Passing Gases: Effusion, Diffusion, and the Velocity of a Gas – Crash Course Chemistry #16


We have learned over the past few weeks that gases have real-life constraints on how they move here in the non-ideal world. As with most things in chemistry (and also in life) how a gas moves is more complex than it at first appears. In this episode, Hank describes what it means when we talk about the velocity of a gas – to understand gas velocity, we have to know what factors effect it, and how. Hank also teaches you about effusion, diffusion and concentration gradients, before showing off a cool experiment that physically demonstrates the things you have just learned. Sound exciting enough for you? Let’s get started.


Transcript Provided by YouTube:

00:00
Welcome to another edition of Crash Course! Today — what is that smell? Oh, thanks for the rotten eggs.
00:06
Who is this — who — why are we doing this?
00:09
I mean, are going to be using this to illustrate some kind of scientific principle?
00:13
Because we probably could have, like, used some, like, some lilacs or something that wasn’t egg.
00:18
So, like, we’re saying, “I can smell it when I’m this close, but if I were farther away, I couldn’t smell it.”
00:24
Now, eggs produce hydrogen sulfide when they start to go bad, which smells like sulfur —
00:28
that’s what we think of when we think of the “sulfur smell.”
00:31
It takes time for the molecules of hydrogen sulfide to make their way to my nose,
00:35
’cause obviously gases don’t travel from one place to another instantly.
00:38
It take some time since, as we’ve learned over the past couple of weeks,
00:41
gases have real-life constraints on how they move here in the non-ideal world.
00:45
These are the rules that determine, say, how fast a leaking tire goes flat;
00:49
or why helium balloons don’t last forever; and, of course, how, where, and when we smell stuff.
00:55
One key to understanding the behavior of a gas is its velocity, that is, the speed and direction that it moves.
01:01
And THAT depends on a few important physical factors.
01:04
You ready to learn more? Let’s do it.
01:06
That smell IS coming from the eggs, isn’t it?
01:07
[Theme Music]
01:17
So. “Velocity of a gas”: what does that even mean? I mean, it’s easy to understand the velocity of a car.
01:22
You can find the velocity by dividing the distance that the thing traveled by the time it took to do it,
01:27
and then tell what direction it’s going, and then you’re done.
01:29
But the velocity of gases is harder t describe, because they move in more than one direction at a time,
01:34
and the overall shape and volume of a gas cloud can change constantly.
01:38
To understand gas velocity, we have to know what factors affect it, and how.
01:42
As you might have guessed, there’s math associated with this.
01:45
There are two ways of studying and talking about gases.
01:48
First, we can consider them as a collection of atoms or molecules that act together as a system.
01:53
When we do that, we often talk about the net velocity,
01:56
or how fast a sample of gas moves from one place to another,
01:59
like the rotten egg smell wafting its way to my nose.
02:01
At other times, we focus on the individual atoms and molecules that make up the gas.
02:06
In that case, we use the average velocity of each of the particles.
02:10
That’s the statistical mean of the speeds of all the individual atoms or molecules in the system.
02:15
There are always faster ones and slower ones, but it all evens out in the mean.
02:19
The net velocity of a gas in any one direction will always be lower than the average velocity of its molecules
02:24
because the overall motion of the gas is hindered by collisions among the individual particles.
02:29
As with most things in chemistry, and also with life, how a gas moves is more complex than it at first appears.
02:35
The individual particles in a gas never move at exactly the same speed or direction for very long,
02:40
instead, they bounce around like crazy, bumping into the walls of the container and each other over and over.
02:45
It’s sort of like a group of kids in a hallway,
02:47
they may be moving fast individually, but they bounce around a lot and get sidetracked.
02:51
They always make it to the lunchroom eventually,
02:53
but the group’s overall speed is lower than the speed of any individual kid.
02:57
So. What makes a gas move faster or slower?
03:00
Well we already know that gas atoms and molecules move faster when the temperature increases.
03:04
We can understand why that happens by remembering what temperature actually is:
03:08
Temperature is a property of matter that is proportional to the average
03:11
or mean kinetic energy of all the atoms or molecules in the system.
03:15
We sometimes think of temperature merely in terms of measuring hotness — not that kind of hotness!
03:20
The hotness or coldness of a material, and it is related to that,
03:24
but when you get right down to it temperature is really just a way of expressing average kinetic energy.
03:28
