THE RELATION OF THE VALUE "a" OF VAN DER 



WAALS' EQUATION TO THE MOLECULAR 



WEIGHT AND THE NUMBER OF 



VALENCES OF THE 



MOLECULE 



BY ALBERT p. MATHEWS 



The discovery of the properties of the molecule upon 

 which cohesion depends is a matter of great interest. I have 

 found that "a" of van der Waals' equation is equal to a con- 

 stant multiplied into the square of the cube root of the product 

 of the molecular weight by the number of valences in the 

 molecule. This enables a calculation of the valence number 

 of a molecule from the critical constants; and on the other 

 hand a calculation of "a" from the valence and molecular 

 weight. Some interesting facts have been discovered rela- 

 tive to the valence of the halogens, of the argon group and 

 some other elements by the application of this rule. 



If the value a/V 2 of van der Waals' equation, which repre- 

 sents the internal, or cohesive, pressure per unit surface, 

 be divided in both the numerator and denominator by N 2 , 

 N being the number of molecules in the volume V, we obtain a 

 value for "a " .which may be called the molecular cohesive pres- 

 sure and which is independent of the volume. If " a " be repre- 

 sented by the expression N 2 M 2 K, in which M is the mass of 

 cohesion of a molecule and K a constant, then since V 2 is 

 equal to N V, v being the volume at the disposal of a single 

 molecule, a/V 2 == N 2 M 2 K/NV == M 2 K/V. This value M 2 K 

 may be computed from "a" by dividing the latter by N 2 . 

 N, the number of molecules in a cc. of gas under standard 

 conditions, is equal to 2.77 X io 19 . In the computations 

 which follow I have taken the value of "a" in dynes instead 

 of atmospheres and wherever possible I have used the value 

 of M 2 K computed by the surface tension formula described 

 in a previous paper. 1 



1 Mathews: Jour. Phys. Chem., 17, 154 (1913). 



