• 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