Respuesta :
Explanation:
It is given that mass is 11 kg. Convert mass into grams as follows.
[tex]11 kg \times \frac{1000 g}{1 kg}[/tex]
= 11000 g (as 1 kg = 1000 g)
Now, calculate the number of moles as follows.
No. of moles = [tex]\frac{\text{Mass of Cr}}{\text{Molar mass of Cr}}[/tex]
= [tex]\frac{11000 g}{52 g/mol}[/tex]
= 211.54 mol
For [tex]Cr^{3+}[/tex], 3 moles of electrons are required
Hence, [tex]3 \times 211.54 mol[/tex]
= 634.62 mol
As 1 mol of electrons contain 96500 C of charge. Therefore, charge carried by 634.62 mol of electrons will be calculated as follows.
Q = [tex]634.62 mol \times 96500 C/mol [/tex]
= [tex]61.24 \times 10^{6} C[/tex] of charge
We know that relation between charge, current and time is as follows.
Q = [tex]I \times t[/tex]
Current is given as 41.5 A and charge is calculated as [tex]61.24 \times 10^{6} C[/tex]. Therefore, calculate the time as follows.
Q = [tex]I \times t[/tex]
[tex]61.24 \times 10^{6} C = 41.5 A \times t[/tex]
t = [tex]1.47 \times 10^{6} sec[/tex]
As there are 3600 seconds in one 1 hour. Therefore, converting [tex]1.47 \times 10^{6} sec[/tex] into hours as follows.
[tex]\frac{1.47 \times 10^{6} sec}{3600 sec/hr}[/tex]
= 4.09 hr
Thus, we can conclude that it takes 4.09 hours to plate 11.0 kg of chromium onto the cathode if the current passed through the cell is held constant at 41.5 A.
