Question

Chromium plating can be applied by electrolysis to objects according to the following unbalanced half-reaction:Cr2O72- + e- + H+→ Cr(s) + H2OHow long (in hours) would it take to apply a chromium plating 0.010 mm thick to a car bumper with a surface area of 0.25 m2 in a cell with a current of 25.0 A? The density of chromium is 7.19 g/cm3.

Answer 1

To calculate the time required to apply a chromium plating, we can use Faraday's laws of electrolysis.

Step-by-step explanation:

To calculate the time required to apply a chromium plating of a certain thickness, we need to use Faraday's laws of electrolysis. The formula we can use is:

T = (m/M) × (z/F) × (1/I) × (A/C)

Where:

T is the time in seconds

m is the mass of the deposited substance (in this case, chromium) in grams

M is the molar mass of the deposited substance (in this case, chromium)

z is the number of electrons transferred in the electrochemical reaction (3 in this case)

F is Faraday's constant (96485 C/mol e-)

I is the current in amperes

A is the surface area of the object in square meters

C is the concentration of the plated substance in the electrolyte solution (not given)

Since the concentration is not given, we cannot calculate the exact time. However, we can provide the formula and explain how it is used.

Answer 2

Step-by-step explanation:

The given data is as follows.

Surface area = 0.25
`m^(2)` , current (I) = 25 A

Density = 7.19 g/
`cm^(3)`

As 1 m = 100 cm. Hence, 1
`m^(3)` =
`10^(6) cm^(3)`

So, density =
`7.19 g/cm^(3) * (10^(6) cm^(3))/(1 m^(3))`

As Height = 0.01 mm =
`10^(-2) * 10^(-3)` =
`10^(-5)` m.

It is known that density is mass divided by volume.

Density =
`(mass)/(volume)`

Also, volume = Area × height. Therefore, substituting it into the above formula as follows.

Density =
`(mass)/(volume)`

Density =
`(mass)/(area * height)`

mass =
`7.19 * 10^(6)g/cm^(3) * 0.25 * 10^(-5)m`

= 17.975 g

As number of moles equal mass divided by molar mass of the substance.

So, No. of moles =
`\frac{mass}{\text{molar mass of Cr}}`

=
`\frac{17.975g}{\text{52 g/mol}}`

= 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
`Cr^(3+)` is 579000 C

And, charge for 0.3457 mol of
`Cr^(3+)` is
`0.3457 mol * (579000 C)/(2)` = 100080 C.

Also, Q =
`I * \Delta t`

where, Q = charge

I = current

`\Delta t` = time in seconds

Now, putting the values into above formula as follows.

Q =
`I * \Delta t`

100080 C =
`25 A * \Delta t`

`\Delta t` = 4003.2 sec

Converting seconds into hours as follows.

1 hr = 3600 sec

So,
`4003.2 sec * (1 hr)/(3600 sec)`

= 1.112 hr

Thus, we can conclude that time taken to apply chromium plating is 1.112 hr.