Definition of an ideal gas, ideal gas law

- [Instructor] Okay, in our last video, we talked about gas pressure, and we got on that subject by making some observations about the air that's inside of a balloon. So, I've got a red balloon, and I'll give it a white string. The balloon gets a string, and then getting back to the observations that we're talking about, for example, we said that pressure, and the pressure inside the balloon was really a measure of the force attributed to all the gas particles colliding with the sides of the balloon walls. So, we've got our particles and they're colliding against the sides of our balloon, and given that temperature is a measure of the energy of those particles in motion, we said that increased temperature would mean increased pressure. Because, if you think about it, all those particles would be moving faster with greater temperature, and just like a speeding car would crash into a wall with more force, these little particles, once they get bumping, they exert more force and increase the pressure. So, written mathematically, we would say that pressure and temperature are directly related. As the temperature is increased, so is the pressure. And we also saw that as volume goes down, the pressure goes up. And again, this makes sense because with less space to move around, the particles will have more collisions with the walls, so pressure will increase. And again, written mathematically, this means that pressure is inversely related to volume, so pressure is related to the inverse of volume, because we see that as the volume is decreased, the pressure is increased. And then we also showed that increasing the number of moles of gas would increase the pressure because moles are just a measure of the number of particles, so if we have more particles, we have more collisions. So again, pressure is directly proportional to moles, and n is the symbol for moles. Now, based on these empirical observations, which means observations that we can actually see, as opposed to just theory, we have the composite formula, if we put them together, we see that pressure is directly related to the moles and the temperature, and inversely related to volume. And so, we have this composite formula, P is directly related to nT over V. And we can make this composite formula an equation if we add a constant. And we could call the constant anything, but we'll call it R. And that'll give us P is equal to R times, and that's our constant, times nT over V. And so, if we multiply both sides by V and do just a little bit of rearranging, we're gonna get a pretty important equation called the ideal gas equation, which is PV is equal to nRT, so PV equals nRT, and we call this the ideal gas equation. So, ideal gas equation. And if you're like me, you're probably immediately curious about what that blue R is, and don't worry, I'm gonna show you how we derive that in the next video, but for now I just want you to enjoy how profound this equation is. And think about what we can do with it. For example, if we know the pressure and the volume and we know the temperature, we can use this formula to find the number of particles that are in the system, and if we know the number of particles and we know the volume and the temperature, we can find the pressure. If we know the number of particles and we know the volume and we know the pressure, then we'd be able to solve for the temperature. And it's pretty incredible, and this is true for any ideal gas. So, the next kinda obvious question is what's an ideal gas? Well, an ideal gas is one that obeys three conditions: the first condition is that the molecules can't exhibit any intermolecular forces, so no intermolecular forces. And we make this condition because if there were intermolecular forces, it would interfere with our assumption that all of our kinetic energy is completely directed to the pressure, so that's our first condition. And the second condition is that the molecules occupy no microscopic volume. In other words, the molecules are point masses and have no volume. And we make this condition because in our equation here, moles and volume are directly related, n is directly related to V, but if our particles take up space, then as they're added, the container's volume would actually go down instead of going up. But the particles are extremely tiny, so kind of assuming their point masses isn't that far-fetched, and it allows our equation to make sense. So, this is an ideal gas, no volume. Now, the third condition is that all collisions are perfectly elastic, so collisions are perfectly, perfectly elastic, because again, we need to assume that none of our kinetic energy is lost in the collisions of these particles. So, we make these three conditions, and while no gases are actually ideal, the ideal gas equation does get us some pretty close approximations, and it helps us answer lots of questions, especially those related to the kind of the before and after conditions when we're changing some of these values for a gas. So, the next step, I'm gonna explain a little bit more about the ideal gas constant, and we'll kinda dig into this R value, and then we're gonna move forward with some specifics about the ideal gas equation.