The reason a stove burns you, is that the fast moving particles of the burner
03:32
make the particles in your hand move so fast that they tear apart your cells and tissues.
03:37
It’s just a transfer of kinetic energy.
03:39
And what does kinetic energy have to do with velocity? Everything.
03:43
And, it also describes the relationship between a particle’s velocity and its mass.
03:48
So, a good understanding of kinetic energy will help a lot as we study the motion of gases.
03:52
So first, the formula for kinetic energy is one half m v squared.
03:57
And as you can see, any changes in the kinetic energy are directly linked to changes in velocity.
04:02
If we rearrange the formula, we find that the velocity of a body equals
04:05
the square root of two times the kinetic energy, divided by its mass.
04:09
This little math exercise highlights two important points.
04:12
One: because the mass is in the denominator, we can tell that it is inversely proportional to the velocity,
04:17
meaning that bigger masses move more slowly than smaller masses that have the same kinetic energy.
04:22
And two: the velocity is proportional to the square root of the mass,
04:26
meaning that a fairly large change in mass is required to make a significant change in the velocity.
04:31
So, now we can show how the velocity of a gas relates to both its temperature,
04:34
and therefore its average kinetic energy; and also to the mass of its particles.
04:38
But, how do we put that all together?
04:41
This is where the Scottish chemist Thomas Graham comes in.
04:43
In 1846, Graham published his research on the motion of gas particles.
04:47
Which he did by passing gases, if you will, through a porous barrier.
04:52
The process by which gases travel through an orifice or opening is known as effusion.
04:56
Graham was interested in how fast the gases pass through the barrier.
04:59
But this is called the rate of effusion, not the velocity.
05:03
That’s because here we’re measuring the amount of gas that passes through at any given period of time,
05:07
not the distance that it moves in that time.
05:09
We might measure amount in terms of moles or in terms of volume, but the rate of effusion never uses distance.
05:14
One more thing before we move on, don’t let the symbols confuse you.
05:18
Notice that lower case v stand for velocity and capital V stands for volume – the perils of symbols.
05:24
Thomas Graham measured the rates of effusion for various gases
05:27
and his results fit perfectly with what we already know: the more massive a gas is, the
05:31
more slowly it moves.
05:32
From his observations, Graham developed a formula — now known as Graham’s Law of Effusion —
05:37
for comparing the rates of effusion of different gases.
05:40
It states: Under identical conditions, the ratio of the rate of effusion of gas a to the rate of effusion of gas b
05:46
is equal to the ratio of the square root of the molar mass of gas b to the square root of the molar mass of gas a.
05:52
It is a mouthful, but it really just confirms what we deduced earlier:
05:55
the rate of motion of a gas is inversely proportional to the square root of its mass.
06:01
For example, if it takes 4.5 minutes for 1.0 liter of helium to effuse through a porous barrier,
06:05
how long will it take for 1.0 liter of chlorine to effuse under identical conditions?
06:11
All we need to figure it out, is Graham’s Law.
06:13
Let’s make the helium gas a, and chlorine will be our gas b.
06:16
First, we have to find helium’s rate of effusion — in this case, we’re using Volume with a capital V.
06:21
So for helium, 1.0 liter in 4.5 minutes gives the rate of 0.22 liters per minute.
06:26
So, we plug that into the main formula — chlorine gas has a molar mass of two times that of atomic chlorine —
06:32
35.5 times two equals 70.9, and helium’s molar mass is 4.00.
06:38
Put those numbers in too.
06:39
Careful calculation shows that Cl2’s rate of effusion under these conditions would be 0.052 liters per minute,
06:46
significantly slower than helium.
06:48
This, of course, is reasonable, because Cl2 is much more massive than helium.
06:52
Graham mainly studied gases passing through orifices in a barrier,
06:54
but gases aren’t usually trapped with an orifice in a barrier.
06:58
They are usually able to just move freely, so how do we study their motion under those conditions?
07:03
When gases are allowed to move freely,
07:04
they tend to move from regions of high concentration to regions of low concentration.
07:08
In a sense, they move away from places where they’re crowded
07:11
and toward places where they have a little bit more elbow room.
07:13
The difference in concentration between two points is called a concentration gradient,
07:17
and it’s kind of like a hill that matter rolls down, always moving from high to low.
07:22
Gases spread out like that until they’ve dispersed evenly throughout the available space.
07:26
This process is called diffusion.
07:28
Now, it’s important to keep in mind that the particles in a gas don’t work together somehow to move in a specific direction.
