0:00:00.000,0:00:03.890
I think it makes sense to keep doing a few more problems just

0:00:03.900,0:00:05.780
so you really get intimately comfortable

0:00:05.780,0:00:08.690
with PV equals nRT, or the ideal gas equation.

0:00:08.700,0:00:16.110
So we have 98 milliliters of an unknown gas.

0:00:16.120,0:00:20.980
They say weighs in the problem, but I'll use mass.

0:00:20.990,0:00:24.310
Its mass is 0.081 grams.

0:00:24.320,0:00:27.420
You shouldn't say weighs 0.081 grams. This is mass.

0:00:27.430,0:00:29.690
Weight would be in newtons if we're in the metric system

0:00:29.700,0:00:33.050
at standard temperature and pressure.

0:00:33.060,0:00:37.190
Calculate the molar mass of the gas.

0:00:37.200,0:00:40.130
So they want to know the mass per mole.

0:00:40.140,0:00:50.090
So the molar mass, or the mass per mole.

0:00:50.100,0:00:55.650
Now, we could just substitute this into PV is equal to nRT.

0:00:55.660,0:00:57.980
We know what standard temperature and pressure are.

0:00:57.990,0:01:00.810
Standard temperature is 273 degrees Kelvin.

0:01:00.820,0:01:10.230
Standard pressure is 1 atmosphere.

0:01:10.240,0:01:15.480
And then, of course, they're giving us 98 milliliters.

0:01:15.490,0:01:20.840
And then you can just solve for how many moles we have.

0:01:20.850,0:01:22.000
And naturally we'll do that.

0:01:22.000,0:01:23.860
But the other way to think about it is that

0:01:23.870,0:01:26.770
at standard temperature and pressure, an ideal gas

0:01:26.780,0:01:29.740
-- and we did this two videos ago.

0:01:29.750,0:01:35.750
We said 1 mole of an ideal gas at standard temperature and pressure

0:01:35.760,0:01:39.460
will fill up a volume of 22.4 liters.

0:01:39.460,0:01:42.700
And I'm normally not a big fan of memorizing things,

0:01:42.710,0:01:44.800
but this might be something handy to memorize

0:01:44.800,0:01:46.740
if you want to get through your chemistry test fast.

0:01:46.750,0:01:48.600
But you can always derive this if you know

0:01:48.610,0:01:51.830
what standard temperature and pressure is by PV equals nRT.

0:01:51.830,0:01:55.670
But if you know that 1 mole is going to take up that much space,

0:01:55.680,0:02:03.640
so one mole is to 22.4 liters, as how many moles,

0:02:03.650,0:02:05.700
let's say x moles in this question.

0:02:05.710,0:02:08.170
We want to figure out how many moles of the gas we have

0:02:08.180,0:02:13.830
and we know we are at 98 milliliters, so 0.098,

0:02:13.840,0:02:15.890
so we set up this proportional equation

0:02:15.900,0:02:18.230
and we could figure out how many moles we're dealing with.

0:02:18.240,0:02:21.340
If 1 mole takes up 22.4 liters,

0:02:21.350,0:02:24.160
then our number of moles are going to take up 0.098,

0:02:24.170,0:02:26.490
and this is an ideal gas in both circumstances.

0:02:26.500,0:02:33.530
So we could say 22.4x is equal to 0.098.

0:02:33.540,0:02:40.920
And then we have x is equal to 0.098 divided by 22.4.

0:02:40.930,0:02:42.600
And this, of course, is in moles.

0:02:42.610,0:03:04.990
So 0.098 divided by 22.4 is equal to 0.004375 moles.

0:03:05.000,0:03:13.030
And they're telling us that this amount has a mass of 0.081 grams.

0:03:13.040,0:03:14.940
So let me get the number.

0:03:14.950,0:03:17.780
So how many grams are there per mole?

0:03:17.790,0:03:23.950
So we take 0.081 grams and we just did the math

0:03:23.960,0:03:30.920
to figure out that we're dealing with 0.004375 moles.

0:03:30.930,0:03:33.560
So how many grams do we have per mole?

0:03:33.560,0:03:36.010
Let's take the calculator out.

0:03:36.020,0:03:49.080
So we have 0.081 divided by 0.004375 is equal to 18.51.

0:03:49.100,0:04:01.880
So it's equals 18.5 grams per mole.

0:04:01.880,0:04:03.400
So now this is an interesting question.

0:04:03.410,0:04:06.820
So we figured out the molar mass of our mystery substance

0:04:06.830,0:04:12.020
that took up 98 milliliters and had a mass of 0.081 grams

0:04:12.030,0:04:14.390
at standard temperature and pressure, and we figured out

0:04:14.400,0:04:18.670
its molar mass, or its mass per mole, is 18.5 grams.

0:04:18.680,0:04:23.870
So any guess as to what molecule we're dealing with?

0:04:25.700,0:04:27.990
And probably it's not going to be exact,

0:04:28.000,0:04:31.660
but at least in my brain, water seems to be a good candidate.

0:04:31.670,0:04:33.930
Water is H20.

0:04:33.940,0:04:37.830
Maybe I should do it in blue because it's water. H2O.

0:04:37.840,0:04:40.400
The mass of each hydrogen is 1.

0:04:40.410,0:04:43.880
Remember, hydrogen, at least in its most standard form,

0:04:43.890,0:04:45.920
doesn't have a neutron, so it's really just a proton

0:04:45.920,0:04:48.270
and an electron, so it has an atomic mass of 1

0:04:48.280,0:04:50.190
or a molar mass of 1 gram.

0:04:50.200,0:04:52.970
And oxygen has a molar mass of 16 grams.

0:04:52.980,0:04:57.410
So you have two hydrogens, so it's 2 plus 16 is equal to 18.

0:04:57.420,0:05:01.540
So it looks like our mystery substance is water.