The Ideal Gas Law: Crash Course Chemistry #12


Gases are everywhere, and this is good news and bad news for chemists. The good news: when they are behaving themselves, it’s extremely easy to describe their behavior theoretically, experimentally and mathematically. The bad news is they almost never behave themselves.


Transcript Provided by YouTube:

00:01
Gas! It’s all around you. It’s in space. It’s on Mars.
00:06
It’s dissolved in your blood, and in your soda.
00:09
It’s everywhere.
00:11
And it’s easy to forget that we’re submerged in an ocean of gas, but it’s there all the time.
00:15
You can feel it if you wave your arms around.
00:17
Can’t look cool while you’re feeling it but you can feel it. It’s there.
00:21
Those little molecules and atoms bumping around against your hands as you wave them around.
00:25
Feel it? Are you doing this?
00:26
I’ve got good news and bad news about gases.
00:28
First the good news, when they’re behaving themselves
00:31
it is extremely easy to describe their behavior theoretically, experimentally and mathematically.
00:36
The bad news is, they almost never behave themselves.
00:39
[Theme Music]
00:50
The first mathematical description of a behavior of a gas was a link between pressure and volume.
00:56
In a closed system like the inside of this balloon,
00:59
when we decrease the volume of the balloon the pressure inside goes up.
01:03
And if we could somehow expand the balloon, then the pressure inside the balloon would go down.
01:09
If I keep pushing on it the pressure inside might go so high that it’ll break.
01:12
I hope…I can’t do it. It’s a very strong balloon!
01:16
The relationship here is a simple one.
01:18
When you multiply the pressure and volume together, you get a constant.
01:21
As long as the temperature and amount of gas stays the same, so does that constant.
01:26
It’s called Boyle’s Law, and it was a pretty big deal back in the 1600s.
01:30
It’s also, one of the greatest scientific mis-attributions of all time.
01:35
Robert Boyle was a super rich Englishman, raised in Ireland.
01:40
His father was so rich that he paid another family to raise his children.
01:44
I guess because he was too busy administering lands or something.
01:47
Boyle had lots of great ideas about science and chemistry.
01:50
His most important one, and this is arguably even more important than Boyle’s Law,
01:54
being that chemists should publish papers not on what they feel is correct,
01:58
but rather on theories that have been backed up by experimentation.
02:01
Richard Towneley a wealthy, but considerably less wealthy, Englishman struck up a relationship with Boyle.
02:07
Telling him about some of his work that would disprove one of those “But it feels right” kind of chemists.
02:12
Boyle published the paper mentioning that work, which he called Towneley’s Hypothesis.
02:17
But which ended up, because of Boyle’s superior scientific standing and possibly his wealth, being called Boyle’s Law.
02:23
But here’s the really messed up thing:
02:24
the experiments that led to the creation of this theory were actually done largely by
02:28
Towneley’s family friend and physician, Henry Power, who’s not a member of the aristocracy at all.
02:34
He was just a working class scientist.
02:36
Power was working on a publication that would have snared him the position as discover of
02:41
the relationship between the pressure and volume of a gas.
02:43
But Boyle, having discussed the ideas with Towneley privately, published his first,
02:48
attributing Towneley as the sole researcher, ensuring that Power’s contributions were all but lost to history.
02:54
Henry Power’s Wikipedia page didn’t even mention Boyle’s Law until a few weeks ago,
02:59
when I personally added a paragraph about it, with proper citations of course.
03:04
But no matter who thought it up or who it got named after, Boyle’s Law is pretty cool.
03:08
For a given amount of gas at a constant temperature, pressure times volume always equals the same number.
03:14
But where is that constant coming from,
03:16
and why is it different for different amounts of gas at different temperatures?
03:20
Well it was more than a hundred years before we’d figure out the answer to those questions,
03:24
with the help of a Frenchman Jacques Charles and our old, Italian house-elf friend Amedeo Avogadro.
03:30
Charles and Avogadro created equations much like Boyle’s law
03:33
with two features of a gas being linked directly together by constants.
03:37
Charles discovered that volume divided by temperature equals a constant,
03:40
as long as the pressure remains the same.
03:42
And then Avogadro figured out that volume divided by the number of moles in the container
03:46
at a constant pressure and temperature gave yet another constant.
03:49
But here’s the crazy cool thing:
03:51
all of these scientists were basically dealing with a different form of the same equation.
03:56
An equation that we must never forget, and is gonna be stuck in my head until I die, and here’s how it works:
04:02
Pressure times volume is equal to the number of moles of substances times a constant times temperature.
04:07
P V equals n R T: The Ideal Gas Law, which works for all gases as long as they behave themselves.
04:14
Now here’s the cool part,
04:15
using this equation we can show how all of these chemists were dealing with the same relationship.
04:20
They were just clumping various variables together in different orders.
04:23
All of the chemists we just mentioned: Charles, Avogadro and Boyle (or more properly Towneley and Power),
04:28
