0.14 The kinetic molecular theory  (Page 5/8)

If the molecules remain the same size but occupy a much larger space, there is only one possible conclusion: the molecules in the gas must be much farther apart in the gas than in the liquid. These distances must be very large. To see this, imagine a crowded elevator completely filled with people who are elbow-to-elbow. When the door opens, imagine that they now enter a room which is 1000 times larger than the elevator. Assuming that the people spread out, think about the large distances between people is this huge room. The space between people is much larger than the size of each person. In fact, the space is so large that the sizes of the individual people become insignificant. In the crowded elevator, the sizes of the people matters. But in the open room, the distances between people are so large that the distances between people are the same whether they are adults or children.

And this must be true of molecules as well. In a gas, the spaces between molecules must be very large, so large that the size of each molecule is insignificant. If we combine this conclusion with our conclusion from Observation 1, we can begin to build a model to explain why the Ideal Gas Law works provided that the gas density is not too high. At reasonable gas densities, the molecules are so far apart that the differences in size, shape, and structure of individual molecules are unimportant.

Observation 3: dalton’s law of partial pressures

An interesting observation related to the Ideal Gas Law is Dalton’s Law of Partial Pressures. We observed this in the previous Concept Development Study. Dalton’s Law described the pressure of a mixture of gases. Let’s say we mix oxygen and nitrogen, as in our atmosphere, and let’s take them in the same approximate proportions as in our atmosphere. In a container of fixed volume, we can put in enough nitrogen to create a pressure of 0.8 atm. We could also put in enough oxygen to create a pressure of 0.2 atm. If we take that same amount of nitrogen and that same amount of oxygen and put them both in the same fixed volume container, we find that the pressure is 1.0 atm. In other words, the total pressure of the gas is equal to the sum of the individual pressures of the gases, called the “partial pressures.”

This observation tells us that the oxygen molecules create the same 0.2 atm pressure whether the nitrogen molecules are present or not. And the same is true of the nitrogen molecules, which create a pressure of 0.8 atm whether or not the oxygen molecules are present. This is a striking observation. It means that the oxygen molecules in a mixture with nitrogen molecules must move in exactly the same way that they would if the nitrogen molecules were not there. It appears from our observations that the motions of the nitrogen molecules and the oxygen molecules do not affect each other at all.

We need to think about why this would be true. If we add this conclusion to the conclusions of Observations 1 and 2, we can see that the molecules in a gas are very far apart from one another and they do not affect each other’s movements. This makes sense: if the molecules are so far apart from one another, then they never affect each other. More specifically, they never (or almost never) exert forces on each other or run into each other.