VARIATION OF MOLECULAR SURFACE-ENERGY WITH TEMPERATURE. G55 
K. 
Ethyl oxide. 2’1716 
Methyl formate. 2’0419 
Ethyl acetate. 2‘2256 
Carbon tetrachloride. 2’L052 
Benzene. 2'1043 
Chlorobenzene. 2'0770 
Mean value of /c . . . • . 2'1209 
Suppose acetic acid gas. consisting' of molecules of C^H^O,, to undergo molecular 
condensation, so that 2 CoHj ^03 = C^HgO^, the pressure of the gas would fall to half' 
of the original pressure, provided volume were kept constamt; i.e., unit volume would 
contain only half the original number of molecules. How would this aifect the 
number of molecules on the surface of a cube representing unit volume ? Clearly, if 
the number of molecules in uuit volume is halved, the number of molecules on unit 
surface will be altered to (- 1 )^; and a similar change will take place in the surface 
energy, one of the factors of which is molecular surface, or (Mu)^. The value of the 
differential of surface-energy with temperature will be similarly altered; the amount 
of association can, therefore, be calculated by the ec[uation 
2-12 
where Tc is the differential found for the dissociating liquid at the temperature chosen, 
and X the unknown factor of association. 
For example, calculating for acetic acid, and for methyl and ethyl alcohols the 
amount of association at — S9°'8, 20°, 100°, and 150°, we obtain the following 
numbers ;— 
Acetic acid. 
' 
1 
IMetliy] alcohol. 
Ethyl alcohol. 
a; X 60 
7 1 
X X 32 
7 , 
X X 46 
t. 
k. 
X. 
= M.W. 
f. 
= M.W. 
r. 
Ah 
ib • 
= M.W. 
20 
0'8815 
.3-73 
223-9 
- 89-8 
0-868 ■ 3-82 
122-2 
- 89-8 
0-949 
3-34 
153-6 
100 
1-058 
2-84 
170-3 
+ 20 
0-932 3-43 
109-8 
P 20 
1-070 
2-79 
128-3 
150 
1-198 
2-36 
140-3 
150 
1-236 2-25 
72-0 
150 
1-569 
1-57 
72 2 
From these numbers it would appear that the limit to the amount of possible 
association is 4. With acetic acid at 20 ° the molecule is chiefly ( 03114 , 03 ) 4 ,; with 
methyl alcohol at — 89°'8 (CH 4 , 0)4 is approached; ethyl alcohol has not reached 
so gTeat a degree of association at such a temperature. 
