Value of "a" of van der Waals' Equation 203 



and compressible molecules it must be slightly diminished 

 as the complexity and compressibility increases. If the lat- 

 ter shall prove to be the case, then most of the exceptions 

 noted in the preceding pages would disappear. The substitu- 

 tion of the value for "M 2 K" computed by my formula from 

 the surface tension would have given a much closer agreement 

 of the calculated and observed valence numbers, but I wished 

 to show that the law holds at least approximately even though 

 we use the approximate values of "a" computed by the usual 

 formula. 



The constant 2.98 X io~ 37 discovered in the foregoing 

 pages, is evidently the factor M 2 K of a substance of unit 

 molecular weight and unit valence. No such substance as 

 this is known, but hydrogen with a weight and valence of 

 two, and helium with a weight of four and valence of unity (?) 

 have values of M^K not very different. Thus for hydrogen, 1 

 M 2 K is between 3.16 and 7.72 X io~ 37 ; and M 2 K of helium 

 lies between the same two values probably. The value of 

 2 .98 X icT 37 is of the order of magnitude of the gravitational 

 attraction of two average molecules. Thus at 20 two mole- 

 cules of ether in the liquid state attract each other gravita- 

 tionally with a force of 3.11 X io~ 37 dynes. The similarity 

 of these values is, however, probably only a coincidence. 



Conclusion 



The facts presented in the foregoing pages enable us to 

 draw the general conclusion: The "mass" of cohesion of a 

 molecule is everywhere proportional to the cube root of the 

 molecular weight multiplied by the cube root of the number 

 of valences in the molecule. Or, to put it in another way, 

 "a" of van der Waals' equation for one cc. of gas under 

 standard conditions is equal to 2.98 X io~ 37 X Mol. Wt 2/3 X 

 Valences 27 ' X (2.77 X io 19 ) 2 dynes; or this number divided 



1 M 2 K for H 2 computed from the value "a" given by Landolt-Bornstein 



27 T 2 



is 5-55 X icr 37 . This was computed by the formula a = 



64 X 273 X r c 



