A car bumper is plated with chromium using chromium(III) ions in solution. If a current of 54 A flows in the cell for 45 min 30 s, determine the mass of chronium deposited on the bumper.
amperes x seconds = coulombs
1 coulomb will plate 1 equivalent weight of Cr.
1 equivalent weight Cr = atomic mass/change in # electrons for the half cell for Cr.
To determine the mass of chromium deposited on the bumper, we need to use Faraday's law of electrolysis. This law relates the amount of substance deposited or liberated during electrolysis to the electric current flowing through the cell and the time of electrolysis.
Faraday's law states that the mass of a substance deposited or liberated during electrolysis is directly proportional to the charge passed through the cell. The equation for Faraday's law is:
m = (Q * M) / (z * F)
Where:
m is the mass of the substance deposited in grams.
Q is the charge passed in coulombs.
M is the molar mass of the substance in grams per mole.
z is the number of moles of electrons transferred per mole of substance.
F is the Faraday constant, approximately 96,485 coulombs per mole.
In this case, we need to find the mass of chromium (Cr) deposited on the bumper.
First, let's calculate the charge passed (Q) using the formula:
Q = I * t
Where:
I is the electric current in amperes (A).
t is the time of electrolysis in seconds (s).
Given:
I = 54 A
t = 45 min 30 s = 45 * 60 + 30 = 2,730 s
Substituting the values into the formula:
Q = 54 A * 2,730 s
Q = 146,820 C
Next, we need to determine the molar mass of chromium (M) from the periodic table. The molar mass of chromium is approximately 52 g/mol.
Now, we need to find the number of moles of electrons transferred per mole of chromium (z). For chromium(III) ions, each ion gains three electrons during reduction, so z = 3.
Finally, we substitute the values into Faraday's law equation:
m = (Q * M) / (z * F)
m = (146,820 C * 52 g/mol) / (3 * 96,485 C/mol)
m ≈ 41.2 g
Therefore, the mass of chromium deposited on the bumper is approximately 41.2 grams.