Final answer:
It will take approximately 530.03 hours to plate 18.0 kg of nickel onto the cathode using a constant current of 31.0 A.
Step-by-step explanation:
To calculate how many hours it will take to plate 18.0 kg of nickel onto the cathode with a current of 31.0 A, we must first convert the mass of nickel to moles using its molar mass. Nickel has a molar mass of 58.69 g/mol. Using Faraday's laws of electrolysis, we can relate the charge passed through the cell to the amount of nickel deposited. The reaction for nickel plating can be written as Ni2+ + 2e- → Ni(s), indicating that two moles of electrons are required to deposit one mole of nickel.
First, we convert the mass of nickel to moles:
18000 g Ni * (1 mol Ni / 58.69 g Ni) = 306.65 mol Ni
Next, we calculate the total charge needed, knowing that 1 mole of electrons corresponds to 1 Faraday = 96485 C:
306.65 mol Ni * (2 mol e- / 1 mol Ni) * 96485 C/mol = 59150695 C
Finally, we use the current (I) to calculate the time (t) needed:
t = total charge / current = 59150695 C / 31.0 A = 1908093 s
Now convert seconds to hours:
1908093 s * (1 hour / 3600 s) ≈ 530.03 hours
Therefore, it will take approximately 530.03 hours to plate 18.0 kg of nickel onto the cathode.