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As you read ebook section 12.1, please skip the rms speed calculations (i.e. E12-1-3). I only expect you know the relative relationship of temperature and mass on molecular speed. In section 12.2, only read to the end of Figure 12-2-1. We will be skipping effusion and diffusion.

Now, we will revisit kinetic molecular theory, which we introduced when we learned about IMFs, and we will use it to model the behavior of gases. As we saw earlier in the course, the central idea behind kinetic molecular theory is that molecules are in constant motion (i.e., molecules have kinetic energy). When kinetic molecular theory is used to model the behavior of gases, it uses the five key postulates that are shown below. Postulate 1 is really important. It states that the average amount of kinetic energy that the gas contains (abbreviated with the Greek letter epsilon, ε) is proportional to temperature. In other words, the average kinetic energy in the gas is determined solely by the temperature. The identity of the gas doesn’t matter, thus any two gases will have the same average kinetic energy if they are at the same temperature. The higher the temperature, the more kinetic energy the molecules have on average. Postulates 2-4 are largely self-explanatory. When we say “elastic collisions” in postulate 5 we mean that when gas molecules collide, the total amount of kinetic energy stays the same (kinetic energy isn’t converted into potential energy during collisions).

1. The mean (average) kinetic energy (ε) is proportional to temperature (in Kelvin)
2. Particles move in straight lines; their direction is random
3. Molecules are small. The volume of the molecules is much smaller than the volume of the container.
4. Molecules do not attract or repel each other (no IM forces).
5. Molecules experience elastic collisions.

These postulates are part of a theoretical model used to describe the behavior of gases. Gases that perfectly follow all of these postulates are known as ideal gases (they behave ideally). In reality no gas is perfectly ideal, and in fact there are times when engineers deliberately make a gas behave non-ideally, but under most conditions, most gases are pretty close to ideal. Therefore, this model is useful for describing the behaviors of most gases.

Molecular Speeds

Molecular speed is influenced by temperature and molar mass. As we have discussed, the kinetic energy is proportional to temperature. At higher temperatures, molecules are moving faster. With respect to mass, faster molecules will move slower than lighter molecules at constant temperature.