The aggregate volume of all the molecules in a given mass of gas may be obtained, to a rough approximation, by several methods, among which we may mention the so-called gas equation," which exhibits the relation between thepressure, density and tem perature of a gas. Equations of this sort have been given by Van der Waals, Clausius and others, and in them a term occurs whose value depends upon the proportion that the bulk of the actual molecules bears to the total bulk of the gas that they constitute. The numerical magnitude of this term may be determined by experiments upon the variation of the pressure of a gas with temperature and density, and hence the aggregate bulk of all the molecules may be determined in a somewhat approximate manner. Roughly, it may be said that at ordi nary densities, the actual total bulk of all of the molecules of a gas is from the thousandth to the ten-thousandth part of the bulk of the entire gas.
We are still far from being able to calculate the diameter of a molecule with any degree of precision, although we have no doubt advanced considerably beyond the point at which we stood when the first edition of the Encyclopedia Americana was published, for at that time ask ing how big a molecule is was much like asking "How big is a crowd?" The question could be answered only in an exceedingly crude way. We now know the individual masses of mole cules with a considerable degree of precision, as will presently be shown; but we cannot hope to be able to determine the geometrical dimen sions of molecules in more than a general way, until we attain to a clearer understanding of the physical constitution of these bodies. It is conventional, at the present time, to under stand, by the expression of a mole cule" the diameter of the smallest sphere that can be imagined to be drawn around the mole cule, consistently with the condition that noth ing could collide with the molecule without penetrating this sphere. German writers have called this imaginary sphere the "Wirkimigs sphare," and French writers call it the °sphere de choc" or "sphere de protection." Clausius and Maxwell showed that the diameter, d, of this collision-sphere may be calculated, in gase ous substances, by means of the expression 1 where d is the diameter in centimeters, L is the mean free path in centimeters and n is the number of molecules present in each cubic cen timeter. The application of this formula to actual gases gives the following values of d (Perrin) : These values, although admittedly crude, are probably of the right general order of magni tude. See below for determination of n.
Considerable progress has been made in the last few years in the way of determining the masses of molecules, and the number of mole cules that exist in a given quantity of matter.
Some of the methods that have been proposed depend more or less directly upon a knowledge of the way in which the kinetic energy of a molecular aggregation is divided or partitioned among the constituent molecules. Our present knowledge with regard to molecular kinetic energy rests on a fairly sound basis in the case of gases, but it is still largely (though not wholly) conjectural in connection with liquids and solids. To facilitate the statement of the facts indicated by the kinetic theory of gases, let us assume that in any given mass of gas there are three intersecting and mutually per pendicular straight lines drawn in fixed posi tions in space, and let us call these lines the axes of X, Y and Z, respectively. The X-axis, for example, may extend in a north-and-south direction and the Y-axis in an east-and-west direction. The Z-axis will then be vertical. The individual molecules will be moving in every possible direction, and with the greatest imaginable variety of speeds, but we may simplify matters somewhat by conceiving the velocity of every one of them to be resolved into three components, each parallel to one of the three fixed axes we have drawn. Then, confining our attention for the moment to a gas containing molecules of only one kind, the kinetic theory tells us that one-third of the total kinetic energy that the molecules of the gas have, in virtue of their motions of translation, will be accounted for by the components that are parallel to each of the three fixed refer ence axes. Furthermore, if each molecule (so far as concerns the applicability to it, as a whole, of the accepted laws of mechanics) is assumed to be a rigid, elastic body in rotation, and if the rotation of every such molecule is resolved into component rotations about axes passing through the centre of gravity of the molecule, and drawn parallel to the fixed axes of X, Y and Z, respectively, a similar statement may be made with regard to the rotational energy. Namely, one-third of the total kinetic energy represented by the rotations of the molecules will be accounted for by the com ponent rotations about the axes that are par allel to the axis of X, and the remaining two thirds will be accounted for by the component rotations about the axes that are parallel to the axes of Y and Z, respectively. Furthermore, the aggregate kinetic energy due to the transla tory motion of the molecules in any one given direction is equal to the total kinetic energy due to the component rotations of the mole cules about axes parallel to any one given di rection. For the modifications to which this principle is subject when it is applied to mole cules that have a number of degrees of freedom greater or less than six, reference should be made to GASES, KINETIC THEORY OF.