figured out their contribution to the Ideal Gas Law experimentally.
04:31
But more interesting to me, is that it can be understood theoretically.
04:35
First, we have to understand what each of these variables actually mean.
04:38
In that same way the atoms and molecules that make up gases
04:41
are bouncing against things, applying pressure to them.
04:44
This balloon is inflated because the molecules are bouncing around inside of it,
04:48
bumping into the inside of the balloon harder than the molecules bouncing off the outside of the balloon.
04:53
Scientists generally measure pressure with the S.I. unit of force:
04:56
Newtons per area, meters squared, which is shortened to pascals.
05:00
But since pascals are so tiny we either use kilopascals
05:03
or we use the pressure here on earth at sea level, that we call one atmosphere or one atm.
05:09
Completely by chance, one atmosphere is equal to 101325 pascals,
05:14
but that’s so close that we often just say that one atmosphere is 100,000 pascals or 100 kilopascals.
05:21
Volume is the amount of space particles have to exist inside of.
05:25
So yeah, that makes sense, when the volume goes down, the pressure goes up,
05:28
because there are more particles in a smaller space, and they’ll each hit the walls more often.
05:32
N is simply the amount of gas, the number of moles in the system.
05:35
Here I am decreasing the amount of gas in the system and in response the volume is decreasing. Obviously.
05:41
But so is the pressure inside the balloon.
05:43
R in the Ideal Gas Law is called the Universal Gas Constant.
05:46
Even though, as we will see in a coming episode, it is neither universal or constant.
05:50
It’s 8.3145 liters kilopascal per kelvin mole.
05:54
Temperature, is experienced by you and me as hot or cold but at the atomic level it’s kinetic energy.
05:59
Literally, how fast or slow the average particle is moving.
06:03
So if temperature goes up, so will the pressure as the particles are moving faster
06:07
and thus will run into the sides of the container more often.
06:10
So now we know about all of the little bits of the Ideal Gas Law, so let’s take a look at it in action.
06:15
We here at Crash Course generally like to be very safe. This is a little bit of overkill here.
06:20
I put a little bit of water into this soda can and now I’m boiling it.
06:23
So instead of atmosphere gas in this can right now there’s water vapor,
06:27
and it’s hot and all the molecules are zipping around like crazy.
06:29
We pick it up and we plop it down inside of that — ooh! — and it crushes itself.
06:36
So what just happened there?
06:38
Well, let’s see what the gas law can tell us.
06:40
So which of these things are changing?
06:42
Starting on the right hand side: R, is constant, so that can’t change.
06:46
The temperature of the gas though, that definitely changed;
06:48
it drops like mad when it’s exposed to the ice water.
06:51
N is decreasing too as water vapor is condensing into liquid water, it thus disappears from the gas phase.
06:56
So the next result on the right hand side is a decrease,
06:59
and that means that the left hand side has to have a decrease too.
07:02
So on to the left hand side.
07:04
The pressure does indeed drop because the lower temperature makes the molecules move more slowly,
07:09
thus bumping into the sides of the can a lot less than before.
07:12
And volume drops too, but not quite for the reason you might think.
07:15
It’s really that the pressure inside the can goes so low, that the pressure outside the can,
07:20
the atmospheric pressure, literally crushes the can.
07:22
Now I understand that you probably don’t think this is as cool as I do,
07:26
but understanding the physical reality of atoms and molecules smacking into things is
07:29
a special kind of beautiful for me.
07:31
It’s also pretty cool that if you know any 3 things about a gas, you can figure out the fourth using the ideal gas law.
07:37
Of course, not all gases behave ideally,
07:39
and all gases deviate from the law at low temperatures or high pressures.
07:43
But we’ll save that discussion for a later episode.
07:46
Jargon fun time.
07:47
STP means standard temperature and pressure,
07:50
which according to the lords of chemistry is 0 degrees Celsius and 100,000 pascals or 100 kilopascals.
07:56
One mole of any ideal gas takes up 22.4 liters of space at STP, which is a fact that can simplify a lot of calculations.
08:04
Absolute zero is the temperature at which all movement of all particles stops.
08:08
It is zero kelvins or -273.15 degrees Celsius.
08:12
And that’s all for this episode. Thank you for watching Crash Course Chemistry.
08:15
If you were paying attention you learned about
08:17
how the work of some amazing thinkers combined to produce the Ideal Gas Law;
08:21
how none of those people were Robert Boyle,
08:24
and how the Ideal Gas Equation allows you to find out pressure, volume, temperature or number of moles,
08:29
as long as you know three of those four things.
08:31
And you learned a few jargon-y phrases to help you sound like you know what you’re talking about.
08:35
This episode of Crash Course Chemistry was written by me.
08:37
The script was edited by Blake de Pastino
08:39
and our chemistry consultants were Dr. Heiko Langner and Edi Gonzalez.
08:43
It was filmed, edited and directed by Nicholas Jenkins.
08:46
Our script supervisor was Caitlin Hofmeister and our sound designer is Michael Aranda.
08:50
Our graphics team is Thought Cafe.


This post was previously published on YouTube.

Photo credit: Screenshot from video

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