gases. When you see a hot air balloon flying, it looks pretty stationary. But if you're

to look at the molecules inside it, if we were to look at the heat inside it we'd see

there's going to be way more hot air at the top then at the bottom. It's less dense. And

that's why the thing is going to float. So when we're looking at gases, basically a real

gas is going to be made up of all of these independent particles that are all just shooting

around, moving around really really quickly. They're not connected together at all. And

so in science what we can do is we can model that using what's called an ideal gas. And

lots of times we'll use the ideal gas law. And this one, PV=nRT is one that you should

learn right away. And learn how to apply it over and over and over again. It's basically

built on two things. The kinetic molecular theory. This idea that molecules are bouncing

around and they have a huge amount of energy as we increase the temperature. And then the

Maxwell-Boltzmann distribution which means that even though they might collide every

once and awhile, the energy that they have is going to remain the same and their state

is going to remain the same. We can use the ideal gas law to figure out absolute zero.

But there are going to be some deviations. In other words times where this model just

doesn't work. And we have to start looking at real gases. And this usually occurs as

we get around condensation. That point at which that gas turns back into a liquid again.

And so this is going to be a real gas. Air, what's between me and the camera right now

is going to be a real gas. And an ideal gas is built on these two theories. First one

is kinetic molecular theory. It's that all of the molecules are bouncing around. Moving

off of each other. And as we increase temperature we're going to increase the molecular speed

of those molecules. And so that's a gas. Remember they're not connected together at all. They're

just moving around randomly. And then we have the Maxwell-Boltzmann distribution. And that

means that even though they might bounce into each other, they're not interacting with each

other. They're all going to be independent. And so this graph, what we're looking at are

a bunch of noble gases. And we're looking at their speed. And the probability of having

found molecules at that specific speed. And what we'll find is that real light noble gases,

like helium, are going to have a higher speed then those for example like argon. They're

going to have lower speed, but they're all independent of one another. And so when we're

looking at an ideal gas, we basically have these five properties. Volume, temperature,

pressure, n which is the number of moles. And then some kind of a gas constant. And

so you're going to have to look at your units to figure out what gas constant to use. But

if we use this model, which we use it three times, v is going to be the volume. So let's

say these are a bunch of gas molecules. Volume is going to be the size of the container that

they're in. T is going to be the temperature. How warm or cold it is. And that remember

is tied to the molecular motion. Pressure is going to be how much it's pushing out.

And if you push in on a balloon you can start to feel that pressure pushing out on you.

And then n is going to be the number of moles. How much stuff is going to be found inside

it. And so if we rearrange this PV=nRT, that's the relationship. Now you could learn all

of the different gas laws. But it's better to just learn the ideal gas law and then apply

it in different situations. And so we're going to use this simulation at phet. And we're

going to look at Boyle's law. And so that's the relationship between pressure and volume.

And so we're going to keep all those other constants, n, R and T are all going to remain

constant. What we're going to look at is how are volume and pressure related. So I'm going

to keep the temperature constant. And if we look at the pressure it's around 0.69 atmospheres.

Now let me decrease the volume. So I'm making the volume get smaller. And so what's going

to happen to the pressure? Well, we have to wait for a little bit. We have to wait for

that temperature to go back down to 300 kelvin again. But once it gets to 300 kelvin now

look, it was 0.69 atmospheres before, and now it's 1.73. And so as we decrease the volume,

pressure went up. Now let's increase the the volume. So we're making the volume go up.

And then let's look at what's going to happen to the pressure. And so we've got to wait

for that temperature to come back to 300 kelvin again. And so now we're going to see that

the pressure has decreased. So by increasing the volume, we decreased the pressure. And

so there's going to be an inverse relationship between pressure and volume. And you could

actually apply this in a problem. Let's say we had a balloon at 1.30 atmospheres. That's

going to be the pressure. It has a volume of 3.2 liters. What will the volume be if

the pressure is decreased to 0.62 atmospheres. And the temperature remains the same? Well,

we just have a before and after. So we have our pressure volume before, initial, and after.

So we'd put in our values before. Our after. And then we're going to solve for this final

volume. And so we could make sure our units are correct. And so what's going to happen

to the volume? The volume is going to increase as the pressure decreases as long as we keep

the temperature the same. And a weather balloon. As you send a weather balloon up, the weather

balloon is going to get bigger and bigger and bigger. There maybe changes in temperature,

but it's related to that relationship. Now let's look at what's called Charles' Law.

