THE SIGNIFICANCE OF THE RELATIONSHIP BE- 

 TWEEN MOLECULAR COHESION AND THE PROD- 

 UCT OF THE MOLECULAR WEIGHT AND THE 

 NUMBER OF VALENCES 



BY ALBERT p. MATHEWS 



In the preceding papers 1 of this series I have shown that 

 the value of "a" of van der Waals, representing molecular 

 cohesion, or the value M 2 K which is the factor "a" for a 

 single molecule, is proportional to the two-thirds power of the 

 product of the molecular weight by the number of valences 

 of the molecule. M 2 K was found to be equal, when expressed 

 in absolute units, to 2.98 X io~ 37 (Mol. Wt. X No. of Val.) 2/3 . 



In this paper I shall discuss the theoretical bearing of the 

 relationship of cohesion to these molecular properties. 



Attempts have been made by others to correlate cohesion, 

 or "a," with molecular weight and the number of valences, 

 but with very partial success. Sutherland 2 at first supposed 

 the molecular attraction to be proportional to the product 

 of the gravitational masses of the molecules. This he found 

 would not do, and in his later papers he stated that the gravita- 

 tional mass of a molecule did not enter into the expression 

 "a." Amagat, 3 also, recently revived the idea that gravita- 

 tional mass plays a role in cohesion and suggested that a/V 2 

 ought to be proportional to the square of the molecular mass. 

 This, however, he did not find to be the case. Leduc 4 has 

 recently confirmed, in part, this view of Amagat 's for gases of 

 similar molecular composition, when taken under the same 

 volume and at corresponding temperatures. Kleeman, 5 also 

 has tried to find a relationship between "a" and gravita- 



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



2 Sutherland: Phil. Mag., [5] 27, 305 (1889); [6] 4, 632 (1902). 



3 Amagat: "Pression interne des fluides," Journal de Physique, [4] 8, 

 617 (1909). 



* Leduc: Comptes rendus, 153, 179 (1911). 



8 Kleeman: Phil. Mag., [6] 19, 783, 840-847 {1910). 



