Hey, guys. So throughout your problems, you may be asked to calculate something called the Mean Free Path. In this video, I want to show you what the mean free path is conceptually, the equations for it, and we'll do a quick example together. Let's check this out. Imagine that I have a canister of gas particles that are sealed inside this little container like this. Now, remember these gas particles aren't stationary. They're all moving all over the place. What happens here is if you look at a random gas particle and its path as it's moving throughout the canister, it eventually travels in a straight line before bumping into another particle. All the collisions are elastic, so these things scatter off in straight lines. But basically, it just keeps on bouncing like this over and over again and these particles just go all over the place. The mean free path is really just the average. That just means the mean distance that the gas particles travel before they collide with another particle. I like to use the analogy of the container gas being like a room full of people. If I'm a person walking through this room and I walk in a straight line, eventually, I'm going to bump into somebody else. If I can only walk in a straight line, I'm just going to keep bumping off people as I walk through the room. So, if the container is full of people, the mean free path is the average distance you walk before bumping into somebody else.

So, how do we calculate it? Well, this is really just a distance. A lot of equations will use lambda for this. Some textbooks might use "l", most of them will use lambda, and this distance here is just equal to velocity times time. Right? This is basically just delta x equals v*t. That's one way to write this. But remember that the goal of the kinetic molecular theory is that we want to express the microscopic properties of the particles, like the distance that they travel, in terms of the variables inside of the ideal gas law, like pressure, volume, and temperature. The equation that you need to know is actually this one:

λ = V 2 ⋅ 4 π r 2 ⋅ nUnfortunately, there isn't really a good way to memorize this equation, but if you ever need it, it will be given to you on a formula sheet. Notice how in the equation, an increase in the number of particles or the radius of a particle decreases the mean free path, because if the number of particles increases or if the particles are physically larger, the average distance before a collision decreases.

We'll check out our example here. We have oxygen molecules at STP. Remember that STP is a set of conditions where the temperature is 273 Kelvin and the pressure is 1.01 ⋅ 10 5 Pa . So, for the first part, we want to calculate the mean free path of oxygen molecules λ₁₄ . We'll use the equation for which we've been given the average speed of the particles. We don't know the time, so we'll use the more complicated equation as follows:

λ = V 2 ⋅ 4 π r 2 ⋅ nWe know the temperature and pressure but need the volume and number of particles. The ideal gas law helps relate these with:

PV = nRTSolving for V/n, we get V n = kBT P . Plugging in values, we find the mean free path for oxygen to be about 93 nanometers.

For the second part, we calculate the average time between collisions using:

T αβεραγε = λ ₂ₒ V αβεραγεThe result is approximately 2.07 times 10^-10 seconds, showing the very rapid collision frequency of oxygen molecules at STP.

That's it for this one. Let me know if you have any questions.