Question

(a) How many coulombs are required to plate a layer of chromium metal \(0.25 \mathrm{~mm}\) thick on an auto bumper with a total area of \(0.32 \mathrm{~m}^{2}\) from a solution containing \(\mathrm{CrO}_{4}^{2-}\) ? The density of chromium metal is \(7.20 \mathrm{~g} / \mathrm{cm}^{3} .\) (b) What current flow is required for this electroplating if the bumper is to be plated in \(10.0 \mathrm{~s} ?(\mathrm{c})\) If the external source has an emf of \(+6.0 \mathrm{~V}\) and the electrolytic cell is \(65 \%\) efficient, how much electrical power is expended to electroplate the bumper?

Short answer

The short answer based on the step-by-step solution: a) To find the number of coulombs required, first calculate the mass of chromium needed by finding the volume and using the density. Then, find the number of moles by dividing the mass by the molar mass of chromium and use Faraday's law to find the coulombs required. b) Calculate the required current by dividing the total charge from part (a) by the total time to plate (10.0 s). c) Calculate the power needed for electroplating by first finding the power provided by the external source (Power = Voltage × Current) and then considering the efficiency of the electrolytic cell to find the actual power used in the plating (Actual Power = Power × Efficiency).

Step-by-step solution

a) Find the mass, moles, and coulombs of chromium

First, we'll calculate the mass of chromium needed to plate the bumper. The volume of chromium needed can be calculated by multiplying the thickness by the total plated area. Then, using the density of chromium, we can find the mass of chromium. The volume of chromium needed to plate the bumper: Volume = Total area × Thickness = \(0.32m^2 × 0.00025m\) Convert volume to cm^3 (1m = 100cm): Volume = \(0.32 \times 100 \times 100 \times 0.00025 \times 100 \mathrm{cm}^3\) Mass of chromium = Volume × Density Mass of chromium = Volume × \(7.20 \frac{g}{cm^3}\) Now, we need to find the number of moles of chromium in this mass. The molar mass of chromium \(M_{Cr}\) is approximately 51.996 g/mol. Number of moles = \(\frac{Mass}{M_{Cr}}\) We'll use Faraday's law to find the number of coulombs required. The charge required to deposit one mole of a substance is equal to the product of the number of moles, the charge of electrons, and Faraday's constant \(F\). Coulombs required = Number of moles × Charge × F = Number of moles × 2 × 96485 C

b) Calculate the required current

Now, we need to find the current flow required for this electroplating, given that it should be completed in 10.0 s. Current (I) = \(\frac{Total\,Charge}{Time}\)

c) Calculate the power needed for electroplating

The electrolytic cell is 65% efficient, which means that only 65% of the electrical power provided by the external source is used for the electroplating process. The rest of the power is lost as heat or other forms of energy. The power provided by the external source can be calculated as: Power = Voltage × Current We need to find the actual power used in the plating by considering the efficiency: Actual Power = Power × Efficiency where Efficiency = 0.65. With this solution method, you should be able to solve the exercise and find the required information for each section.