The basic reaction occurring in the cell in which Al₂O₃ and aluminum salts are electrolyzed is Al³⁺ + 3 e⁻ → Al(s). If the cell operates at 5.0 V and 1.0 x 10⁵ amps, and you want to produce 600 pounds of aluminum metal (2.7 x 10⁵ g), how many hours will you need to operate the cell?
To find the number of hours needed to operate the cell to produce a certain amount of aluminum, we need to calculate the total amount of charge required for the given quantity of aluminum and then use the given current to determine the time.
Let's break down the steps:
Step 1: Calculate the moles of aluminum required.
To calculate the moles of aluminum, divide the given mass in grams by the molar mass of aluminum.
Molar mass of aluminum (Al) = 26.98 g/mol
Moles of aluminum = Mass of aluminum / Molar mass of aluminum
Moles of aluminum = 2.7 x 10⁵ g / 26.98 g/mol
Step 2: Calculate the total charge required.
Since we know that 3 moles of electrons are required to produce 1 mole of aluminum, we can calculate the total charge using Faraday's law:
Total charge (Q) = moles of aluminum x Faraday's constant
Faraday's constant (F) = 96,485 C/mol
Total charge (Q) = moles of aluminum x Faraday's constant
Step 3: Calculate the time required.
Using Ohm's law, we can calculate the time required using the given voltage and current:
Q (charge) = I (current) x t (time)
Therefore, t (time) = Q (charge) / I (current)
Now, let's put the values into the equations:
Step 1: Calculate the moles of aluminum required.
Moles of aluminum = 2.7 x 10⁵ g / 26.98 g/mol
Step 2: Calculate the total charge required.
Total charge (Q) = Moles of aluminum x Faraday's constant
Step 3: Calculate the time required.
t (time) = Q (charge) / I (current)
By following these steps, you can calculate the time required to operate the cell and produce the desired amount of aluminum.