Value of "a" of van der Waals' Equation 197 



How accurately the number of valences can be calculated 

 by the first formula is shown by Table IX, which is, of course, 

 little more than a rearrangement of the results already stated 

 in the preceding tables, except that in this instance I have 

 used the approximate values of "a" given in the Landolt 

 tables computed by the formula a = 27T c 2 /(64 X 273* X P c ). 



An inspection of Table IX will, I think, convince all that 

 molecular cohesion, as expressed by the value "a" of van 

 der Waals' equation, is a function of the weight and valence 

 of the molecule. If "a" is calculated for all these substances 

 from the critical temperature and pressure by the formula : 

 a = = 27T 2 C /64P C x 273 2 , the number of valences is calculated, 

 with a remarkable degree of approximation, from the as- 

 sumption that a --= CN 2 Wt 2/3 Val 2/3 , by the formula given at 

 the beginning of the table. It will be noticed that all asso- 

 ciating substances give by this formula a larger number of 

 valences than that calculated for the normal substance, and 

 that the degree of excess of trie number of valences is more 

 or less proportional to the degree of association. Thus 

 the largest excess is in the case of water, where the cohesion 

 calls for 22 valences, and in some of the nitriles; whereas sub- 

 stances like the esters, which associate very little, have only 

 a few valences in excess. Putting aside associating substances, 

 of which the deviation from the rule is to be expected, there 

 are certain exceptions characteristic of certain observers. 

 The coefficient 3.2 X io 5 was taken from Young's data for 

 ether. It will be seen that always Nadejdine's critical con- 

 stants give a value for "a" lower than Young's, where both 

 observers have worked on the same substances. So the sub- 

 stances computed from Nadejdine's critical data generally 

 show a deficit of two or three valences to the molecule. I 

 think in these cases Young's values are to be accepted. Vin- 

 cent and Chappuis' determinations, also, generally come a 

 little low, though they are very close, The main constant 

 deviation from the law is to be observed in the case of sub- 

 stances like methane and hydrogen of very low molecular 

 weight and great molecular simplicity; and those substances 



