Partial Pressures & Vapor Pressure: Crash Course Chemistry #15


This week we continue to spend quality time with gases, more deeply investigating some principles regarding pressure – including John Dalton’s Law of Partial Pressures, vapor pressure – and demonstrating the method for collecting gas over water.


Transcript Provided by YouTube:

00:00
Imagine, if you will, a state dinner at the White House. These are not small intimate affairs.
00:05
300 or so adults mingle in close quarters,
00:08
yet somehow it’s a quiet gathering where people behave gently, move around slowly,
00:13
and almost never run into a wall.
00:14
However, as a group they do take up a lot of space, they give off a lot of heat, and lots of things get moved around.
00:21
In these ways the room is changed by their very presence.
00:25
Now picture a five-year old’s birthday party; a very different situation.
00:28
You would not call that quiet or formal.
00:31
But that is not enough. Imagine the most popular five-year old in the world.
00:35
His birthday party; 300 kindergartners in one room for several hours,
00:39
shoving each other, running like crazy, and definitely banging into walls.
00:43
Their bodies are smaller but because of their faster motion,
00:46
they collectively take up just as much of the room and give off just as much heat as the slow moving adults do.
00:51
And things get shoved around just as much.
00:54
Now imagine we have a surprise for those 300 adults at the state dinner all very formal and tucked in.
00:59
There are 300 5-year-olds in the next room, bouncing off the walls and suddenly we drop the wall. Excellent.
01:06
First of all those kids are going to run all around the room, squeezing in between the more sedate adults,
01:10
that will cause the adults to move apart a little, maybe even bumping in a wall now and again.
01:14
But because the adults are moving more slowly, they’ll get in the way of the kids running and slow them down some,
01:19
and that might even cause the kids to run into the walls a little less often.
01:22
The most important thing here is that the overall bouncing against walls,
01:26
will be equal to the bouncing of the adults plus the bouncing of the kids when they were in separate rooms.
01:32
And you will not be shocked to find that we are currently in and amongst an elaborate analogy to do with gases.
01:38
[Theme Music]
01:48
It shouldn’t surprise you to learn that this particular party was started by John Dalton,
01:52
the English teacher, the science teacher from England.
01:56
He wasn’t an English teacher, he was English,
01:58
who in 1803 was the first person to use real science to figure out what atoms are and how they behave.
02:03
His theory included a few misconceptions, but it contained enough facts to be super useful.
02:08
Daltons’s atomic theory began when he expanded French chemist’s Joseph Louis Proust’s Law of Definite Proportions,
02:15
to develop the Law of Multiple Proportions,
02:18
which says elements combine in simple, whole number ratios of their masses.
02:22
But here’s the cool part: That exact same research also led to an important gas law.
02:27
Dalton studied gases basically by mixing them together.
02:30
He was measuring how much of one element would react with a given amount of another.
02:34
But as he mixed those gases he noticed something else.
02:37
The total internal pressure of his container was always equal to
02:41
the sum of the individual pressures of the gases that he had added.
02:44
Upon recognizing that this happened every single time no matter what gasses were used
02:48
or what amounts were added, Dalton stated his discovery as the Law of Partial Pressures.
02:54
As long as the gases don’t react chemically, the total pressure exerted by a mixture of gases
02:59
is equal to the sum of the pressures that the individual gases would exert if they were alone.
03:03
Here’s an example; scuba tanks often contain a mixture of oxygen for breathing, obviously,
03:10
and helium which helps prevent decompression sickness
03:13
because it’s released from the blood more readily than nitrogen in air.
03:17
That allows divers to return to the surface more quickly with less risk of gas bubbles forming in their blood.
03:22
We’re going to use some approximations here so don’t yell at me if you know exactly how big this tank is.
03:26
But we’re gonna say that it’s 10 liters, and we’ll to say that it contains 4 moles of helium and 1.1 moles of oxygen gas.
03:34
The temperature in this room is about 22 degrees Celsius or 295 Kelvin.
03:38
So what’s the total pressure inside the tank?
03:42
