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aluminum metal can be recycled from scrap metal by melting the metal tube to evaporate impurities calculate the amount of heat needed to purify one mole of aluminum originally at 298 Calvin by melting it the melting point of aluminum is 933 Calvin the molar heat capacity of aluminum is 24 joules per mole Calvin and the heat of fusion of aluminum is 10.7 kilojoules per mole alright so we did think about the heat needed to raise its temperature from 298 Calvin to raise the temperature this one will of aluminum from 298 Calvin to 933 Calvin I'm gonna do that by looking at the molar heat capacity and then we'd add to that the heat of fusion the heat necessary to actually melt it so as to that in steps so heat he needed heat needed to raise temperature sure by how many how many how much we are raising the temperature byron from 298 to 933 to see if you raised by to get to 300 and the injuries by another six hundred and thirty-three that's going to be so we're raising our temperature by 635 Calvin thats to get it to the melting point so the heat needed to raise temperature by 635 Calvin well we have we have one goal one mole of aluminum I can write 1.00 the so that we have two significant did your three significant digits there one more of aluminum times the specific or the molar heat capacity should say so 24 jewels her mole per mole Calvin timed so this right over here to buy the G to raise it by one calvin but now has multiplied by which to raise it by 635 kalin 635 Calvin and the unit's work out lolz canceled with moles Kelvin cancels it cancels Calvin cancels with Calvin and then we get to you let me get my child around here so 24 times 635 is equal to fifteen thousand 240 and are a product of a bunch of stuff three significant figures two significant figures 3 significant figures so we should only we should write only two significant figures will round to fifteen thousand joules this is going to be fifteen fifteen thousand joules just to raise the temperature to 1933 Calvin and then we have the heat heat of fusion heat to melt once at melting point melting sweet well that is going to be one goal one more times the heat of fusion times 10.7% so this is going to give us 10.7 kilojoules or if you want a ride in jewels to this is ten point seven children which is equal to 10,700 jewels and so the total the total is going to be the sum of these so we could say it is 25,700 believe two significant figures here so we could round that and so we could say 26,000 26,000 jewels or you could write 2626 kilojoules right now part be part of the equation for the overall process of extracting aluminum from aluminum oxide is shown below its own low which which requires less energy recycling alloy existing aluminum extracting aluminum from aluminum oxide justify your answer with the calculation alright so this reaction this reaction right over here if and this is this the the heat necessary for a mall of their reactions if you get a mole of aluminum oxide you put in this much heat you're going to get to moles of aluminum and 1.5 goals of molecular oxygen so the equation so question for the overall process so to extract to extract one more one more of aluminum from aluminum oxide requires so this machine will produce two goals so to do one more you said to have half of that requires 1675 kilojoules divided by two so this is going to be 1670 5/2 is equal to see it's going to be 830 7.5 837 point 530 7.5 kilojoules yeah that's happy and i'd for significant digits here and I still have four significant digits extracting doing it from which requires less recycling existing aluminum extracting it well to to recycle one requires we just figured out 26 kilojoules 26 kilojoules everything here is a quote jewels which is much less energy is much less energy and we are done