We're just going to look at volume and temperature. And what happens to the volume as the temperature

changes? Let's use this simulation again. We're going to try to keep the pressure constant.

And the same number of moles inside there as well. And so now we're going to increase

temperature. So we're adding heat. And watch what happens to the volume. As we increase

the temperature, the volume got bigger. As long as we kept the pressure the same? Why

is that? As we're increasing temperature there's more kinetic movement. Now let's lower the

temperature. As we decrease the temperature, those molecules aren't moving as quickly.

And what happens? Not pushing out as much. And so the volume is going to go down. So

if we increase temperature volume goes up. If we decrease temperature, volume is going

to go down. And so there is a direct relationship between the two. And so hopefully you're learning

how to apply ideal gas law. If they're both on the same side, we had an inverse relationship.

But now since they're on opposite sides of the equal sign it's going to be a direct relationship.

What's an application of this? Well you could find absolute zero in a basic chemistry class.

So what we could do is take a balloon and we could measure the volume of the balloon

when the gas is around freezing. And so let's say we do that by measuring the circumference

around the balloon and then using a little geometry to figure out its volume. If we increase

the temperature, so let's say we bring it inside, and we really increase the temperature,

the volume is going to increase. And if we really lower the temperature, put it in a

freezer, then we're going to decrease the temperature. And what you'll find is a linear

relationship. And so you could extrapolate that line and we could get to negative 273.

Which is going to be absolute zero. That's when there's no molecular motion and everything

has kind of come to a stop. Now let's look at Avogadro's law. Now we're looking at volume

and n. n remember is going to be the number of moles of the gas that we put in. So let's

look at this simulation right here. Well there's no temperature and no pressure inside the

container. And that's because there's no gas. And so let me squirt a little bit of gas inside

there. As we increase that, now those molecules are going to start bouncing around. And so

we have a specific volume. What do you think is going to happen as I increase the number

of molecules inside there? The number of moles inside there? Well, we're going to try to

keep the pressure constant, try to keep the temperature constant. And what's going to

happen is look, the more molecules we put in there, now we're increasing that. We're

really increasing that volume. And so we've got a direct relationship. More moles, more

volume. And so this is for an ideal gas remember. PV=nRT only works if we have an ideal gas.

What is an ideal gas? It's a gas where these things are randomly moving around. And there

also is no attraction between those. Those molecules aren't pulling on each other. If

they start to pull on each other then this is going to fall apart. And also an ideal

gas only works when we have an infinite number of, an infinite volume, which we're not always

going to have. But let's say we do have an ideal gas. If I just solve for n, this should

always be equal to 1. In other words, PV over RT should always be equal to 1 for any kind

of a gas. And so let me just plot that for a specific gas. Let's say we're looking at

nitrogen right here. It's ideal gas at different pressures should stay exactly at 1.0. But

let me throw up some data. This is what nitrogen looks like at 1000 kelvin. This is what it

looks like at 500 kelvin. This is what it looks like at 200 kelvin. And so these are

real gases. One's that have been measured. And so what are we finding? Is that they don't

fit the ideal gas law. And why is that? Well, as we slow everything down, as we make it

cooler, we start to get attraction between those molecules. And also we are going to

have a finite volume. In other words it's in a container when we're measuring it. And

so what we have to do is we have to start to look at real gas interactions as we get

towards condensation. And what's condensation remember? That's the point at which the gas

becomes a liquid. And so this would be water that was in the air that's becoming liquid

water on this cool bottle right here. And as we get closer and closer to condensation

then we have to throw out some of those ideal gas laws and use real gas interactions. And

so did you learn the following? To use KMT, that's kinetic molecular theory and force

concepts to make macroscopic predictions of what's going on? Remember those are the two

things that guide ideal gas law. KMT, things are moving around. And then this Maxwell-Boltzmann

distribution. They interact with each other, but they're not going to influence each other.

Even though they might bounce into each other. And the idea that faster molecules are generally

going to be lighter in a gas. Also could you apply ideal gas law, PV=nRT. We did that in

a number of different simulations. And then finally could you use this to solve some problems?

And we did this for a basic pressure volume kind of a problem. And so those are gases.

They're everywhere. And I hope that was helpful.