Question

How many minutes will it take to plate out 2.19 g of chromium metal from a solution of Cr3+Cr3+ using a current of 55.2 amps in an electrolyte cell?

Answer 1

Answer : The time it take to plate out will be, 3.69 minutes.

Explanation :

First we have to calculate the moles of Cr.

$\text{Moles of }Cr}=\frac{\text{Mass of Cr}}{\text{Molar mass of Cr}}$

Molar mass of Cr = 51.9 g/mol

$\text{Moles of }Cr}=\frac{2.19g}{51.9g/mol}=0.0423mol$

The cathode half-reaction is,

$Cr^{3+}+3e^-\rightarrow Cr$

From this we conclude that,

The number of electrons (n)  in the reaction are 3.

The quantity of charge required for the reduction of 1 mole of $Cr^{3+}$ = $3\times F$

The quantity of charge required for the reduction of 0.0423 mole of $Cr^{3+}$ = $0.0423\times 3\times F=0.1269F=0.1269\times 96500C=12245.85C$

Now we have to calculate the time taken.

We know that,

$q=I\times t$

$t=\frac{q}{I}=\frac{12245.85C}{55.2A}=221.845s=3.69min$

Thus, the time it take to plate out will be, 3.69 minutes.