A technician wants to electroplate 5.8g of gold onto a ring by immersing it in a solution of AuCl3(aq) and using a power source that supplies 5.15 A of current. For what length of time in minutes, should the cell be allowed to operate?

Answer 1

To determine the length of time in minutes, the technician should operate the cell, we need to calculate the amount of charge required for the electroplating process.

1. Calculate the number of moles of gold using its molar mass (Au = 196.97 g/mol):
Number of moles of gold = mass of gold / molar mass
= 5.8 g / 196.97 g/mol

2. Since we have one mole of gold ions (Au³⁺) for every three moles of gold (Au), we need to calculate the number of moles of gold ions:
Number of moles of gold ions = (number of moles of gold) / 3

3. Next, calculate the number of electrons transferred during the electroplating process. Each gold ion (Au³⁺) gains three electrons (3e⁻):
Number of electrons transferred = (number of moles of gold ions) × (3e⁻/1mol)

4. Calculate the amount of charge required using Faraday's constant (F = 96485 C/mol):
Amount of charge required = (number of electrons transferred) × (F C/1mol)

5. Finally, calculate the time required (t) using the equation:
Amount of charge = current × time
time = (Amount of charge required) / (current)

Let's calculate the time in minutes:

1. Calculate the number of moles of gold:
Number of moles of gold = 5.8 g / 196.97 g/mol = 0.0294 mol

2. Calculate the number of moles of gold ions:
Number of moles of gold ions = 0.0294 mol / 3 = 0.0098 mol

3. Calculate the number of electrons transferred:
Number of electrons transferred = 0.0098 mol × 3e⁻/1mol = 0.0294 mol e⁻

4. Calculate the amount of charge required:
Amount of charge required = 0.0294 mol e⁻ × 96485 C/mol = 2834.289 C

5. Calculate the time required:
time = 2834.289 C / 5.15 A = 550.7 s

To convert the time to minutes, divide by 60:
time in minutes = 550.7 s / 60 = 9.18 minutes (rounded to two decimal places)

Therefore, the cell should be allowed to operate for approximately 9.18 minutes in order to electroplate 5.8g of gold onto the ring.