00:01
For this problem, we are looking at a situation where we have a hypothetical skier.
00:06
I'll just draw over here.
00:09
And we're given two different situations, which makes sense given the fact that we are indeed skiing, something like this, although let's make the poles a different color.
00:21
So we're given two different situations.
00:23
We have the top of the hill and the bottom of the hill.
00:27
Now, at the top of the hill, at the ski run, we can think about.
00:31
We're given a few different measurements.
00:34
We're told the temperature, which i'll do in blue, is negative 5 degrees celsius.
00:42
And we're told that the pressure is, i'll do this in red, 713 millimeters mercury, which is a pressure reading.
00:54
It's units for pressure.
00:56
And then once our skewer gets down to the bottom of her run, towards the bottom of the hill, we would expect.
01:03
We're told that the temperature is higher, which makes sense.
01:07
Typically, it's colder, the higher the elevation that you are.
01:11
Zero degrees celsius.
01:13
And then we would also expect the pressure to be a bit higher because there's more air, more stuff that we would experience as gases.
01:22
And this is going to be 734 millimeters mercury.
01:29
Now, with this information given to us, we are asked to find, and how many moles of oxygen does a skier take in with a lung full of air at the bottom of the run than at the top? so how many more moles of oxygen? so in order to do this, we need to find the amount of oxygen at the top and at the bottom.
02:00
So how do we do this? how many more moles of oxygen does a skier take in with a lung full of air? so the key here is lung full of air because where i'm going with this is with the units and the measurements that are given to us, we should immediately be thinking about the ideal gas law because this is a tool that allows us to find different measurements regarding gases by giving us a relationship between all of them.
02:35
So pv equals nrt.
02:38
This is the gas law, or p equals pressure, v equals volume, n equals moles, r is a constant, and t is temperature.
02:47
So let's see what units we have, because with this sort of equation, you just want to see if you have one missing, so you can plug everything else in and solve for the missing variable, like a typical algebra problem.
02:59
So we're given temperature.
03:02
We are given pressure.
03:05
R is a constant.
03:07
So we're always given r.
03:09
But we don't have volume.
03:11
That isn't explicitly given to us.
03:13
Now the keyword, the operative word there is explicitly.
03:17
Now, volume is the amount of space, right? it's the amount of space that something could potentially occupy.
03:23
So the operative word in the word problem now is lungful, because that is going to be our working space.
03:29
We need to find how much oxygen is in that area, which is the lungs.
03:35
Okay.
03:36
So how we need to know what is the volume of a lung.
03:43
And it turns out that the average volume of a lung is about six liters.
03:48
This is what we will use.
03:50
Ultimately, it just matters if we're consistent because we need to find the amount of oxygen at both conditions, right? we have the set of conditions here and this set of conditions here.
04:00
And we need to find the amount of oxygen and moles in both so then we can find the difference between the two.
04:04
So now when we're using the ideal gas, we're using the ideal gas.
04:07
Law.
04:08
What we really need to do is just make sure everything is in the correct units so that we can plug it in.
04:12
So let's do the top of the hill on the left here.
04:15
I'll do this in green.
04:18
So i'll just write t for top.
04:21
And let's make sure we convert our units.
04:23
So we have temperature in celsius, which we need to convert to kelvin.
04:27
And this is the conversion.
04:29
You just add 273 .15.
04:33
When we plug that in, we get 268 .15 degrees kelvin.
04:41
Not degrees kelvin, just kelvin.
04:43
Then we also need to change the pressure.
04:46
We have millimeters of mercury, but we need to convert to atmospheres.
04:50
So this is the conversion for that.
04:56
One atmosphere has 760 tor or millimeters of mercury.
05:02
They're both the same in this context.
05:09
So then once we do that conversion, divide 730.
05:13
By 760, we get 0 .94, which i rounded atmospheres.
05:21
Beautiful.
05:23
So now we have everything we need to plug into the gas law.
05:26
So let's just isolate things.
05:27
So we're solving for n.
05:30
So n, which is moles, is equal to pressure, which is 0 .94 atmospheres.
05:40
I'm going to exclude the units from this this calculation here, but just keep in mind that normally it would help to have them consistent, so you would say organized...