0.11 The kinetic molecular theory  (Page 3/7)

Therefore, it is a characteristic of a gas that the molecules are far apart from one another. In addition, thelower the density of the gas the farther apart the molecules must be, since the same number of molecules occupies a larger volume atlower density.

We reinforce this conclusion by noting that liquids and solids are virtually incompressible, whereas gases areeasily compressed. This is easily understood if the molecules in a gas are very far apart from one another, in contrast to the liquidand solid where the molecules are so close as to be in contact with one another.

We add this conclusion to the observations in and that the pressure exerted by a gas depends only on the number of particles in the gas and is independent of the typeof particles in the gas, provided that the density is low enough. This requires that the gas particles be far enough apart. Weconclude that the Ideal Gas Law holds true because there is sufficient distance between the gas particles that the identity ofthe gas particles becomes irrelevant.

Why should this large distance be required? If gas particle A were far enough away from gas particle B that theyexperience no electrical or magnetic interaction, then it would not matter what types of particles A and B were. Nor would it matterwhat the sizes of particles A and B were. Finally, then, we conclude from this reasoning that the validity of the ideal gas lawrests of the presumption that there are no interactions of any type between gas particles.

Postulates of the kinetic molecular theory

We recall at this point our purpose in these observations. Our primary concern in this study is attempting torelate the properties of individual atoms or molecules to the properties of mass quantities of the materials composed of theseatoms or molecules. We now have extensive quantitative observations on some specific properties of gases, and we proceed with the taskof relating these to the particles of these gases.

By taking an atomic molecular view of a gas, we can postulate that the pressure observed is a consequence of thecollisions of the individual particles of the gas with the walls of the container. This presumes that the gas particles are in constantmotion. The pressure is, by definition, the force applied per area, and there can be no other origin for a force on the walls of thecontainer than that provided by the particles themselves. Furthermore, we observe easily that the pressure exerted by the gasis the same in all directions. Therefore, the gas particles must be moving equally in all directions, implying quite plausibly that themotions of the particles are random.

To calculate the force generated by these collisions, we must know something about the motions of the gasparticles so that we know, for example, each particle’s velocity upon impact with the wall. This is too much to ask: thereare perhaps $10^{20}$ particles or more, and following the path of each particle is out of the question. Therefore, we seek a model whichpermits calculation of the pressure without this information.