From: Lara Kipperman (chemkipp@mac.com)
Date: Sat Oct 11 2003 - 10:31:46 PDT
Date: Sat, 11 Oct 2003 10:31:46 -0700 Subject: re: real gases/van der waals From: Lara Kipperman <chemkipp@mac.com> Message-Id: <C9DE72C0-FC10-11D7-96E1-000502B71BAF@mac.com>
Sally,
You have the basic concepts correct but you've confused a few things.
So, I'll try to clear it up for you. :)
As you know, PV=nRT is the ideal gas law. I think of Van der Waals (P
+ na^2/V^2)(V - nb) = nRT as the real gas law.
As you know, we humans like to understand things in the pure sense
(ideally) before we apply those principals to the real world because
the real world can be a really crazy place! We generalize, we
classify, and we estimate to simplify things. PV=nRT does all that for
us.
Yes, gas molecules do, in reality take up space. And also, yes, gases
do experience attractions (like LDF and dipole-dipole). Van der Waals'
equation can describe that reality for us.
However, if we idealize the gases (using KMT) to say that that the
volume occupied by the gas is very small compared to the volume of a
container and to say that the pressure affected by the gas is very
small compared to the pressure of the collisions against the walls of
the container, we can use our real world measurements and plug them
right into the ideal gas law. And, as a result, in reality, for a
simple, nonpolar gas, PV=nRT is a very good method.
The pressure component times the volume component IS directly related
to the moles times the temperature as in the ideal gas law.
But as you said, PV=nRT breaks down at low temperatures and high
pressures for the following reasons that you mentioned:
1.
> At low temperatures, the molecules are moving more slowly and
> therefore do
> experience attractive forces. This causes molecules headed for the
> container
> wall to experience a slight pull back into the container and thus the
> force
> with which they hit the wall is slightly lower than we expect.
Think about how this would affect the MEASURED pressure. It would be
too small. We have to ADD BACK IN the component of pressure caused by
those interactions. So, that yields the first part of van der waal's
eqn... (P + na^2/V^2)
2.
> Likewise, at high pressure, the molecules do take up some space, so the
> calculated volume is less than the experimentally measured volume.
Right, the measured volume would be too big because the combined volume
of the gas particles has impact, so as a result, we need to subtract
off the volume the gas particles "occupy" and as a result have the
second correction to the law (V - nb)
I think of it this way -- van der waals is the real mccoy but it's not
necessary for normal conditions with simple gases so we can just use
the much much simpler ideal gas law. Our students should understand
that we're idealizing whenever we use PV=nRT. We're leaving in the
volume of the gases and ignoring their interactions whenever we use the
ideal gas law. If the volume and interactions have value, we should
use the more complex van der waals equation.
Best,
Lara Kipperman
GWHS
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