2015 AP Chemistry free response 7 | Thermodynamics | Chemistry | Khan Academy

Aluminum metal can be recycled from scrap metal by melting the metal to evaporate impurities. Calculate the amount of heat needed to purify one 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.

All right, so we need to think about the heat needed to raise its temperature from 298 Kelvin to raise the temperature of this one mole of aluminum from 298 Kelvin to 933 Kelvin. We're going to do that by looking at the molar heat capacity, and then we need 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 to raise temperature? Sure. By how much are we raising the temperature? We're going from 298 to 933. So, if you raise by two, you get to 300, and then you have to raise by another 633. So, that's going to be, we're raising our temperature by 635 Kelvin; that's to get us to the melting point.

So, the heat needed to raise the temperature by 635 Kelvin...? Well, we have one mole of aluminum. I can write 1.00 to show that we 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 Kelvin times... So this right over here would be the amount of heat to raise it by one Kelvin. But now, let's multiply by... we have to raise it by 635 Kelvin.

635 Kelvin. The units work out; moles cancel with moles, Kelvin cancels with Kelvin. And then we get to... let me get my calculator out here. So, 24 times 635 is equal to fifteen thousand two hundred forty.

And we're taking the product of a bunch of stuff: three significant figures, two significant figures, three significant figures. So, we should only... we should write only two significant figures, so we'll round to fifteen thousand joules. So, this is going to be 15,000 joules just to raise the temperature to 933 Kelvin.

And then we have the heat of fusion; heat to melt once at melting point... well, that is going to be one mole times the heat of fusion times 10.7 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 joules. But we only have two significant figures here, so we could round that and say 26,000 joules. Or I guess we could write twenty-six kilojoules.

All right, now part B. The equation for the overall process of extracting aluminum from aluminum oxide is shown below.

All right, as shown below, which requires less energy: recycling existing aluminum or extracting aluminum from aluminum oxide? Justify your answer with a calculation.

All right, so this reaction, this reaction right over here... if this is... 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 two moles of aluminum and 1.5 moles of molecular oxygen.

So the equation... the equation for the overall process. So, to extract one mole of aluminum from aluminum oxide requires this much heat. It will produce two moles. So to do one mole, you just have to have half of that, which requires 1,675 kilojoules divided by 2.

So this is going to be 1,675 divided by 2 is equal to... let's see, it's going to be 837.5 kilojoules. Yup, 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 one 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.