In order to solve that we need to know the pressure exerted by each gas individually,
03:45
and we can find that with the Ideal Gas Law.
03:47
Starting with the helium, we don’t know the pressure so we’re solving for P.
03:50
The volume is 10 liters, and we have 4 moles of helium.
03:54
R is always the same, and the temperature is 295 K.
03:59
The calculations should show that the helium would have a pressure of 980 kilopascals, if it were alone.
04:05
Now for the oxygen, all the numbers are the same except for the moles which is 1.1 for the oxygen.
04:10
According to the calculations, the oxygen alone would have a pressure of 270 kilopascals.
04:14
The Law of Partial Pressures says that the total pressure is equal to the sum of the individual pressures,
04:19
so in this case 980 plus 270 equals 1250 kilopascals, or 1.25 megapascals.
04:27
Eaaasy peasy.
04:29
This additive property of pressures is closely related to the fact that mixing gases combines their particles,
04:34
thus increasing the total moles of gas present.
04:36
The ratio of moles of the individual gases in a mixture to the total number of moles is called the mole fraction.
04:42
And of course, mole fraction gets to have its own little esoteric symbol to represent it,
04:47
the lower case Greek letter, chi.
04:49
Chi sub 1, the mole fraction of an individual gas equals n sub 1, the number of moles of that gas,
04:54
divided by n sub total, the total number of moles in the mixture.
04:58
And because the total number of moles is the sum of the moles of all the gases,
05:03
we can also say that chi sub 1 equals the moles of any one gas
05:06
divided by the sum of the moles of all the individual gases.
05:10
You see how that last formula looks a lot like the one for partial pressures?
05:14
That’s because they’re basically the same thing.
05:17
Through the ideal gas law, the number of moles is directly related to the pressure of gas it exerts,
05:22
as long as the volume and temperature remain constant.
05:24
So you may have figured this out already,
05:26
rather than having to calculate individual pressures first every time as we did with the scuba tank,
05:30
or calculate the individual moles in the opposite situation,
05:33
we can often calculate what we need directly from what we already know.
05:37
Let’s give it a try. The air that we breathe is about 21% oxygen or 21 parts oxygen, and 100 parts air.
05:44
What is the partial pressure of O2 in air at a total atmospheric pressure of 97.8 kPa?
05:50
We can substitute moles for parts and use the mole fraction formula to solve this problem.
05:55
Plug in 21 moles of oxygen for the individual gas and 100 moles for air for the total amount,
06:01
and then put in the total atmospheric pressure, 97.8 kPa and do the equation.
06:05
With correct rounding, that will give you a partial pressure of 21 kilopascals for oxygen.
06:10
Sometimes however, gases mix together in ways that aren’t so predictable.
06:14
For instance, one way to collect a gas is by bubbling it through a column of water to
06:18
trap the gas at the end of the column.
06:20
This is called collecting a gas over water.
06:23
The only problem is liquid water constantly is giving off a small amount of water vapor.
06:28
That’s why if you leave a glass on a desk for long enough, there will eventually be no water in it.
06:32
There’s always going to be a few molecules with enough kinetic energy to escape the liquid.
06:37
The amount of vapor that’s released depends on the temperature of the water.
06:40
The more heat energy it has, the more vapor we get.
06:43
Like all gases, the water molecules move around a lot,
06:46
sometimes bump into the sides of the container, thus creating pressure.
06:50
This is called the water’s vapor pressure.
06:52
The water molecules mix with the gas that is being collected and when that happens,
06:56
as good ol’ John Dalton taught us,
06:58
total pressure in the column equals the pressure of the collected gas plus the vapor pressure of the water.
07:03
So to know how much gas we really collected,
07:06
we have to subtract the vapor pressure of the water from the total pressure.
07:10
This gives us the pressure exerted from the collected gas and from that, we can calculate the moles of gas present.
07:16
Here’s how it’s done.
07:17
Here I have a tub of water and a graduated cylinder that I have put into the water and then filled with water,
07:22
so now you can see, it’s got no gas in it, just water.
07:26
And we are going to capture gas in here and see how much gas we can capture.
07:30
Here I have a bottle and it’s sealed with this little tube.
