WEBVTT

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This is Giancoli Answers
with Mr. Dychko.

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The specific gravity of
the mixture will be

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the density of the mixture divided by
the density of water

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and the density of the mixture is
the mass of the mixture

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divided by its volume

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and we need to know what these things are

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so we need to know the mass of
the mixture then.

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So the mass of the mixture will be
the mass of the antifreeze solution

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plus the mass of the water that's combined

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and the mass of the antifreeze will be
antifreeze's density

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multiplied by its volume

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and then mass of the water will be
the water's density times its volume.

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And we know the specific gravity of
the antifreeze is 0.80

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so that means the density of antifreeze
divided by density of water is 0.80

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and we can multiply both sides by
density of water and we get

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density of the antifreeze is 0.80
times density of water

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and then we can substitute that here
in the next line.

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So I put 0.80<i>ρ w</i> in place of <i>ρ a</i>

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so the mass of the mixture is 0.80
times density of water times

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the volume of the antifreeze plus

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density of the water times
the volume of the water.

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So then we can factor out
this common factor <i>ρ w</i>

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and we have <i>ρ w</i> times
0.80<i>V a</i> plus <i>V w</i>

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and that is what we'll substitute in for
mass of the mixture

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into this formula on the next line.

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So we have, returning to the very beginning,
where we have

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specific gravity of the mixture,

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density of mixture divided by
density of water

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is the mass of the mixture which
we just figured out here

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divided by the volume of the mixture

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divided by density of water and these
density of water's will cancel

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leaving us with 0.80<i>V a</i>
plus <i>V w</i> over <i>V m</i>.

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And the antifreeze volume is 4.0

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and the water volume is 5.0

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and they combine to make
a mixture volume of 9.0

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and you put all that into your
calculator and you get

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0.91 is the specific gravity of this mixture.