Chromium plating is done using a dichromate solution. How long would it take to plate 1.0x10-2mm thick onto a car bumper with surface area 0.25m^2 in a 25.0 Amp electrolytic cell? (density of chromium is 7.19g/cm^3)
Cr2O7^2- + 14H^+ ==> 2Cr(s) + 12e + 7H2O
The 0.25m^2 is 25 cm x 25 cm x 1.0E-4 cm thick for volume of 0.625 cc but you should confirm that.
mass Cr = 7.19 x 0.625 = estimated 4.5 g.
96,485 coulombs will plate one (1) equivalent weight of Cr which is 52/6 g Cr or about 8.7 g but you should be more accurate. (2 Cr for 12e makes 1 Cr for 6e.)
96,485 x (8.7/4.5) = ? coulombs.
amperes x seconds = coulombs. Substitute and solve for time.
To calculate the time required to plate chromium onto a car bumper, you need to consider the following parameters:
1. Faraday's law: The mass of substance deposited on an electrode during electrolysis is directly proportional to the amount of electricity passed through it. The equation for Faraday's law is:
Mass (grams) = (Current (amps) x Time (seconds) x Molar mass (grams/mol)) / (Faraday's constant (C/mol))
2. Density: The density of chromium is required to convert the mass into volume.
Let's break down the steps to solve this problem:
Step 1: Calculate the mass of chromium required
- The car bumper's surface area is given as 0.25 m^2
- The given thickness is 1.0 x 10^-2 mm, which is equivalent to 1.0 x 10^-5 cm
- Volume = Surface area x Thickness
= 0.25 m^2 x 1.0 x 10^-5 cm
- The density of chromium is given as 7.19 g/cm^3
- Mass = Volume x Density
= (0.25 m^2 x 1.0 x 10^-5 cm) x 7.19 g/cm^3
Step 2: Calculate the time required using Faraday's law
- Current is given as 25.0 Amps
- Molar mass of chromium = 51.996 g/mol
- Faraday's constant = 96485 C/mol (constant for charge conversion)
- Mass (g) = (Current (A) x Time (s) x Molar mass (g/mol)) / Faraday's constant (C/mol)
- Time (s) = (Mass (g) x Faraday's constant (C/mol)) / (Current (A) x Molar mass (g/mol))
Step 3: Substitute the values into the equation and calculate the time
- Time (s) = ((0.25 m^2 x 1.0 x 10^-5 cm) x 7.19 g/cm^3 x 96485 C/mol) / (25.0 A x 51.996 g/mol)
By plugging in the values and performing the calculations, you can find the time required to plate chromium onto the car bumper.