ADSOLUTE DIMENSIONS OF MOLECULES.
The fundamental hypotheses of the kinetic the ory of gases lead to the proposition that at any given temperature the volume of a gas is in versely proportional to its pressure, This rela tion. \vide!) had been known as a matter of fact long before it was established deduetively, may also be expressed by saying that the product of the pressure and volume of a gas is constant: C.
From the point of view of the kinetic. theory. p represents in this formula the empty space with ill Which the molecules of the gas move—i.e. the total volume tilled by the gas, minus the volume actually occupied by its molecules. long the gas is not too highly compressed, the total volume may be used in the above formula instead of the unknown intiqmolecular space. For. under low pressures, the difference between the volume of a gas and the volume of its empty intermolecular space is very slight. and hence the error emm»itted amount; practically to nothing. But as the pressure exert... I on the gas increases, its volume beeumes small. and the fraction Of that volume actually ovenpied by the nodtwules considerable. In other words. the difference between the volume tilled by the gas and the empty intermolecular space 110,1.0111VA too great to be neglected. the same time as the distance betfleent the molemdes be comes smaller. they begin to exercise a certain amount of attraction upon one another. and therefore the pressure exerted by I he _•as on the vessel containing it is somewhat diminished. toiler such t he simple formula men( Mined above ceases. 111 exprev+ the between the observed pressure and volume of gases, and the formula. first sug
gested by Van der Wails. has to be employed instead: In this formula p denotes the pressure actually observed. To conform to the theoretical law, we add to it the quantity depending on the specific mutual attraction of the molecules, and therefore also upon the volume occupied by the gas. The factor ( r — b ) in the formula repre sent; the total volume tilled by the gas, dimin ;shed by four times the volume :lethally occupied by its molecules, which are assumed to he spher ical. We thus have the ideal pressure—i.e. the pressure determined by the motion of the mole• cute: and undiminished by their mutual attract tion—and we have the actual volume within which the molecules are free to move: the prod uct is evidently the same as in the ease of the simpler law, = c, under low pressures.
The attraction of the molecules and their vol. ante depend, of course, the nature of the gas, By actually determining the pressures and volumes of various gases, numbers may be sub stituted for e, p, and in Van tier Waal,', mula, and thus equation: may be obtained eon taining only two unknown quantities, a and b, the numerieal values of which can then he easily computed. The following table shows the value., of b (i.e. the fraction of the volume of a gas actually occupied by its molecules) for a few gases and vapors. These values are calculated for the temperature of freezing water anti for normal atmospheric pressure: