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# 2015 AP Chemistry free response 7

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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