If a current of 3.00 A is applied to a cell containing a 400g copper anode, determine the final mass of the copper anode after the cell runs for 48.0h

coulombs = amperes x seconds

C = 3.00 x 48hr x (60 min/hr) x (60 s/min) = approx 518,000 C but you need to do that more accurately.

We know that 96,485 coulombs will use 1 equivalent of Cu (1 eq of Cu is 63.54/2 = approx 32 g). So how much Cu is used? That's approx
(63.54/2) x (518,000/96,485) = Cu used. Then Cu left is approx 400g-g Cu used = ?final mass Cu.
Remember to redo the estimates.
The only thing I've not disclosed is how do you know the Cu is being subtracted and not added to the 400 g Cu bar. If it's the anode it must be dissolving and that means subtracting.

To determine the final mass of the copper anode, we need to calculate the amount of copper that is deposited on the cathode during the electrolysis process. The amount of substance (copper) deposited can be calculated using Faraday's laws of electrolysis.

Faraday's first law states that the mass of a substance deposited during electrolysis is directly proportional to the amount of electric charge passed through the cell.

The formula for calculating the amount of substance deposited is given by:

mass = (charge × molar mass) / (Faraday's constant × valency)

In this case, we know the current (I = 3.00 A), time (t = 48.0 h), and the molar mass of copper (Cu) is 63.55 g/mol.

First, let's convert the time from hours to seconds:

48.0 h × 3600 s/h = 172,800 s

Now let's calculate the amount of charge (Q) passed through the cell using the formula:

charge = current × time

Q = 3.00 A × 172,800 s = 518,400 C

Now, let's calculate the amount of substance deposited:

mass = (charge × molar mass) / (Faraday's constant × valency)

The Faraday constant (F) is 96,485 C/mol, and the valency (Z) of copper is 2 because it forms Cu2+ ions in the solution.

mass = (518,400 C × 63.55 g/mol) / (96,485 C/mol × 2)

mass ≈ 169.74 g

Therefore, the final mass of the copper anode after the cell runs for 48.0 hours is approximately 169.74 grams.