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## Class 11 Physics (India)

### Unit 17: Lesson 1

Ideal gas equation- The ideal gas law (PV = nRT)
- Worked example: Using the ideal gas law to calculate number of moles
- Worked example: Using the ideal gas law to calculate a change in volume
- Calculations using the ideal gas equation
- Derivation of gas constants using molar volume and STP
- Boyle's law
- Charles's law
- Avogadro's law
- Gas mixtures and partial pressures
- Worked example: Calculating partial pressures
- The Maxwell–Boltzmann distribution
- Dalton's law of partial pressure
- Gas phase questions

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# The ideal gas law (PV = nRT)

AP.Chem:

SAP‑7 (EU)

, SAP‑7.A (LO)

, SAP‑7.A.1 (EK)

The ideal gas law (PV = nRT) relates the macroscopic properties of ideal gases. An ideal gas is a gas in which the particles (a) do not attract or repel one another and (b) take up no space (have no volume). No gas is truly ideal, but the ideal gas law does provide a good approximation of real gas behavior under many conditions. Created by Sal Khan.

## Video transcript

- [Instructor] In this
video we're gonna talk about ideal gasses and how we can describe what's going on with them. So the first question you
might be wondering is, what is an ideal gas? And it really is a bit of
a theoretical construct that helps us describe
a lot of what's going on in the gas world, or at least close to what's going on in the gas world. So in an ideal gas, we imagined that the individual particles
of the gas don't interact. So particles, particles don't interact. And obviously we know
that's not generally true. There's generally some
light intermolecular forces as they get close to each other or as they pass by each other or if they collide into each other. But for the sake of what we're
going to study in this video, we'll assume that they don't interact. And we'll also assume that the particles don't
take up any volume. Don't take up volume. Now, we know that that isn't exactly true, that individual molecules
of course do take up volume. But this is a reasonable assumption, because generally speaking, it might be a very, very infinitesimally
small fraction of the total volume of the space that they are bouncing around in. And so these are the
two assumptions we make when we talk about ideal gasses. That's why we're using the word ideal. In future videos we'll talk
about non-ideal behavior. But it allows us to make
some simplifications that approximate a lot of the world. So let's think about how we
can describe ideal gasses. We can think about the volume of the container that they are in. We could imagine the pressure
that they would exert on say the inside of the container. That's how I visualize it. Although, that pressure would be the same at any point inside of the container. We can think about the temperature. And we wanna do it in absolute scale, so we generally measure
temperature in kelvin. And then we could also think about just how much of that gas we have. And we can measure that in
terms of number of moles. And so that's what this lowercase n is. So let's think about how these four things can relate to each other. So let's just always put
volume on the left-hand side. How does volume relate to pressure? Well, what I imagine is, if
I have a balloon like this and I have some gas in the balloon, if I try to decrease the volume by making it a smaller balloon without letting out any other air or without changing the temperature, so I'm not changing T and n, what's going to happen to the pressure? Well, that gas is going
to, per square inch or per square area, exert
more and more force. It gets harder and harder for
me to squeeze that balloon. So as volume goes down, pressure goes up. Or likewise, if I were to
make the container bigger, not changing, once again, the temperature or the number of moles I
have inside of the container, it's going to lower the pressure. So it looks like volume and pressure move inversely with each other. So what we could say is
that volume is proportional to one over pressure,
the inverse of pressure. Or you could say that
pressure is proportional to the inverse of volume. This just means proportional to. Which means that volume would be equal to some constant divided
by pressure in this case. Now how does volume relate to temperature? Well, if I start with my balloon example, and you could run this example
if you don't believe me, if you take a balloon and you were to blow it up at room temperature, and then if you were to
put it into the fridge, you should see what happens. It's going to shrink. And you might say, "Why is it shrinking?" Well, you could imagine that the particles inside the balloon are a little less vigorous at that point. They have lower individual
kinetic energies. And so in order for them
to exert the same pressure to offset atmospheric
pressure on the outside, you are going to have a lower volume. And so volume you could say is
proportional to temperature. Now how does volume
compare to number of moles? Well, think about it. If you blow air into a balloon, you're putting more
moles into that balloon. And holding pressure and
temperature constant, you are going to increase the volume. So volume is proportional
to the number of moles. If you were to take air out, you're also going to decrease the volume, keeping pressure and temperature constant. So we can use these three relationships, and these are actually known as, this first one is known as Boyle's law, this is Charles' law,
this is Avogadro's law. But you can combine them to
realize that volume is going to be proportional to
the number of moles times the temperature divided by the pressure. Divided by the pressure. Or another way to say it is, you could say that volume is going to
be equal to some constant, that's what proportionality
is just talking about, is gonna be equal to some
constant, let's call it R, times all of this business, RnT over P. Over P. Or another way to think about it is we can multiply both sides by P. And what will you get? We will get P times V,
this might be looking somewhat familiar to some of you, is equal to, and I'll just change
the order right over here, n, which is the number of moles, times some constant times T, our temperature measured in kelvin. And this relationship right
over here, PV is equal to nRT, is one of the most
useful things in chemistry. And it's known as the ideal gas law. And in future videos
we're going to apply it over and over again to
see how useful it is. Now, one question you
might be wondering is, "What is this constant?" It's known as the ideal gas constant. And you can look it up, but
it's going to be dependent on what units you use for a pressure or volume and temperature. And we will see that in future videos.