How many grams of aluminum can form by passing 305 C through an electrolytic cell containing a molten aluminum salt?

Faraday's laws of electrolysis are fundamental for understanding how the amount of substance formed during electrolysis relates to the electric charge passed through the electrolyte.
Faraday's First Law states that the mass of a substance produced at an electrode during electrolysis is proportional to the quantity of electricity (charge) passed through the electrolyte.

Mathematically, this is represented as:





Faraday's Second Law states that when the same quantity of electricity is passed through different electrolytes, the masses of the different substances produced at the electrodes are proportional to their equivalent weights.
Simply put, Faraday's laws help us calculate how much of a substance will form during electrolysis based on the electric charge and the type of electrochemical reaction.

Electrochemical reactions involve the transfer of electrons between a chemical species. These reactions are crucial in processes like electrolysis, batteries, and corrosion.

In an electrolytic cell, an external source of electrical energy drives a non-spontaneous chemical reaction. The reaction in the problem involves the reduction of aluminum ions (

at the cathode:
\[ Al^{3+} + 3e^- \rightarrow Al \]



This is a reduction reaction where aluminum ions gain electrons to form aluminum metal.
Electrochemical reactions are governed by the principles of charge conservation and stoichiometry, making them predictable and calculable with the right equations.

Molar mass is a fundamental concept in chemistry and is crucial for calculations in electrolysis. It represents the mass of one mole of a given substance and is usually expressed in grams per mole (g/mol).
The molar mass of aluminum (Al) is 26.98 g/mol.


The calculation uses this molar mass in conjunction with Faraday's laws to determine the amount of aluminum formed.
Here, we use Faraday's equation:
\[ m = \frac{Q \times M}{n \times F} \]

where Q is the charge passed (305 C), M is the molar mass of aluminum (26.98 g/mol), n is the number of electrons involved in the reaction (3), and F is Faraday's constant (
C/mol).
By plugging these values into the equation, we can calculate the mass of aluminum formed:
\[ m = \frac{305 \times 26.98}{3 \times 96485} \]
Simplifying this gives:

\[ m \approx 0.028 \text{ g} \]
This mass represents the grams of aluminum produced after passing 305 C of electricity through the electrolytic cell.