TRANSACTIONS OF SECTION B. 4.97 
In erder to calculate the boiling-points of all mixtures of two closely related 
_ liquids under normal pressure we should require to know the vapour pressure of 
each substance at temperatures between their respective boiling-points under that 
pressure. Thus, chloroform boils at 132°0, and bromobenzene at 156°-1, and we 
must be able to ascertain the vapour pressure of each substance between 132° and 
156°. 
The percentage molecular composition of mixtures which exert a vapour pres- 
sure of 760 mm. must then be calculated at a series of temperatures—say every two 
2) 
degrees—between these limits by means of the formula m=100. aes , where, in 
this case, P = 760. aa Py 
Lastly, the molecular percentages of A, so calculated, must be mapped against 
the temperatures, and the curve drawn through the points will give us the 
required relation between boiling-point and molecular composition under normal 
pressure. In the case of six pairs of closely related liquids the greatest difference 
between the observed temperature and that read from the curve constructed as 
described was 0°27. 
For liquids which are not closely related the differences are usually much 
greater, and particular mixtures of constant (minimum or maximum) boiling-poirt 
are not unfrequently met with, especially when the molecules of one or both 
substances are associated in the liquid state. 
The formula for the composition of the vapour from a mixed liquid suggested 
independently by Berthelot and by Wanklyn, ts. WiPAD, 
tz _W5P3Ds 
and P,,, D, and D,, have the same meaning asin the equation for non-miscible liquids, 
and W, and W, are the relative weights of the two components in the liquid 
mixture), was shown by F. D. Brown to be incorrect, and he proposed the simpler 
(where 2, and zs, Ps 
Va = A 
formula, lee ow, 
The subject was investigated mathematically by Duhem and by Margules, and 
experimentally and mathematically by Lehfeldt and by Zawidski, The two last- 
named observers deduced workable formule from the fundamental equation of 
Duhem and Margules, and it is noticeable that both Lehfeldt’s and Zawidski’s 
formule, in their simplest form, become identical with Brown’s. Zawidski’s, how- 
where ¢ is a constant which does not differ greatly from a 
B 
ever, assumes the form “t= P. F Ww: This formula is certainly not, as a rule, 
“B B B 
true for mixtures of liquids which are not closely related; but, on the other hand, 
in the very few cases examined the equation “*=c . ws 
= 
a B 
mP, + (100—m)P® 
100 
appears to hold for those 
mixtures for which the equation P = is true; that is to say, 
generally, for closely related liquids, 
The question, however, whether c= ™ is an open one; but it is interesting to 
B 
remark that if this equality holds it should be possible in many cases to calculate 
the vapour pressure at any temperature, the boiling-point under any pressure, and 
the composition of the vapour, of any mixture of two very closely related liquids, if 
the boiling-point of one of them under any one pressure, and the vapour pressures 
of the other within sufficiently wide limits of temperature, are known. For the 
boiling-points on the absolute scale of the two liquids at the same pressure bear a 
constant ratio to each other, or = = = ; hence the vapour pressures or boiling- 
B B 
points of one substance can be calculated if those of the other are known. Again, 
from the vapour pressures of the pure substances we can calculate the vapour pres- 
sures and the boiling-points of all mixtures; and, lastly, if c= Pp” we can make use 
B 
of Brown’s formula, “* = as to calculate the composition of the vapour from 
1904. KK 
