Question

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 18.0 kg of chromium onto the cathode if the current passed through the cell is held constant at 45.0 a ? assume the chromium in the electrolytic solution is present as cr3+ .

Answer 1

The chromium in the electrolytic solution is present as cr³⁺ will take 6.19 hours  will it take to plate 18.0 kg of chromium onto the cathode if the current passed through the cell is held constant at 45.0 A.

It is given that mass is 18 kg. Converting mass into grams

18 x (1000g / 1 kg)

= 18000 g

So, 18 kg = 18000 g

Now, calculate the number of moles

No. of moles = mass of Cr / molecular mass of Cr

No. of moles = 18000 / 52 g/mole

No. of moles = 346.15 mole

For , Cr³⁺, 3 moles of electrons are required

Hence,

3 x 346.15 mole

1038.45

As 96500 C of charge are present in 1 mole of electrons. As a result, the charge held by 1038.45 mole of electrons will be determined as follows.

= 1038.45mol x  96500 C / mole

= 10.02 x 10⁷ C

As, we know that relation between charge, current and time is as follows.

Q = I x T

Current is given as 45 A

Therefore, charge is calculated  

T = Q / I

T = 100.21 x 10⁶ / 45

T = 2.227 x 10⁶

As there are 3600 seconds in one 1 hour. Converting 2.227 x 10⁶ into hours are

= 2.227 x 10⁶ / 3600 sec/h

= 6.19 hours

Thus, if the current flowing through the cell is maintained constant at 45 A, we may estimate that it will take 6.19 hours to plate 18 kg of chromium onto the cathode.

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