Chromium plating is applied by electrolysis to objects...

Chromium plating is applied by electrolysis to objects suspended in a dichromate solution, according to the following (unbalanced) half-reaction: $\mathrm{Cr}_{2} \mathrm{O}_{7}^{2-}(a q)+e^{-}+\mathrm{H}^{+}(a q) \longrightarrow \mathrm{Cr}(s)+\mathrm{H}_{2} \mathrm{O}(l)$ How long (in hours) would it take to apply a chromium plating $1.0 \times 10^{-2} \mathrm{~mm}$ thick to a car bumper with a surface area of $0.25 \mathrm{~m}^{2}$ in an electrolytic cell carrying a current of $25.0 \mathrm{~A} ?$ (The density of chromium is $7.19 \mathrm{~g} / \mathrm{cm}^{3} .$ )

Chromium plating is applied by electrolysis to objects suspended in a dichromate solution, according to the following (unbalanced) half-reaction:
$\mathrm{Cr}_{2} \mathrm{O}_{7}^{2-}(a q)+e^{-}+\mathrm{H}^{+}(a q) \longrightarrow \mathrm{Cr}(s)+\mathrm{H}_{2} \mathrm{O}(l)$
How long (in hours) would it take to apply a chromium plating $1.0 \times 10^{-2} \mathrm{~mm}$ thick to a car bumper with a surface area of $0.25 \mathrm{~m}^{2}$ in an electrolytic cell carrying a current of $25.0 \mathrm{~A} ?$ (The density of chromium is $7.19 \mathrm{~g} / \mathrm{cm}^{3} .$ )

Key Concepts

Density and Volume-to-Mass Conversion

Calculating the mass of metal deposited from a given plating thickness involves converting the thickness and surface area into volume and then using the material’s density to convert this volume to mass. This conversion is essential when determining how much metal needs to be deposited in processes such as chromium plating.

Current-Time Relationship

The relationship between current and time, expressed by the equation Q = I × t (where Q is the charge, I is the current, and t is the time), is fundamental in electrolytic processes. This relationship allows one to calculate the total charge that has passed through the system, which can then be related to the amount of metal deposited using Faraday’s laws.

Electrolysis

Electrolysis is the process of driving a non-spontaneous chemical reaction through the application of an external electric current. In plating, electrolysis is used to deposit a thin layer of metal onto a substrate by reducing metal ions in solution to solid metal on the object's surface.

Faraday’s Laws of Electrolysis

Faraday’s laws relate the amount of substance deposited or dissolved at an electrode to the total electrical charge passed through the electrolyte. The first law states that the mass of the substance altered at an electrode is directly proportional to the quantity of electricity that passes through the electrolyte, providing a crucial link between current, time, and the amount of deposition in plating applications.

Stoichiometry in Electrochemical Reactions

Stoichiometry in electrochemical reactions involves using the balanced chemical equation to relate the moles of electrons transferred to the moles of metal deposited. This stoichiometric relationship is key to determining how much metal is deposited for a given amount of electrical charge, and it often requires balancing complex half-reactions to find the electron-to-metal ratio.

Transcript

00:01 So ultimately, this is mostly just a unit conversion problem for most, which is a little bit of electrolysis.

00:08 And so we want to find the volume of chromium that we're gonna need because that will let us figure out the mass and then the moles of chromium.

00:19 And so to figure that out, we're going to multiply the thickness which it'll call t times the area.

00:30 And so we're after nature, those in the same unit.

00:31 So we have chance that i get a second millimeters.

00:35 But if we want this meters, that's gonna be tense.

00:39 A negative fifth mila tense and i get 50 meters as a thickness and then our area is 0.25 meters squared.

00:48 So you will pump out that the volume are looking for is 2.5 times tense and i just six cubic meters.

00:57 That's how much chromium we're gonna need.

01:00 Now we want to turn this into cubic centimeters because that's where our density is it.

01:04 And so to go from 2.5 times since the negative six meters cubed, you're gonna have to multiply by are, uh yes.

01:13 So for every a meter cube that is equal to 10 to the sixth cubic centimeters.

01:24 No, if you're not comfortable, this issue go to practice these conversions basically because, you know, you would normally do tend to the second for each meter.

01:33 Two centimeter, but they're cubed us heads the six and so nice number.

01:37 Here we get 2.5 cubic centimeters as our volume of, uh, chromium that we're looking for.

01:45 And so now if you want to find the density, you take the 2.5 cubic centimeters of chrome on that we have and multiply it by 7.19 grams her cubic centimeter so you can see those units cancel out, and we will find that we have 17.985 grams.

02:09 Now we want to figure out the amount of moles a problem.

02:11 So he takes 17.985 grams.

02:15 And if i that both of the molecular weight, which is 57 points 99 grams per mole and so thes grams units, cancel out and you're gonna be left with 0.345 moles of chromium.

02:33 And now we're finally to the charles is part...

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