70 THE TRUE VALUE OF a OF VAN DER WAALS' 



drogen atoms when they are in the state of molecular hydrogen 

 and when they are in the condition of hydrogen in a molecule of 

 octane. It may be shown that in the latter case they occupy less 

 volume and are hence less compressible than in the former. The density 

 of elemental hydrogen at absolute zero may be calculated from the den- 

 sity of .07G3 at 14.83° Abs. by the formula d = d { (T c — T)/T c f 3 

 to be 0.094. From this the volume of a gram mol, or V u , will 

 be 21.29 c.c. In octane there are 18 hydrogen atoms or 9 gram 

 mois in a gram mol of octane. The density of octane at absolute 

 zero is computed to be 0.9119, computed in the same manner as 

 the density of hydrogen. From this the volume of a gram mol of 

 octane at absolute zero is 125.0 c.c. If the hydrogen had the 

 same volume in octane as it has in elemental hydrogen it would 

 occupy the space of 9 X 21.29 c.c. or 191. G c.c. But the whole 

 volume occupied by the 8 carbon atoms and the IS of hydrogen 

 is only 125.0 c.c. or in other words only 0.G5 of the space which 

 would be occupied by the hydrogen alone if the atoms were not 

 greatly compressed. Since the hydrogen atoms in octane are so com- 

 pressed that they occupy only half the space that they do in 

 hydrogen itself at absolute zero, it follows that they must be under 

 tremendous intramolecular pressure in the case of octane, a pressure 

 enormously greater than in the case of elemental hydrogen. As they 

 are already greatly compressed in octane it follows that a molecule 

 of octane must be far less compressible than one of hydrogen, not 

 more compressible. The value for a gives us, therefore, a value of 

 b c for hydrogen which indicates that the molecule of hydrogen deviates 

 more from that of a gas with incompressible molecules than does 

 octane, and this appears to me to be in entire consonance with 

 what is shown to be the ease, namely that the atoms of hydrogen 

 do occupy less space in the molecule of octane than in hydrogen 

 and must therefore be more rigid in the latter case. 



A similar relationship will be found, 1 do not doubt, for oxygen 

 and nitrogen gas, the atoms in these gases also occupying more 

 space than they do in molecules having far greater cohesions. It 

 seems to me not impossible that the large amount of heat liberated 

 by hydrogen and oxygen when they unite to form water represents 

 the heat liberated when this compression of the atoms occurs. Their 

 volume is reduced and heat is liberated just as happens when a gas is 

 condensed. Flow great this compression is in the case of water may be 

 seen from the fact that a gram mol of water occupies at the tempe- 

 rature of 4° C. the space of only IS c.c. and at absolute zero its 

 volume is presumably less than this. There is a gram mol of hydro- 



