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 naturally we'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?

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. H2O.

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 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.