07:34
Remember those kids making their way down the hall?
07:37
They all know where the lunchroom is, and they’re hungry,
07:39
so even though there are a lot of distractions, they move purposely toward their destination.
07:43
Gases, on the other hand, only appear to move in a specific direction.
07:47
It’s really just random collisions pushing the molecules apart, thus making them spread out in every direction.
07:52
In other words, the gross eggy gas that I smelled earlier didn’t travel just toward my nose;
07:57
its particles spread out in every direction from the eggs,
08:00
and my nose simply noticed the ones that happened to have spread in THAT direction.
08:04
Because diffusion is completely free movement,
08:07
calculating the motion of individual particles becomes even more complicated.
08:09
Now, we’re not gonna get into the super complex mathematics of all these collisions,
08:13
but it is possible to make decent estimates regarding the net velocity of gases
08:16
simply by disregarding the collisions and applying Graham’s Law of Effusion to diffusion as well.
08:22
Here’s how it works: This is a simple acrylic tube — nothing fancy.
08:25
On one side, we have a cotton ball that’s soaked with concentrated ammonia,
08:29
and on the other side, a cotton ball soaked with concentrated hydrochloric acid,
08:33
which is why we’re doing this in a lab, and not at my desk.
08:35
Both of these substances are very smelly, because they’re giving off lots of fumes,
08:39
or in other words, a lot of the molecules in the liquid are being released in gas form.
08:43
When we put the cotton balls in the glass tube and close off the ends, those gases continue to spread,
08:49
but they have no where to go except farther into the tube.
08:52
Fun fact: ammonia and hydrochloric acid react together readily to form a solid — ammonium chloride.
08:58
That’s a precipitation reaction, but this time it’s happening in a mixture of gases, not liquids.
09:03
Because the ammonium chloride is a solid at room temperature,
09:06
it forms a superfine white powder where the two gases meet in the tubes,
09:09
so we’ll be able to tell exactly how far each gas traveled before they met.
09:13
Let’s try to figure out where that’s going to be.
09:15
First of all, remember that Graham’s Law is only an estimate when applied to diffusion,
09:19
but it’s a good enough estimate to work for our purposes, here.
09:22
The molar mass of ammonium, which we call “gas a,” is 17 and the molar mass of hydrochloric acid, “gas b,” is 36.
09:29
If we plug those into Graham’s Law, and set hydrochloric acid’s rate of diffusion at 1.0,
09:33
since we are only looking for a ratio, here,
09:35
we’ll find that ammonia’s rate of diffusion will be about 1.5 times as fast as that of hydrochloric acid.
09:41
That means that the ammonium chloride should form about 3/5 of the way down the tube from the NH3
09:46
and about 2/5 of the way from the HCl.
09:49
And, there it is. See that white cloud? That’s the ammonium chloride powder forming.
09:55
It’ll eventually settle in the glass,
09:56
but it’s so fine that even the tiny currents that occur as the two gases mix are enough to toss it around a little.
10:01
The ammonia has indeed moved through about three fifths of the tube.
10:04
Meanwhile the hydrochloric acid has only traveled through about two fifths of the tube.
10:08
So, we’ve proven now that Graham’s Law, as an estimate at least, works.
10:11
The distances that the two gases traveled were indeed proportional to their molar masses. Makes sense.
10:16
That’s one of the cool things about science: it always ends up making sense, once you know what you’re looking for.
10:21
And that’s it for this episode of Crash Course Chemistry. Thank you for watching.
10:24
If you listened carefully, you learned the difference between the net velocity of a gas
10:28
and the average velocity of its particles,
10:30
and that both things have a lot to do with the mass and kinetic energy of the particles.
10:34
You learned about effusion and what Thomas Graham’s Law of Effusion tells us about it,
10:38
and how the law of effusion can also be applied to diffusion, but not as reliably.
10:42
You also learned that the collisions that occur among the particles of a gas
10:45
have a huge effect on both its motion and our attempts to calculate it.
10:50
You learned what a concentration gradient is,
10:52
and finally, you learned how to do a precipitation reaction with gases.
10:56
This episode of Crash Course Chemistry was written by Edi González.
10:58
Who I have to commend for only making one fart joke in the whole script!
11:02
The script was edited by Blake de Pastino and myself.
11:04
And our chemistry consultant was Dr. Heiko Langner.
11:07
It was filmed, edited, and directed by Nicholas Jenkins. Our script supervisor was Caitlin Hofmeister.
11:11
Our sound designer is Michael Aranda. And our graphics team is Thought Café.


This post was previously published on YouTube.

Photo credit: Screenshot from video

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