07:33
This is the only way for gas to get out of here and in here right now I have vinegar,
07:37
an aqueous solution of acetic acid.
07:40
This is baking soda; more properly sodium hydrogen carbonate, or sodium bicarbonate.
07:46
I think we all know what will happen when this comes in contact with vinegar.
07:51
Now to prevent that from happening before I want it to happen, I made it a little boat for it.
07:56
And the boat is theoretically, I hope, going to sit on top of the level of the vinegar,
08:03
and float there without spilling.
08:09
Yeah, yeah, yeah. I did it.
08:12
Before the big action scene, let’s talk about what’s actually happening chemically speaking
08:15
because as you know, I love to speak chemically.
08:19
The acetic acid and sodium bicarbonate combine to form sodium acetate, carbon dioxide and water.
08:25
The sodium acetate dissolves readily in water and will stay that way.
08:28
The carbon dioxide, on the other hand, is the source of all our fun.
08:32
It’s a gas and it forms so many little bubbles in the surrounding liquid
08:35
that it’s almost a foam expanding quickly and dramatically.
08:38
As the carbon dioxide escapes through the foam,
08:41
it goes through the tubing and bubbles through the column of water so we get double the bubbles; double the fun.
08:46
And don’t forget, at the end we will be able to calculate how many moles of CO2 are produced by this reaction.
08:52
Let’s get to it.
08:53
It going to take more than two hands to do this so I have a lab assistant with me today.
08:57
This is Michael Aranda.
08:58
All right Michael put the tube into the cylinder there, and I get to do the fun part,
09:03
which is to shake this and make bubbles.
09:07
Bubbles! Little more, little more.
09:15
So we have collected exactly, about 9, almost exactly 90 milliliters, like 90.5 milliliters of carbon dioxide.
09:30
You can go away now.
09:33
We also know because I know that the atmospheric pressure is 101.8 kilopascals.
09:38
Remember we also need to know what the vapor pressure of the water was that we have to subtract.
09:42
The amount of vapor pressure that the water gives off depends on its temperature,
09:46
and there’s a table we can look at.
09:48
The water is at 19 degrees Celsius.
09:50
According to the table, the vapor pressure is 2.2 kilopascals.
09:53
So now finding the pressure of the carbon dioxide alone is easy.
09:56
We simply subtract 2.2 kilopascals from 101.8 to give us a pressure of 99.6 kilopascals for the carbon dioxide.
10:04
Finally we have to make sure the pressure inside the graduated cylinder is the same as the atmospheric pressure
10:08
and to do that, we just have to make sure that the levels of both of the liquids are the same.
10:14
In doing that I can see that it is almost exactly 90 milliliters of carbon dioxide in the cylinder.
10:21
Now we plug everything into the Ideal Gas Law.
10:23
P is 99.6 kilopascals, V is 0.090 liters, n is what we are trying to find,
10:30
R is always the same, and the temperature is 292 Kelvin.
10:34
One quick calculation and we find that we have collected 0.0037 moles of CO2.
10:40
At a molar mass of 44 grams per mole that’s 0.16 grams of carbon dioxide.
10:45
I am excited by our success here! That might not sound like a lot,
10:49
but collecting a fairly substantial amount of gases and being able to make accurate measurements of them
10:54
with a simple apparatus like that is pretty impressive.
10:56
For me, it sounds like time for party.
10:59
Thank you for watching this episode of Crash Course Chemistry.
11:02
If you weren’t late to the party, you learned that John Dalton built both his theory of the atom
11:07
and his Law of Partial Pressures on the foundation laid by Joseph Louis Proust
11:12
and that you can add up the pressures of mixed gases just as you can do with their amounts.
11:16
You also learned that the chemical reaction that occurs with vinegar and baking soda,
11:20
how to collect a gas over water,
11:21
and how to use that technique to figure out exactly how much of the gas you have.
11:26
This episode of Crash Course Chemistry was written by Edi Gonzalez.
11:28
The script was edited by Blake de Pastino and our chemistry consultant was Dr. Heiko Langner.
11:32
It was filmed, edited, and directed by Nicholas Jenkins.
11:35
Our second camera operator was Henry Reich.
11:37
Our script supervisor and sound designer is Michael Aranda. He was also our lab assistant.
11:42
And our graphics team is Thought Cafe.


This post was previously published on YouTube.

Photo credit: Screenshot from video

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