156 Mr Kleeman, On the Properties of a liquid 
The Polymerization of Molecules in a Substance. 
The equations * 
T.= H, (22) (SVM) (7) 
and i (Be) (3m) .....00 (8) 
and the relations + connecting the internal heat of evaporation, *| 
surface tension, and other quantities with one another, obtained — | 
by giving the function () in the law of molecular attraction — 
different forms, may be used to investigate whether a substance © 
1s polymerized. The quantities 7,, p., pc, denote the critical — 
temperature, pressure, and density respectively of a substance of 
molecular weight m, m, denotes the atomic weight of an atom 
in the molecule and H, and M are constants. If a relation does 
not fit the facts, it signifies that the molecular weight does not | 
| 
: 
correspond to that indicated by the chemical formula, but to — 
some multiple of it. Provided the substance does not consist of 
a mixture of molecules polymerized to different extents the actual 
molecular weight can be determined by finding the factor of the 
chemical molecular weight which gives an agreement with the 
facts. Oetvos’ surface tension equation has been used in this 
way. By means of it Ramsay and Shields found that water, 
acetic acid, and the alcohols are more or less polymerized. This 
may be verified by applying to these substances the latent heat — 
and other relations quoted. 
A few additional important cases of polymerization will be 
pointed out here. By means of Dieterici’s equation f 
m Po 
_ giving the internal heat of evaporation L in terms of the densities 
p, and p, of the liquid and vapour respectively, it can be shown 
that NH, is considerably polymerized in the liquid state. The 
constant K instead of being equal to 1:75, the value it has for 
liquids that are not polymerized, varies from 2°6 to 3:9 when the 
temperature varies from —10° to 40°C. It will also be found 
that the critical quantities of O, do not fit in with equation (8), 
-and Q, is therefore to a certain extent polymerized. Mercury 
is usually supposed not to be polymerized. It will, however, be 
found that if the internal heat of evaporation is calculated by 
means of Clapeyron’s thermodynamical equation, and substituted 
* Phil. Mag. May 1910, pp. 783—809. 
+ Ibid. Jan. 1911, pp. 83—102 
+ Ibid. Oct. 1910, pp. 688, 689. 
