- [Instructor] We've already spent some time
looking at the ideal gas law, and also thinking about
scenarios where things might diverge
from what at least the ideal gas law might predict.
And what we're going to do in this video
is dig a little bit deeper into scenarios
where we might diverge a little bit
from the ideal gas law, or maybe I guess, a lot of it
in certain situations.
So I have three scenarios here.
This first scenario right over here,
I have a high temperature, high temperature,
and I have a large volume.
And both of these are really important
because when we think about when we get close
to being ideal, that situation's where the volume
of the particles themselves are negligible to the volume
of the container.
And at least here, looks like that might be the case
'cause we're dealing with a very large volume.
Even this isn't drawn to scale.
I just drew the particles this size
just so that you could see them.
And high temperature, that helps us realize
that well maybe the intermolecular interactions
or attractions between the particles
aren't going to be that significant.
And so in a high temperature, large volume scenario,
this might be pretty close to ideal.
Now it's not gonna be perfectly ideal
because real gases have some volume,
and they do have some intermolecular interactions.
But now let's change things up a little bit.
Let's now move to the same volume.
So we're still dealing with a large volume.
But let's lower the temperature.
So low temperature.
And we can see because temperature is proportional
to average kinetic energy of the particles,
that here, these arrows on average are a little bit smaller.
And let's say we lower the temperature
close to the condensation point.
Remember, the condensation point of a gas,
that's a situation where the molecules are attracting
each other, and even starting to clump up together.
They're starting to, if we're thinking about say,
water vapors, they're starting to get into little droplets
of liquid water, because they're getting so attracted
to each other.
So in this situation,
where we have just lowered the temperature,
the ideal gas law would already predict that if you keep
everything else constant, that the pressure would go down.
If we solve for pressure,
we would have P is equal to nRT over V.
So if you just lowered temperature,
the ideal gas law would already predict
that your pressure would be lower.
But in this situation with a real gas,
because we're close to that condensation point,
these gases, these particles are more and more attracted
to each other.
So they're less likely to bump into the sides
of the container, or if they do,
they're going to do it with less vigor.
So in this situation for a real gas,
because of the intermolecular attraction
between the particles, you would actually have
a lower pressure than even the ideal gas law would predict.
Ideal gas law would already predict
that if you lower the temperature, pressure would go down.
But you would see that a real gas in this scenario,
P, even lower, even lower for a real gas.
Now let's go to another scenario.
Let's go to a scenario where we keep the high temperature
that we had in the original scenario,
but now we have a small volume, small volume.
Maybe this top of the container is a piston,
and we push it down like this.
Well the ideal gas law, if we just solve for P again,
P is equal to nRT over V.
It would already predict
that if you decrease the denominator here,
that's going to increase the value of the entire expression.
So it would already predict that you would have
a higher pressure, that the particles will bounce
into the sides of the container more frequently,
and with more vigor.
But if we have a really small volume of the container,
we no longer can assume that the volume
of the particles themselves are going to be negligible
compared to the volume of the container.
And so the effective volume, to move around in
is even lower than we're seeing in this equation.
So these particles have even less space to bounce around in
because they take up some of the space.
So they're going to bounce off the sides of the container
more frequently and even more vigor.
So here, pressure even higher for a real gas
than what is predicted by the ideal gas law.