 Let's try this problem now. It's I guess a more difficult Redox problem. It says chromium plating is applied by electrolysis to objects suspended in a dichromate solution according to the following Unbalanced half reaction. So that's pictured up there How long and hours would it take to apply chromium plating? 1.0 times 10 to the negative 2 millimeters thick to a car bumper with a surface area of 0.25 meters squared and an electrolytic cell carrying a current of 25.0 amperes The density of chromium is 7.19 grams per cubic sound. Okay, so I think I've written all the pertinent information up here. I think the Best thing to do, honestly, you can approach this problem from a number of different ways But I think the way I'm going to do it is to figure out the number of moles of chromium that we've got first Okay, so how am I going to do that? Well, I've got an area of chromium and a height of chromium So I can figure out what the volume of chromium is Okay, I'm going to do that in meters. I'm gonna Since this one's in millimeters that one's in meters squared. I'm going to get the volume in meters cube. Okay so 1.0 times 10 to the negative 2 millimeters Let's convert that to meters there. Okay, so one meter 1000 millimeters So Cancel cancel. So that's in meters now. So let's now just multiply 2.25 meters squared That'll give me the volume of chromium in meters meters cube Okay, so now remember One meter equals 100 centimeters We're trying to get to centimeters because I want to figure out well how much grams of chromium are we going to have okay, but One meter cube equals 100 centimeters cubed. Okay, so in order to do that Remember the conversion factor so one meter 100 centimeters, but we're going to cube both of those like that So that'll cancel with that and then when we do this 2.5 centimeters Okay, so that's how much chromium Need to electro plate the whole bumper. So well, what's the density of chromium we've got? So what would be that the mass of that chromium? In fact, let's go so far as to say well, we need a number of moles of the chrome Okay, so for a number of moles of chromium We can get the mass directly or we're going to need the molar mass of chromium Get that from the periodic table. So what is that over there? 0.00 Chromium so let's go all the way to moles Chromium 7.19 grams of chromium 52.50 grams chromium one mole Cancel Cancel cancel We're going to get over here number of moles of chromium kind of by 52 We'll keep it to 0.35 moles of chromium Anybody follow me to there? So I'm going to erase this at least this top part here and the next thing we're going to do So like I said, we could have approached this problem from a number of different ways The other way we could do it to start with balancing that half reaction, but now we're going to actually Balance the half reaction in the second step. So you like I said, you could have done it Like it's there actually imbalanced so if you didn't catch that you're not going to get this problem correct Okay, so we've got to balance it So how do we balance a reaction equation? Well Is this going to be a reduction or an oxidation? Can you guys tell? It's a reduction. Yeah Reduction right? Why? Because there's a number of reasons, right? It's gaining electrons. That's probably the most obvious But look at the chromium. It's losing oxygen. Okay, so that's another way to check it out Okay, so how do we balance our half reaction? So we're going to first balance the non oxygen non hydrogen atoms Okay, so that's chromium. We've got two over here and then over here. So we're gonna put it to that Okay, so now we see well, we've got seven oxygens over here and only one over here Okay, so what are we going to do? We're gonna multiply that hot water by seven, right? so We've got a seven there now, so we've got seven oxygens there seven oxygens there now we've got 14 hydrogen here and only one Hydrogen on the other side right so we're gonna have to add 13 more Or multiply that by 14 right so now we have 14 here 14 here Oxygens oxygens are balanced chromiums are balanced the only thing that is in balance now is the what? The charges right the electrons so what do we see well? We've got three negatives 14 positives and a zero over on this right, so we're gonna have to add electrons to this side, right? so well minus Our 14 minus 2 is going to be 12 right, so that's how many electrons we're going to have here Okay, so if you want to Re-add it up right 12 negatives plus two negatives is 14 minus right and Plus 14 plus that's going to equals zero, which is what we've got over here. Okay, cool with that Okay, so now it's right. Yes, okay So we can now figure out well What is the number of moles of electrons that have been transferred when? 0.35 moles of chromium get transferred. Okay, so let's figure that out number of moles of electrons We're going to be 0.35 For every two moles Chromium is 12 moles of 21 moles of electrons well so What do we want to know now? Well, how much charge is associated with that number of electrons? Okay, so We've got to go back to the charge per mole of electrons Conversion that'll give you so one mole of electrons equals 96 500 Remember also, we're going to be using this equation I equals Q divided by T. Okay, so amps cool arms divided by time And one coulomb equals one amp second. Okay, so you're going to know all about it. So you should memorize these two so What's the number of coulombs of this number of electrons? It's going to be one mole 2.0 times 10 to the Everybody said So, what are we looking for though? We're looking for time, right? So let's rearrange this equation So when we do that, let's do it over here. So time is going to be cool Coulombs per amp, right? Like that, but this is going to come out in seconds Because remember this over here. So we're going to come we can convert it right away or we can convert it eventually whatever you guys want So I'll just convert it right away. We'll get it in seconds. Okay, so Q point zero Times 10 to the fifth Coulombs and 25.0 amps and one amp second, just one coulomb okay, so Amps cancel, coulombs cancel. So we're going to end up with seconds there So if you wanted to do it, well, let's do it in two steps. Just to make it easier Or you got to so provide that by 25 And we get 8,000 seconds, essentially 8,000 in five seconds 8.0 times 10 to the third second And then say for every hour Because we wanted it now first remember so they wanted it now Cancel cancel like that So divide that by 3600 And to two safe things 2.2 hours So 2.2 hours is the time But it's going to take you to plate your bumper with chrome Any questions on that one? No guys This is a tough problem