# Kinetic theory of gases

The intermolecular distance between the molecules are much greater than the diameter of the gas molecules so we neglect their volume compared to the volume of container. "The rapidly moving particles constantly collide among themselves and with the walls of the container. All these collisions are perfectly elastic. This means, the molecules are considered to be perfectly spherical in shape, and elastic in nature". How then are molecules thought to be perfectly spherical in shape although its volume is neglected.

• They are thought of as spheres with negligible volume? Which is to say that they do have a volume, but it can be ignored for all practical purposes, because it is small relative to the volume of the container. The average distance separating two such balls is much larger than their combined volume. – getafix Oct 20 '15 at 23:08

The basic explanation that you've recited for the Kinetic Theory of gases is trying to present a simple complete and consistent model which explains the observed behavior. Thus to give a consistent perspective it is easiest to think of gas molecules as elastic spheres. Of course, the assumption about the negligible size of the molecules does indicate that the shape of the molecules is irrelevant to the volume of the gas. But if you consider the molecules as having edges, or different moments of inertia about the three axis then the "simple" model gets too complicated for "simple" mathematics. Think of the all the additional variables that would be needed.

The basic model neglects other factors of course. In the real world gravity plays a part. The atmosphere decreases in density as the altitude increases. So the basic model is trying to illustrate the key factors necessary to understand the kinetic theory of gases, not all the factors.

Edit - The basic gas law PV=nRT has been modified by a number of expressions where correction factors have been used to make the equation more accurate and to give the equation more dynamic range. See some of the equations in the following wikipedia article.

• Thanks MaxW, i have got another question, sorry to bother you again,is it assumed that collision are elastic(no energy is lost) because it is a closed system. – Abmon98 Oct 21 '15 at 0:15
• Elastic collisions and a closed system are mostly independent assumptions. A closed system is mainly implying that neither the gas nor the container is extracting energy from the other. Elastic collisions are mostly about how gas molecules interact with each other. Think of a helium atom (molecule) and an diatomic oxygen molecule. You could really "better" model oxygen as two weights connected with a spring. With such a model calculating how a helium molecule and oxygen molecule would collide would be vastly more complicated mathematically with scant improvement in the model's accuracy. – MaxW Oct 21 '15 at 3:18
• If we model molecules connected together by springs. Does that mean that energy would be conserved?.If there is an elastic collision between one particle and another can one particle stop moving after the collision or not? – Abmon98 Oct 25 '15 at 9:31
• (1) The spring model isn't used for most models. It just makes the mathematics too complicated. But is not wrong. (2)at a given temperature the energy of the molecules is x-y-z movement, vibrational energy within the molecule, and rotation of the molecule. Thus helium would be expected to conform to the ideal gas laws better than oxygen. (3) It is possible, not probable, that an individual molecule could stop dead still before quickly having a collision with another molecule. – MaxW Oct 25 '15 at 16:04
• I edited the answer and added a link to a Wikipedia article that has gas equations with various correction factors. You'd need to tabulate all the experimental gas data and calculate the coefficients and see which equation gives the best results for the gas in which you have an interest. – MaxW Oct 25 '15 at 16:09

I am not a master at this, but from what I know, the volume of the molecule necessarily need not depend on the shape of the molecule. Hence the volume of the molecule does remain negligible when compared to the volume of the gas. Plus, if you must have read about the Vanderwaal's Real Gas Equation although not flawless, accounts for the correction in the Volume of the molecules which we assumed to be negligible in case of Ideal Gases. And as such, in real life we won't encounter a perfectly ideal Gas. So the Real Gas Equation shall help you considerably with your doubt. Hope you understood:-)

• Well wikipedia has a good article (en.wikipedia.org/wiki/Real_gas) on various "real gas" equations. Examination will show that the models just have various "fudge factors" for the basic ideal gas equation PV=nRT. Tables of fudge factors for various models, for a given range of conditions, and for a particular gas would allow more accurate calculations. But the "fudge factors" are determined experimentally, not theoretically. There are models and conditions (e.g. very high pressure) where the volume of the gas molecules is not negligible. – MaxW Oct 22 '15 at 0:16
• I totally agree with what you have to say. And basically what I would say is that chemistry is a subject where you can't predict a las and then check whether it's true or not. You first experiment and based on observations we make laws. Hence though sometimes a law maybe flawless for a particular case it maybe totally useless for another few. – Adit Daftary Oct 22 '15 at 2:28