THE MOLECULAR VOLUMES OF LIQUIDS 191 



divided into the molecular weight gave what may be termed 

 the specific or molecular volume of the liquid at the normal 

 boiling-point, or at the temperatures at which the inter- 

 molecular pressures of all liquids are presumably the same, 

 or at least very approximately the same. If the appropriate 

 units are chosen, the molecular volume may be defined as the 

 volume in cubic centimetres at the normal boiling-points 

 occupied by the molecular weights of the liquid expressed in 

 grammes. Thus, to take a case : the normal paraffin heptane 

 C 7 H 16 , boils under standard conditions at 98-43°, has a relative 

 volume at this temperature of r14.u1 (vol. at o° = 1), and a 

 specific gravity at o°/4° of 0*70048. Then since the molecular 

 weight of heptane is 100*16 (o = 16), its molecular volume, 

 that is, the number of cubic centimetres occupied by 100-16 

 grammes of the hydrocarbon, at its normal boiling-point is 



ioo*i6 x 1*1411 1 - - 



-2 = 163-16 c.c. 



0*70048 



This volume may be legitimately assumed to be proportional 

 to the real volume of the molecules together with the interspaces 

 in which they (or the atoms) vibrate. That this assumption 

 is valid may be shown by other considerations. Thus it has 

 been established that the volumes of liquid compounds, how- 

 ever variable, at their normal boiling-points are 1-5 times 

 their volume at the absolute zero. Hence both volumes are 

 proportional to the real molecular volumes. 



Since the time of Kopp, and more especially during the 

 last thirty or forty years, the subject has been experimentally 

 studied by numerous investigators, among whom may be 

 mentioned Zander, Buff, Schiff, Gartenmeister, Naubeck, Pinette, 

 Dobriner, Elsasser, and Lossen ; and a considerable body of 

 literature has been accumulated, mainly in the form of 

 detached memoirs dealing with, special aspects of the general 

 problem. Until quite recently the most noteworthy attempt 

 to co-ordinate this large amount of observational work, and 

 to incorporate its main results into the systematic literature 

 of the science, was made by Horstmann in successive editions 

 of Graham-Otto's Lehrbuch der Chemie — a work not generally 

 accessible to English students. In the autumn of last year, 

 however, Mr. Gervaise Le Bas published a careful digest on 

 the subject, as one of the excellent series of Monographs on 



