How long must a constant current of 50.0 A be passed through an electrolytic cell containing aqueous Cu2+ ions to produce 4.00 moles of copper metal?
4.29
It takes 96,485 coulombs of electricity to plate (deposit) 1/2 mole copper metal. Use that information to calculate coulombs. Then amperes x seconds = coulombs.
2.5
To determine the time required to produce a certain amount of copper metal in an electrolytic cell, you need to use Faraday's law of electrolysis.
Faraday's law states that the amount of substance (in moles) produced or consumed at an electrode is directly proportional to the quantity of electric charge (in coulombs) that passes through the cell. The relationship can be expressed as:
n = Q/F
where:
n is the amount of substance produced or consumed (in moles)
Q is the electric charge (in coulombs)
F is Faraday's constant, which represents the charge of one mole of electrons and is equal to 96,485 coulombs/mol
In this case, you are given the amount of substance to be produced (4.00 moles of copper metal) and the current passing through the cell (50.0 A). You need to calculate the electric charge (Q) required to produce this amount of copper.
First, calculate the number of coulombs needed using the formula:
Q = n * F
Q = 4.00 mol * 96,485 C/mol
Q = 385,940 C
Now that we know the amount of charge needed, we can calculate the time by using the equation:
t = Q/I
where:
t is the time (in seconds)
Q is the electric charge (in coulombs)
I is the current (in amperes)
t = 385,940 C / 50.0 A
t ≈ 7718.8 seconds
Therefore, a constant current of 50.0 A must be passed through the electrolytic cell for approximately 7718.8 seconds to produce 4.00 moles of copper metal.