A car bumper is plated with chromium using chromium (III) ions in solution. If a current of 53.2 A flows in the cell for 49 minutes and 40 seconds, determine the mass of chromium deposited on the bumper. (Value: 5 pts)
To calculate the mass of chromium deposited on the bumper, we can use Faraday's law of electrolysis, which states that the mass of a substance deposited during electrolysis is directly proportional to the charge passed through the cell.
The formula to calculate the mass of a substance deposited is:
mass = (charge × molar mass) / (Faraday's constant × number of electrons)
First, we need to calculate the charge passed through the cell. We can use the formula:
charge = current × time
Since the current is given as 53.2 A and the time is 49 minutes and 40 seconds, we need to convert the time to seconds:
time = 49 minutes + 40 seconds = 49 × 60 + 40 = 2980 seconds
Now we can calculate the charge passed through the cell:
charge = 53.2 A × 2980 s = 158,896 C
Next, we need to calculate the number of moles of chromium deposited. We can use the equation:
moles = charge / (Faraday's constant × number of electrons)
The Faraday's constant is 96,485 C/mol, and in the case of chromium (III) ions, the number of electrons involved in the reaction is 3.
moles = 158,896 C / (96,485 C/mol × 3) = 0.5482 mol
Finally, we can calculate the mass of chromium deposited using the molar mass of chromium, which is 51.9961 g/mol:
mass = 0.5482 mol × 51.9961 g/mol = 28.45 g
Therefore, the mass of chromium deposited on the bumper is 28.45 grams.