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- [Instructor] In this video, we're gonna talk about something called kinetic molecular theory,
which sounds very fancy. But as we'll see in the next few seconds, or the next few minutes, it actually helps build our intuition for what is actually going on with the gas or at least an approximation of what's going on with the gas. So first, let's think
about the types of things that we know we can measure about a gas at a macro level. Now, what do I mean at a macro? I'm saying at a large scale,
at a scale that's much larger than the scale of atoms or molecules. And we know the types of
things that we can measure. We can measure pressure. How do we do you do that? Well, pressure is just
force per unit area. So, you can do this. There's various contraptions
you can use to measure pressure depending what you're using it for. Force, you can measure with springs and you can apply a certain
forces to certain square areas. But these are all ways that
you can measure pressure and we can measure the pressure
of a gas in a container. You can measure volume of a container. That's actually pretty straightforward. You can imagine a container that looks something
like this, it's volume. We know how to find the volume of a rectangular prism like this, or even if it was sphere or
some other type of figure. There's many ways of measuring the volume without even being able to observe or even know that things
like molecules exist. We know how to measure temperature, and we can do that in different scales. Kelvin is what we use 'cause
it's more of an absolute scale, but you can use literally thermometers to measure temperature. And once again, you
can measure temperature without knowing anything
about atoms or molecules or whether they even exist. And you can also measure
an amount of a substance. And in particular, we could say, you can measure the number of moles. Now you might say don't moles
involve a certain number of a molecule or an atom. Well, they do, but the notion
of a mole actually existed even before we knew
exactly how many molecules, how many particles made up a mole. It was just viewed as an amount where people knew it must
be some number of particles, but they didn't know exactly. So all of these things, we
can measure at a macro level. And we know that we can connect them all with the ideal gas equation that tells us that pressure times volume is equal to the amount of
the gas we're dealing with. And this is, of course, we're
talking about an ideal gas and in future videos, we'll talk about how some gases
approach being an ideal gas while some are less than ideal. But the amount we have
measures the number of moles. You have your ideal gas constant that just helps us make
all the units work out depending on our units
for everything else. And then you have your
temperature measured in Kelvin. And, scientists long before
we were actually able to know about things like
atoms or even observe atoms or molecules directly, or even indirectly, they were able to
establish this relationship using these macro measurements. But how do these macro
measurements and this relationship actually make sense at a molecular level? And that's what kinetic
molecular theory provides us. It says, imagine the gas is being made up of a bunch of really,
really the small particles. Those are really the gas molecules. And their collective volume is very small compared to the volume of the container. So, it's mostly empty space
between those particles. Now, the pressure is
caused by these particles bouncing into the sides of the container. Because at any given moment, you have enough particles
bouncing off the side of any unit area that it's
providing a force per unit area. It's providing a pressure. It assumes that those collisions are what's known as elastic, which we'll study in much more
detail in a physics course, but it really says that your
kinetic energy is preserved. You might already be
familiar with the notion that kinetic energy is equal to one half times mass times velocity squared. And so the kinetic energy
of these particles, when they bounce off,
their mass doesn't change. The mass of the particles still there. And we're saying that the
velocity is going to be preserved. So you have all of these
really small particles, even their collective volume is small compared to the volume of the container. They're providing the pressure by having these elastic collisions with the side of the container. And temperature is related
to the average kinetic energy of these particles. It would be proportional. The higher the temperature, the higher average kinetic energy. Now average kinetic
energy is really important because some of these particles might be moving faster than others. And of course, N, the number of moles, tells us how many particles
we're dealing with. We know that each mole has
Avogadro's number of particles. So, if you just multiply the
most times Avogadro's number, you have the number of particles. And what's cool about
kinetic molecular theory, I know it's built as a theory, but this is fundamentally what chemists and physicists visualize when they imagine a gas in
a container of some kind. And just to make it a
little bit more clear, the axioms you could say of
kinetic molecular theory, the assumptions of it,
I'll give them here. And it's important to realize
that these are assumptions and the real world, we have
slight variation from it, but these assumptions get us a long way to explaining the behaviors of gases. So, we've already talked about it. Gas consists of particles
in constant random motion. We've already talked about that. They're bouncing off the
side of the container. The combined volume of the
particles is negligible compared to the total volume
in which the gas is contained. And that also matters when you talk about
things like ideal gases, because if it stops becoming negligible, then you have to start
thinking about the repulsive and attractive interactions,
a little bit more. The particles exert no attractive or repulsive forces on each other. And that kind of builds into
the last point I just made, which is if they did, then we're getting closer to
being a less than ideal gas. And we'll talk about that in other videos. The collisions between the
particles are completely elastic. So, they preserve kinetic energy and it's actually, they
would also preserve momentum. And that the average kinetic
energy of the particles is proportional to the Kelvin temperature. And we already talked about that, that the macro variable, the macro measurement of temperature is giving us an indication, it's proportional to the
average kinetic energy of the particles.