Hey, everybody. So let's go ahead and check out this problem here. We have a graph that shows the probability distribution for oxygen gas. Remember that this probability distribution applies to a specific temperature, so there's one specific temperature of this curve right now. For example, if the curve looked like this, it would have a different temperature, and if it looked like this, it would have an even different temperature. What we want to do is figure out the temperature of this sample of oxygen gas, given that the probability curve looks exactly like this. The one thing that we are told here is that the farthest tick mark on the x-axis is 1200 meters or meters per second. We are also told what the molar mass of oxygen is. Let's go ahead and get started. Which equation are we going to use in our probability distributions? Remember, there are three of them: the most probable, the average, and the RMS. This right here is the most probable velocity. It's the very top of the curve. So, how do we find what this velocity is? We can use our scale here for the velocity. Working backwards, if this is 1200 and there is equally spaced, this is going to be 11, 10, 9, 8, 7, 6, 5, and 400 meters per second. Right? This is 300, 200, and 100. We're having to work backwards to figure out what the tick marks are, but then if you look ahead, you'll see that this line corresponds perfectly to the dot that I just drew. We can tell from this graph that the most probable velocity here is 400 meters per second. Now that we know what this most probable velocity is, we know we're going to be looking at this equation over here. Because what's the target variable again? Remember, we're looking for the temperature.

We're going to use the V_MP equation. We're told what the molar mass of oxygen is, so we're just going to use this format over here, the one with capital M. We have that V_MP is equal to the square root of 2RT divided by big M. Now that we know the V_MP is the velocity we found, which was 400 meters per second, we're going to square this to get rid of the square root, making it 400², removing the square root, resulting in 2RT divided by big M. Now, we just need to move this m to the other side and then divide by 2R. Putting this all together, we have 400² times the molar mass, which is given in grams per mole but should be converted to 0.032 kilograms per mole. So, this is going to be times 0.032, then we just divide by 2 times 8.314. This calculation will give us the temperature, and if you work this out, what you're going to get is 307.9 degrees Kelvin. That's the answer.

Alright folks, that's it for this one.