 x (60 x 15)

= 1980 C 

• Step 4: Calculate the mass of magnesium deposited by simple proportion using the relative atomic mass of Mg

Calculating the mass of a substance deposited at an electrode table

Therefore, 0.25 g of magnesium is deposited at the cathode

Calculating the volume of gas liberated at an electrode

• To calculate the volume of gas liberated at an electrode, you need to be able to:
  • Write the half-equation at the electrode
  • Determine the number of coulombs needed to form one mole of substance at the specific electrode using Faraday’s constant
  • Calculate the charge transferred during electrolysis
  • Use simple proportion and the relationship 1 mol of gas occupies 24.0 dm³ at room temperature

Worked example: Calculating the volume of a gas produced at an electrode

Answer

The oxygen gas is formed from the oxidation of negatively charged hydroxide (OH^-) ions at the anode-

• Step 1: Write the half-equation at the anode

4OH^-(aq)         →         O₂(g)               +          2H₂O(l)            +          4e^-

4 mol                           1 mol                           2 mol                           4 mol

• Step 2: Determine the number of coulombs required to form one mole of oxygen gas at the anode

For every one mole of electrons, the number of coulombs needed is 96 500 C mol^-1

So, for four moles of electrons, the number of coulombs needed is:

F = 4 x 96 500

F = 386 000 C mol^-1

• Step 3: Calculate the charge transferred during the electrolysis

Q = I x t

Q = 0.75 x (60 x 35)

= 1575 C

• Step 4: Calculate the volume of oxygen liberated by simple proportion using the relationship 1 mol of gas occupies 24.0 dm³ at room temperature

Calculating the volume of a gas liberated at an electrode table

Therefore, 0.0979 dm³  of oxygen is formed at the anode

Worked example: Calculating the volume of hydrogen gas produced at an electrode

The hydrogen gas is formed from the reduction of positively charged hydrogen (H⁺) ions at the cathode

• Step 1: Write the half-equation at the cathode

2H⁺ (aq)   +     2e^-       →         H₂ (g)              

2 mols             2 mols             1 mol   

• Step 2: Determine the number of coulombs required to form one mole of hydrogen gas at the cathode

For every one mole of electrons, the number of coulombs needed is:

F = 96 500 C mol^-1

F = 1 x 96 500

F = 96 500 C

So, for two moles of electrons, the number of coulombs needed is:

F = 2 x 96 500

F = 193 000 C

•  Step 3: Calculate the charge transferred during the electrolysis

Q = I x t

Q = 3.25 x (60 x 17.5)

= 3 413 C

• Step 4: Calculate the volume of hydrogen liberated by simple proportion using the relationship 1 mol of gas occupies 24.0 dm³ at room temperature

Calculating the volume of hydrogen gas produced at an electrode table

Therefore, 0.42 dm³ of hydrogen is formed at the cathode