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- [Voiceover] Aluminum metal can be recycled from scrap metal by melting the metal to evaporate impurities. Calculate the amount of head needed to purify 1.00 mole of aluminum originally at 298 kelvin by melting it. The melting point of aluminum is 933 kelvin. The molar heat capacity of aluminum is 24 joules per mole kelvin. And the heat of fusion of aluminum is 10.7 kilojoules per mole. Alright, so we didn't think about the heat they'd need to raise its temperature from 298 kelvin we raise the temperature of this one mole of aluminum from 298 kelvin to 933 kelvin, and we're going to do that by looking at the molar heat capacity. And then we're going to add to that the heat of fusion, the heat necessary to actually melt it. So let's do that in steps, so heat needed heat needed to raise temperature by how much are we raising the temperature by? We went from 298 to 933, so if we raise it by two we get 300 and then you have to raise it by another 633. So that's going to be, so we're raising our temperature by 635 kelvin. That's to get us to the melting point. So the heat needed to raise temperature by 635 kelvin. Well, we have one mole one mole of aluminum I can write 1.00, so we can have two significant digits, or three significant digits there. One mole of aluminum times the specific or the molar heat capacity I should say. So 24 joules per mole per mole kelvin times, so this right over here would be the amount of heat to raise it by one kelvin but now lets multiply by, we have to raise it by 635 kelvin 635 kelvin And the units work out, moles cancel with moles. Kelvin cancels with kelvin, and then we get to let's see let me get my calculator out here. So 24 times 635 is equal to 15,240. and we're taking the product of a bunch of stuff three significant figures, two significant figures three significant figures, so we should write only two significant figures we'll round to 15,000 joules. So this is going to be 15,000 joules temperature to 933 kelvin. And then we have the heat of fusion heat to melt once at melting point. Melting point. Well that is going to be 1.00 mole 1.00 mole times the heat of fusion. times 10.7 kilojoules kilojoules per mole. So this is going to give us 10.7 kilojoules or if we want to write it in joules, so this is 10.7 kilojoules which is equal to 10,700 joules. And so the total is going to be the sum of these so we could say it is 25,700, but we only have two significant figures here so we could round that so we could say 26,000 joules or I guess we could write 26 kilojoules. Alright, now part B. Part B. The equation for the overall process of extracting aluminum from aluminum oxide is shown below, alright? Which requires less energy, recycling existing aluminum or extracting aluminum from aluminum oxide? Justify your answer with a calculation. Alright, so this reaction right over here and this gives us the heat necessary for a mole of the reaction, so if you get a mole of aluminum oxide you put in this much heat, you're going to get 2.00 moles of aluminum and 1.5 moles of molecular oxygen. So the equation for the overall so to extract 1.00 mole 1.00 mole of aluminum from aluminum oxide requires so this much heat will produce 2.00 moles. So to do 1.00 mole you just have to have half of that. Requires 1,675 kilojoules divided by two. So this is going to be 1,675 divided by two is equal to, let's see it's going to be 837.5. 837.5 837.5 kilojoules, yep that's half here. and I had four significant digits here and I still have four significant digits. Extracting, doing it from, which requires less recycling existing aluminum or extracting it? Well to recycle 1.00 mole requires we just figured out, 26 kilojoules. 26 kilojoules. Everything here is in kilojoules, which is much less energy. Which is much less energy. And we are done.