B Y .'iLBEKT
P . MATHETT-S
The discovery of the properties of the molecule upon \r-hich cohesioii depends is a matter of great interest. I h a w found t h a t "ti of van der U-aals' equatioii is eqttal to a constant multiplied into the square of the cube root of the prodLtct of the molecular Tveight by the number of \-alenct:s in the tiiolecule. This enable:; a cdculation of the valence number of a molecule from thc critical constants; :md on the other lmnd a calculation of ti from the \-alerice a ~ i dmolecular \\-eight. Some interestill: facts ha\-e been disco\-ered relative to the valence of the halogens, of the argoii grotip aricl some other elements b y the application of this rule. If the \ d u e (7 1.' of 'ran der 11-aals' equation. Ivhich represents the internal or cohesil-e. pressure per tinit surface, tie divided in both the numerator and denominator by S ', X being the number of molecules in the x-olunie I-, n-e obtaiii a 1-aluefor "(z which may be called the molecular cohesi\-e presSure and Ivhich is independent of the 1-olume. If ii ' * be represerited by the expression S'11'K3 in Ivhich 11 is the mass of cohesion of a molecule and K a constant, then since 1.' is equal to S'i", 71 being the volume a t the disposal of a single molecule, u = S ' W K S'L - = 1I'K 7 ' ' . This l-alue 1f'K may be computed from " t i " by dividing the latter by S 2 . ?,; the number of molecules in a cc. of gas iinder standard conditions, is eyual to 2 . 7 7 x I O ' " . In the computations Ivhich folloiv I have taken the value of (7 in dynes instead of atmospheres and where\-er possible I ha\-e used the value of 1I'K computed by the surface tension formula described in a previous paper.' "
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Nathews: Jour. Phys. Chem., 17, I j4 (1913).
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Tables I and I1 bring o u t the relationship that AI is some function of the molecular weight and the number of valences in the molecule, or l12K = f iITt i (I-alence) The relationship t o molecular weight appears if \ye compare compoundi of the same valence number as shon-n in Table I .
T \1< I O "; a n d J12K of helium lies Ihetn-een the same tivo values probably. The \yiltie of ._ z cis x 1 0 is of the order of niagnitude of the grar-itatiorial :.ittr:ti:tion of t\vo average nioleciiles. Thus a t 20' tlvo molecu1c.s o f ether in the liquid state attract each other gra\-itii.. tioiict'lly \\-ith a force o f j . I I > Io " dyne.;. The similarity ( i f rhe5e \-slues is. hon-ever, probably only :I,coiiicideiice. "
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Conclusion . 3
I h e facts presented iii the foregoiyg pages eiialile 115 t o tlran the general coiiclLisioii : The 111; of cohesion of a iiioleciile is e\-eryi\-liere proportional t o the ctilie root of the inoieciilar iveight multiplied by the cul)r root of the iiuniber o f \.alences in the molecule. Or. to p u t i t i i i m o t h e r \ w y . ti o f i - a ~ ider \ITaals' equation for orie cc. of gas under staiitlml conditions is eciu to 2 . gx x I O Ii r: 1101. \\rt- x "
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T-alellces2
x .~
( 2 .; ;
x
Io
dynes; or this numtier tlivit-ied
by I ,0135 X IO' atmospheres. This formula gives a value for "a" somewhat higher than the ordinary formula and it may be t h a t the coefficient should be taken a little lower. The theoretical significance of this relationship of cohesion t o the molecular n-eight and the number of valences is very interesting, but I shall reserve its consideration for a subsequent paper. l.?izzersztj of Chicago
