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## Ideal gas equation

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# Introduction to partial pressure

## Video transcript

- [Voiceover] Partial
pressure is the pressure that is exerted by one gas when
you have a mixture of gases. So it's a pressure from
one gas in a mixture, and we're going to be talking about gases that behave like ideal gases. The important thing to
remember about ideal gases for this particular application is that they behave, the gas molecules the gas molecules behave independently. What I mean by that is that well, that's exactly what it means. They don't care. If you're a gas mixture,
if you're a gas molecule in this mixture, you don't actually care what the other molecules are doing. You kind of just do your
own thing no matter what. So if I were to draw a picture
of what this might look like, let's say we have this container and our container has nitrogen gas in it. And the nitrogen gas
is going to be purple. So we have these nitrogen
gas molecules in here. That's N2 and the gas molecules are whizzing around in the
box with some velocity, and the velocity and
direction of the gas molecules I'm going to indicate with these arrows. And they're flying around,
they're bouncing off the walls of the container, and when
they bounce off the walls of the container, they create pressure. So for this particular example, the pressure of our
container, of the gases in our container rather
is two atmospheres. And so each of these gas molecules, it's doing its own thing,
and it's not interacting with other molecules, but
let's say we add another gas. So we have our container
and we add some oxygen gas. And I'm going to draw the
oxygen molecules in pink. Our container has the same volume, and we haven't changed the temperature. And there's no reaction going on either, so we still have our molecules of N2, and they're still flying around with the same average velocity because the temperature didn't change except now, we also have
additional gas molecules. Let's actually make that green. So now we have these other
gas molecules in here, and these are the O2 molecules. So that's O2, and they're also, they're also moving with some velocity. So now we have more gas molecules than we had originally, and our pressure has gone up as a result. So the pressure of the
gases in our container, which I will call the total pressure. The total pressure is now 2.5 atmospheres. We might ask ourselves, "What is "the partial pressure of the nitrogen "or the partial pressure of the oxygen?" And that is usually written
with this kind of notation, with the little subscript for whatever you're trying to figure out, and we said earlier that the gas molecules behave independently, and because
they behave independently, we can actually just add
up the partial pressures in a mixture to get the total pressure. So one equation that you'll
see for partial pressure is that the total pressure is just equal to the sum of all of the
gases in your mixture, all of the partial pressures
of the gases in your mixture. Plus dot, dot, dot, and
this is called Dalton's Law of partial pressures. So that is one way that we can figure out the partial pressure. If we know the total pressure and we know the partial pressures
of all the other gases in our mixture, we can actually figure out the one unknown partial pressure, and that's how we're gonna do it here. So if we write this out
for our particular system, we can say P total, which
we know the total pressure. Here, it's 2.5. We know that P total must be equal to the partial pressure from the nitrogen plus the partial pressure from the oxygen. We actually know with a
partial pressure for nitrogen. The partial pressure for nitrogen is actually 2.0 atmospheres. It doesn't actually change here. So partial pressure of nitrogen
is still 2.0 atmospheres even though we added oxygen gas, and the reason why that
is is because well, the ideal gas law says, the ideal gas law says PV equals nRT, and if we rewrite this
in terms of the pressure, it's just P equals nRT over volume. And so if our nitrogen gas is
behaving like an ideal gas, its pressure will only change if we change the number of moles of gas,
the temperature, or the volume. And since we've done none
of those things here, we just added another gas,
since we didn't change the moles of gas, temperature, or volume, the partial pressure, or the pressure exerted by the nitrogen gas molecules is still going to be two atmospheres. So then, we know that P
total is 2.5 atmospheres and the partial pressure of nitrogen, as we just mentioned, is 2.0 atmospheres and then we want to still figure out the partial pressure of oxygen. But now, we can just
rearrange this equation to find P O2. So P O2 is equal to our total
pressure, 2.5 atmospheres minus the partial pressure of nitrogen. So we can see that our partial pressure of oxygen is just 0.5 atmospheres. So now, we know how to use this particular expression of Dalton's
Law of partial pressures to find a partial pressure when you know the total pressure and the other partial pressures.