Electrolysis and Faraday's Law

Electrolysis is a process in which an electric current is used to cause a chemical reaction. Faraday's laws of electrolysis provide a quantitative relationship between the amount of substance produced or consumed during electrolysis and the amount of electricity passed through the electrolyte.

Faraday's First Law of Electrolysis

Faraday's first law states that the mass of a substance produced or consumed during electrolysis is directly proportional to the quantity of electricity passed through the electrolyte. Mathematically, it can be expressed as:

m = Z * F * Q

where:
m is the mass of substance produced or consumed,
Z is the electrochemical equivalent (the amount of substance produced or consumed per unit of electricity),
F is Faraday's constant (the charge of one mole of electrons, approximately 96,485 C/mol),
Q is the quantity of electricity passed through the electrolyte in coulombs.

Calculating the Quantity of Electricity

To determine the amount of electricity required to produce a given amount of a substance, we must first calculate the quantity of electricity (Q) using Faraday's first law equation:

Q = m / (Z * F)

where:
m is the mass of the substance produced or consumed,
Z is the electrochemical equivalent of the substance.

Calculating the Electrochemical Equivalent

The electrochemical equivalent can be determined experimentally. It represents the amount of substance produced or consumed per unit of electricity passed through the electrolyte. For example, to calculate the electrochemical equivalent of calcium (Ca), we can perform the following steps:

1. Determine the molar mass of calcium (40.08 g/mol).
2. Calculate the number of moles of calcium produced (20.0 g / 40.08 g/mol = 0.499 mol).
3. Using the balanced equation for the electrolysis of molten CaCl2, determine the stoichiometric ratio between calcium and electricity. The equation is:
Ca2+ + 2e- -> Ca
From the equation, we can see that 2 moles of electrons are required to produce 1 mole of calcium.
4. Calculate the electrochemical equivalent of calcium:
Z = 0.499 mol / 2 = 0.2495 mol/C

Calculating the Quantity of Electricity Required

Using the electrochemical equivalent, we can now calculate the quantity of electricity required to produce the given amount of substance. For example:

Q = m / (Z * F)
Q = 20.0 g / (0.2495 mol/C * 96,485 C/mol)
Q ≈ 0.082 C

Therefore, approximately 0.082 coulombs of electricity are required to produce 20.0 grams of calcium from molten CaCl2.

Similarly, the quantity of electricity required to produce 40.0 grams of aluminum (Al) from molten Al2O3 can be calculated using the same steps as outlined above. The electrochemical equivalent of aluminum and the stoichiometric ratio between aluminum and electricity should be determined from the balanced equation for the electrolysis of molten Al2O3.