Answer: It will take 425 hours to plate 19.5 kg of copper onto the cathode if the current passed through the cell is held constant at 38.5 A.
Explanation:
The half-reaction equation is as follows.
[tex]Cu^{2+} + 2e^{-} \rightarrow Cu[/tex]
According to the standard values, 1 mole of an electron carries 96500 C. Therefore, charge carried by 2 moles of electrons is [tex]2 \times 96500 C[/tex].
Also, atomic mass of Cu is 63.5 g. According to the equation 2 moles of electrons are depositing 63.5 g of Cu.
Hence, charge required to deposit 19.5 kg (1 kg = 1000 g) or 19500 g of Cu is calculated as follows.
[tex]19500 g Cu \times \frac{2 \times 96500 C}{63.5 g Cu}\\= 5.92 \times 10^{7} C[/tex]
Formula used to calculate time is as follows.
[tex]Q = I \times t[/tex]
where,
Q = charge
I = current
t = time
Substitute the values into above formula as follows.
[tex]5.92 \times 10^{7} C = 38.5 \times t\\t = \frac{5.92 \times 10^{7} C}{38.5}\\= 1.53 \times 10^{6} sec[/tex]
As 1 hour contains 3600 seconds. So, converting seconds into hours as follows.
[tex]1.53 \times 10^{6} sec = 1.53 \times 10^{6} sec \times \frac{1 hr}{3600 sec}\\= 425 hr[/tex]
Thus, we can conclude that it will take 425 hours to plate 19.5 kg of copper onto the cathode if the current passed through the cell is held constant at 38.5 A.
