Ideal Gas Example 4

Figuring out the molar mass of a mystery molecule at STP.

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

so you really get intimately
comfortable with PV equals

nRT, or the ideal
gas equation.

So we have 98 milliliters
of an unknown gas.

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

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

grams. This is mass.

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

standard temperature
and pressure.

Calculate the molar
mass of the gas.

So they want to know
the mass per mole.

So the molar mass, or
the mass per mole.

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

We know what standard
temperature and pressure are.

Standard temperature is
273 degrees Kelvin.

Standard pressure
is 1 atmosphere.

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

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

And actually, maybe
I'll do that.

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

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

two videos ago.

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

pressure will fill up a
volume of 22.4 liters.

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

might be something handy to
memorize if you want to get

through your chemistry test
fast. But you can always

derive this if you know what
standard temperature and

pressure is by PV equals nRT.

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

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

let's say x moles in
this question.

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

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

set up this proportional
equation and we could figure

out how many moles we're
dealing with.

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

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

gas in both circumstances.

So we could say 22.4x
is equal to 0.098.

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

And this, of course,
is in moles.

So 0.098 divided by 22.4 is
equal to 0.004375 moles.

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

0.081 grams. So let
me get the number.

So how many grams are
there per mole?

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

out that we're dealing
with 0.004375 moles.

So how many grams do
we have per mole?

Let's take the calculator out.

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

So it's equals 18.5
grams per mole.

So now this is an interesting
question.

So we figured out the molar mass
of our mystery substance

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

at standard temperature and
pressure, and we figured out

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

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

18.5 grams.

And probably it's not going to
be exact, but at least in my

brain, water seems to
be a good candidate.

Water is H20.

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

The mass of each
hydrogen is 1.

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

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

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

mass of 1 gram.

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

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

So it looks like our mystery
substance is water.