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.