Question

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 minutes, determine the mass of chromium deposited on the bumper.

Answer 1

The mass of chromium deposited on the bumper when a current of 54 A flows through for 45 minutes is approximately 26.2 g. This is calculated by using Faraday's laws of electrolysis to find the charge passed, converting that charge to moles of chromium, and then converting those moles to mass using the molar mass of chromium.

Step-by-step explanation:

To calculate the mass of chromium deposited on the bumper, we first need to use Faraday's laws of electrolysis which state that the amount of a substance produced at an electrode during electrolysis is proportional to the amount of electricity that is passed through the solution.

Here's the calculation to determine the mass of chromium deposited:

1. Calculate the total charge Q that passed through the solution. Q = current (I) x time (t). Given that the current is 54 A and time is 45 minutes, which needs to be converted to seconds: Q = 54 A x (45 min x 60 sec/min) = 145800 C.
2. Using the given stoichiometry, where 3 moles of electrons are required for the reduction of one mole of chromium ions:
   1 mol Cr requires 3 mol e- x Faraday's constant (96485 C/mol e-).
3. Calculate the number of moles of chromium deposited using the charge Q from step 1 and the charge required to deposit 1 mole of Cr from step 2:
   moles of Cr = Q / (3 x 96485 C/mol).
4. Finally, convert moles of Cr to mass using the molar mass of chromium (approximately 52 g/mol): mass = moles of Cr x 52 g/mol.

Carrying out the calculations:

• Total charge (Q) = 145800 C.
• Moles of Cr = 145800 C / (3 x 96485) ≈ 0.504 mol.
• Mass of Cr = 0.504 mol x 52 g/mol ≈ 26.2 g.

Hence, approximately 26.2 g of chromium is deposited on the bumper.