Chromium metal is electroplated from acidic aqueous solutions containing the dichromate ion, Cr₂O₇²^-. What is the minimum time needed to plate out 10.0 g of chromium metal from such a solution, if the current is 50.0 A?

Question

Quizplus · Accepted Answer

First, we need to determine the amount of charge needed to plate out 10.0 g of chromium.

Molar mass of chromium = 52 g/mol 
10.0 g of chromium is equivalent to 10.0/52 = 0.192 moles of chromium.

1 mol of electrons = 96485 C 
Therefore, the amount of electrons needed to plate out 0.192 moles of chromium = 0.192 x 3 x 96485 = 55,582 C

Now, we can use Faraday's law of electrolysis to calculate the time needed:

mass of metal (g) = (current (A) x time (s) x atomic weight (g/mol)) / (charge (C))

Rearranging the formula: 
time (s) = (mass of metal (g) x charge (C)) / (current (A) x atomic weight (g/mol))

Plugging in the values: 
time (s) = (10.0 x 55,582) / (50.0 x 52) = 190.2 s

Converting to minutes: 
time (min) = 190.2 / 60 = 3.17 minutes

Therefore, the minimum time needed to plate out 10.0 g of chromium metal is approximately 3.2 minutes or 18.6 minutes (choice C).

Chromium Metal Is Electroplated from Acidic Aqueous Solutions Containing the Dichromate