0.11 The kinetic molecular theory

Foundation

We assume an understanding of the atomic molecular theory postulates, including that all matter is composedof discrete particles. The elements consist of identical atoms, and compounds consist of identical molecules, which are particlescontaining small whole number ratios of atoms. We also assume that we have determined a complete set of relative atomic weights,allowing us to determine the molecular formula for any compound. Finally, we assume a knowledge of the Ideal Gas Law , and the observations from which it is derived.

Goals

Our continuing goal is to relate the properties of the atoms and molecules to the properties of thematerials which they comprise. As simple examples, we compare the substances water, carbon dioxide, and nitrogen. Each of these iscomposed of molecules with few (two or three) atoms and low molecular weight. However, the physical properties of thesesubstances are very different. Carbon dioxide and nitrogen are gases at room temperature, but it is well known that water is aliquid up to 100°C. To liquefy nitrogen, we must cool it to -196°C, so the boiling temperatures of water andnitrogen differ by about 300°C. Water is a liquid over a rather large temperature range, freezing at 0°C. In contrast,nitrogen is a liquid for a very narrow range of temperatures, freezing at -210°C. Carbon dioxide poses yet anothervery different set of properties. At atmospheric pressure, carbon dioxide gas cannot be liquefied at all: cooling the gas to-60°C converts it directly to solid "dry ice." As is commonly observed, warming dry ice does notproduce any liquid, as the solid sublimes directly to gas.

Why should these materials, whose molecules do not seem all that different, behave so differently? What are theimportant characteristics of these molecules which produce these physical properties? It is important to keep in mind that these areproperties of the bulk materials. At this point, it is not even clear that the concept of a molecule is useful in answering thesequestions about melting or boiling.

There are at least two principal questions that arise about the Ideal Gas Law . First, it is interesting to ask whether this law always holds true, or whether there are conditionsunder which the pressure of the gas cannot be calculated from $\frac{nRT}{V}$ . We thus begin by considering the limitations of the validity of the Ideal Gas Law . We shall find that the ideal gas law is only approximately accurate and that there are variations which do depend upon thenature of the gas. Second, then, it is interesting to ask why the ideal gas law should ever hold true. In other words, why are thevariations not the rule rather than the exception?

To answer these questions, we need a model which will allow us to relate the properties of bulk materials tothe characteristics of individual molecules. We seek to know what happens to a gas when it is compressed into a smaller volume, andwhy it generates a greater resisting pressure when compressed. Perhaps most fundamentally of all, we seek to know what happens toa substance when it is heated. What property of a gas is measured by the temperature?