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I think it makes sense to keep
doing a few more problems just

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so you really get intimately
comfortable with PV equals

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nRT, or the ideal
gas equation.

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So we have 98 milliliters
of an unknown gas.

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They say weighs in the problem,
but I'll use mass.

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Its mass is 0.081 grams. You
shouldn't say weighs 0.081

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grams. This is mass.

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Weight would be in newtons if
we're in the metric system at

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standard temperature
and pressure.

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Calculate the molar
mass of the gas.

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So they want to know
the mass per mole.

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So the molar mass, or
the mass per mole.

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Now, we could just substitute
this into PV is equal to nRT.

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We know what standard
temperature and pressure are.

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Standard temperature is
273 degrees Kelvin.

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Standard pressure
is 1 atmosphere.

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And then, of course, they're
giving us 98 milliliters.

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And then you can just solve for
how many moles we have.

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And actually, maybe
I'll do that.

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But the other way to think about
it is that at standard

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temperature and pressure, an
ideal gas-- and we did this

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two videos ago.

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We said 1 mole of an ideal gas
at standard temperature and

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pressure will fill up a
volume of 22.4 liters.

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And I'm normally not a big fan
of memorizing things, but this

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might be something handy to
memorize if you want to get

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through your chemistry test
fast. But you can always

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derive this if you know what
standard temperature and

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pressure is by PV equals nRT.

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But if you know that 1 mole is
going to take up that much

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space, so one mole is to 22.4
liters, as how many moles,

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let's say x moles in
this question.

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We want to figure out how many
moles of the gas we have and

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we know we are at 98
milliliters, so 0.098, so we

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set up this proportional
equation and we could figure

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out how many moles we're
dealing with.

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If 1 mole takes up 22.4 liters,
then our number of

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moles are going to take up
0.098, and this is an ideal

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gas in both circumstances.

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So we could say 22.4x
is equal to 0.098.

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And then we have x is equal
to 0.098 divided by 22.4.

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And this, of course,
is in moles.

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So 0.098 divided by 22.4 is
equal to 0.004375 moles.

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And they're telling us that
this amount has a mass of

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0.081 grams. So let
me get the number.

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So how many grams are
there per mole?

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So we take 0.081 grams and we
just did the math to figure

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out that we're dealing
with 0.004375 moles.

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So how many grams do
we have per mole?

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Let's take the calculator out.

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So we have 0.081 divided by
0.004375 is equal to 18.51.

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So it's equals 18.5
grams per mole.

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00:04:01,460 --> 00:04:03,330
So now this is an interesting
question.

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So we figured out the molar mass
of our mystery substance

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that took up 98 milliliters and
had a mass of 0.081 grams

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at standard temperature and
pressure, and we figured out

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its molar mass, or its mass per
mole, is 18.5 grams. So

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any guess as to what molecule
we're dealing with?

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18.5 grams.

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00:04:25,630 --> 00:04:28,990
And probably it's not going to
be exact, but at least in my

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brain, water seems to
be a good candidate.

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Water is H20.

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Maybe I should do it in blue
because it's water.

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The mass of each
hydrogen is 1.

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Remember, hydrogen, at least
in its most standard form,

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doesn't have a neutron, so it's
really just a proton and

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and an electron, so it has an
atomic mass of 1 or a molar

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mass of 1 gram.

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And oxygen has a molar mass of
16 grams. So you have two

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hydrogens, so it's 2 plus
16 is equal to 18.

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So it looks like our mystery
substance is water.

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