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Purification of chromium can be achieved by electrorefining chromium from an impure chromium anode onto a pure chromium cathode in an electrolytic cell. How many hours will it take to plate 11.5 kg of chromium onto the cathode if the current passed through the cell is held constant at 38.0 A ? Assume the chromium in the electrolytic solution is present as Cr3+ .

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dsdrajlin

Answer:

468 h

Explanation:

Let's consider the reduction of chromium (III) to chromium that occurs in the electrolytic purification.

Cr³⁺ + 3 e⁻ → Cr

We can establish the following relations.

  • 1 kg = 1,000 g
  • The molar mass of Cr is 52.00 g/mol
  • 1 mole of Cr is deposited when 3 moles of electrons circulate
  • The charge of 1 mole of electrons is 96,468 c (Faraday's constant)
  • 1 A = 1 c/s
  • 1 h = 3,600 s

The hours that will take to plate 11.5 kg of chromium onto the cathode if the current passed through the cell is held constant at 38.0 A is:

[tex]11.5kgCr \times \frac{1,000gCr}{1kgCr} \times \frac{1molCr}{52.00gCr} \times \frac{3mole^{-} }{1molCr} \times \frac{96,468c}{1mole^{-}} \times \frac{1s}{38.0c} \times \frac{1h}{3,600s} = 468 h[/tex]