Respuesta :
Explanation:
The given data is as follows.
Surface area = 0.25 [tex]m^{2}[/tex] , current (I) = 25 A
Density = 7.19 g/[tex]cm^{3}[/tex]
As 1 m = 100 cm. Hence, 1 [tex]m^{3}[/tex] = [tex]10^{6} cm^{3}[/tex]
So, density = [tex]7.19 g/cm^{3} \times \frac{10^{6} cm^{3}}{1 m^{3}}[/tex]
As Height = 0.01 mm = [tex]10^{-2} \times 10^{-3}[/tex] = [tex]10^{-5}[/tex] m.
It is known that density is mass divided by volume.
Density = [tex]\frac{mass}{volume}[/tex]
Also, volume = Area × height. Therefore, substituting it into the above formula as follows.
Density = [tex]\frac{mass}{volume}[/tex]
Density = [tex]\frac{mass}{area \times height}[/tex]
mass = [tex]7.19 \times 10^{6}g/cm^{3} \times 0.25 \times 10^{-5}m[/tex]
= 17.975 g
As number of moles equal mass divided by molar mass of the substance.
So, No. of moles = [tex]\frac{mass}{\text{molar mass of Cr}}[/tex]
= [tex]\frac{17.975g}{\text{52 g/mol}}[/tex]
= 0.3457 mol
As there is transfer of total 6 electrons and it is known that charge on 1 mole of electron is 96500 C.
Hence, charge on 6 electrons will be as follows.
96500 C × 6 = 579000 C
This means that charge for 2 moles of [tex]Cr^{3+}[/tex] is 579000 C
And, charge for 0.3457 mol of [tex]Cr^{3+}[/tex] is [tex]0.3457 mol \times \frac{579000 C}{2}[/tex] = 100080 C.
Also, Q = [tex]I \times \Delta t[/tex]
where, Q = charge
I = current
[tex]\Delta t[/tex] = time in seconds
Now, putting the values into above formula as follows.
Q = [tex]I \times \Delta t[/tex]
100080 C = [tex]25 A \times \Delta t[/tex]
[tex]\Delta t[/tex] = 4003.2 sec
Converting seconds into hours as follows.
1 hr = 3600 sec
So, [tex]4003.2 sec \times \frac{1 hr}{3600 sec}[/tex]
= 1.112 hr
Thus, we can conclude that time taken to apply chromium plating is 1.112 hr.
