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Electrolysis of molten sodium chloride edited

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- [Instructor] Here's a simplified diagram for the electrolysis of molten Sodium chloride. So, if you melt solid Sodium chloride, you get molten Sodium chloride, so you get Sodium ions, liquid Sodium ions, and you get liquid Chlorine anions, so that's what we have here. We have Sodium ions and chloride anions. Remember, in an electrolytic cell, the negative terminal of the battery delivers electrons. In this case, delivers electrons to the electrode on the right, and when those liquid Sodium ions come in contact with those electrons, we get a reduction half reaction, so let me write this is a reduction, half reaction. Sodium ions gain electrons and are reduced to form liquid Sodium metal, so liquid Sodium metal is one of our products, and this would form at the cathode. Remember, reduction occurs at the cathode. Let me drawn in some liquid Sodium metal here forming on the electrode on the right, forming on the cathode. The other half reaction, right at our other electrode, we know that their battery draws electrons away from this electrode, so oxidation is occurring at this electrodes. This would be the anode. So, liquid chloride anions are oxidized to Chlorine gas. So we lose two electrons, so chloride anions are oxidized to Chlorine gas at the anode, and so we'd have bubbles of Chlorine gas forming at this electrode. This is an important reaction in industry, all right? So to form Sodium metal, this is a good way to do it. How long does it take to produce 1.00 times 10 to the third kilograms of Sodium, so that's a lot of Sodium, with a constant current of 3.00 times 10 to the fourth Amps? So we have another quantitative electrolysis problem here. This one's a little bit harder than the one we did before, but we're gonna start the same way, we're gonna start with the definition of current, so current is equal to charge over time, so Q over t, where charge is in Coulombs and time is in Seconds. So, right now, we know the current is three times 10 to the fourth Amps, so 3.00 times 10 to the fourth is equal to the charge over the time. We want to know the time. We want to know how long it takes to make that much Sodium, so we're trying to find the time. If we could find the charge, then we could find the time using this equation. So let's do that. Let's find the charge, and we know we can start with the mass of Sodium here, so we're given 1.00 times 10 to the third kilograms. We need to get that into grams, so what is 1.00 times 10 to the third kilograms in grams? So, of course, 1.00 times 10 to the sixth grams. Next, we could find the Moles of Sodium that we're trying to produce. So, if we have grams of Sodium, this is grams of Sodium, how do we figure out Moles of Sodium? We could divide by the molar mass, so we divide by the molar mass of Sodium, which is 22.99, and that would be grams per Mole. If we divide by the molar mass, the grams cancel out and we would get Moles of Sodium. Zero times 10 to the sixth. All right, that's how many grams of Sodium we have. If we divide that by 22.99, the molar mass of Sodium, we get 4.35 times 10 to the fourth Moles of Sodium. So how does that help us, right? If we have Moles of Sodium, how does that help us find our charge? Well, we can relate the Moles of Sodium to the Moles of electrons, so let's go back up here to our half-reaction. All right, where we have our Moles of Sodium, so right here, so we're trying to make 4.35 times 10 to the fourth Moles of Sodium. So how many electrons do we need to do that? Well, the Mole ratio is two to two, so you need the same number of Moles of electrons. You need 4.35 times 10 to the fourth Moles of electrons, and that helps us out, so let me go back down here, we have some more room, and let me write down 4.35 times 10 to the fourth, so because of our Mole ratios, we know this is the same number of Moles of electrons that we need. We're trying to find charge. We're trying to find this charge here, and we know we can go from Moles of electrons to the total charge using Faraday's constant. Right, Faraday's constant is the charge carried by one Mole of electrons, and we know that's 96,500, so there's a charge of 96,500 Coulombs for every one Mole of electrons. So if we multiply these together, we'll get charge, 'cause the Moles of electrons will cancel and we will get the charge, so we get 4.20 times 10 to the ninth, that would be Coulombs. That's how much charge we need to make this many Moles of Sodium. All right, so we have the charge, and so now we can plug that back into here and solve for the time, so let's do that. We have 3.00 times 10 to the fourth, that was our current. And current is equal to charge over time, so our total charge is 4.20 times 10 to the ninth, and that's all over the time, so to solve for the time, we just need to divide this number, so let's do that. That's 4.20 times 10 to the ninth. We're going to divide that number by 3.00 times 10 to the fourth, and that should give us our time in seconds. So the time in seconds is 1.40 times 10 to the fifth, so we have our time. I guess we could leave the answer like that, but let's convert that into something that's a little bit easier to comprehend, 38.9 hours. So it would take us 38.9 hours to make. Let's go back up here to remind ourselves how much Sodium, to make 1.00 times 10 to the third kilograms of Sodium. We can also figure out how many liters of Chlorine gas are produced when we make our Sodium. So let's say we are at STP here, so Standard Temperature and Pressure. Remember, standard temperature is zero degrees C, and standard pressure is one atmosphere, so we've already found that we're trying to make 4.35 times 10 to the fourth Moles of Sodium, so how many Moles of Chlorine gas will we make? Well, look at our Mole ratios here. This'd be a two-to-one Mole ratio. So we can set up a proportion, so we could do Sodium to Chlorine, so this would be a two-to-one Mole ratio, so for every two Moles of Sodium that are produced, one Mole of Chlorine gas is produced. So, two over one is equal to 4.35 times 10 to the fourth. That's how many Moles of sodium we were making over x, where x represents the Moles of Chlorine that we would make. So, 2x is equal to 4.35 times 10 to the fourth, so x is equal to 4.35 times 10 to the fourth divided by two, so this would be 21,750 Moles of Chlorine gas that are produced. We're trying to find liters of Chlorine gas that are produced, so one thing we could do to make our lives easy would be to say we know that one Mole of an ideal gas occupies 22.4 liters at STP, so if we have this many Moles, and we assume this is an ideal gas, we could find out how many liters that is by multiplying that number by 22.4, so 21,750 Moles, if we multiply that by 22.4, then we should get the volume in liters, 4.87 times 10 to the fifth liters of Chlorine. So there's another way to do it, if you don't want to take the shortcut, you can actually plug everything into PV is equal to nRT, so you can use "Pivnert." So, PV is equal to nRT. We're at STP, so standard pressure is one atmosphere, and temperature is zero degrees C, or 273.15 Kelvin, so we can plug those in, so our pressure is one atmosphere, our temperature would be 273.15 Kelvin. We're trying to find the volume, we're trying to find liters, so we're trying to find V. "n" would be equal to the number of Moles, all right? So that would be 21,750, so we have 21,750 Moles. R is equal to 0.0821, and I didn't leave room for the units in there, but the units would cancel out to give us liters for the volume, and if you solve this, you will get 4.87 times 10 to the fifth liters, so you can plug it all into "pivnert," or you could use the shortcut way. Either way, you're gonna get the same volume of Chlorine produced.