4.96 REPORT—1904. 
It might be expected that in the case of less closely related substances con- 
traction would be accompanied by evolution of heat and expansion by absorption 
of heat, but this is by no means invariably the case; for example, on mixing 
40 gram-molecules of propyl alcohol with 60 gram-molecules of water there is 
a contraction of 1:42 per cent., but a fall of 1°15 in temperature was observed. 
Taking the alcohols as a group, it is found that, the higher the boiling-point, the 
smaller is the heat evolution or the greater the absorption on admixture with 
water. 
Properties of Mixtures. 
The behaviour of two non-miscible liquids when heated together is well 
known, and I need only refer to the fact that the vapour pressure is equal to 
the sum of the vapour pressures of the pure components at the same tem- 
perature; that the boiling-point is the temperature at which the sum of the 
vapour pressures of the components is equal to the pressure under which the 
liquid is being distilled, provided that evaporation is taking place freely and the 
vapour is not mixed with air; and, lastly, that the composition of the vapour 
is independent of that of the liquid (so long as both components are present 
in sufficient quantity), and is expressed by the equation = ~ a 
Us BU, 
and «2, are the relative weights of the two components in the vapour, P, and P® 
their vapour pressures at the observed boiling-point, and D, and D, their vapour 
densities. 
The vapour pressure, boiling-point, and vapour composition, then, can be 
calculated for non-miscible liquids, and it has been stated that such liquids have 
never any close chemical relationship, and are usually not related at all. 
On the other hand, it has been mentioned that when the chemical relationship 
is very close the liquids are invariably miscible in all proportions, and that there 
is very little, if any, volume or heat change on admixture. 
So, also, the vapour pressure and boiling-point of a mixture of closely related 
liquids are easily ascertained from those of the pure components, and the com- 
position of the vapour bears a simple relation to that of the liquid. 
The vapour pressure of the mixture is given, at any rate with a very close 
approach to accuracy, by the equation P = mP, + es ait) Pp where P, Py, 
and P, are the vapour pressures of the mixture and of the components, A and B, 
at the observed boiling-point, and m is the molecular percentage of A. 
Van der Waals concluded from theoretical considerations that this relation 
should be true when the critical pressures are equal and the molecular attractions 
agree with the formula proposed by Galitzine and by D. Berthelot, a,..= 4/4;'@2, 
where a,., represents the attraction of the unlike molecules and a, and a, the 
respective attractions of the like molecules. That is certainly the case with 
chlorobenzene and bromobenzene, which, as already mentioned, show no heat or 
volume change on admixture, for the maximum difference between the observed 
and calculated pressure in three experiments was less than 0°1 per cent. 
But the relation is, at any rate, very nearly true for closely related substances 
when the critical pressures are not equal, for in the case of methyl and ethyl 
alcohol the difference between the observed and calculated pressure was within 
the limits of experimental error, and with four other pairs of closely related 
substances the greatest mean difference (for three readings each) was only 0°6 per 
cent. It is not, however, as Speyers suggested, true for all non-associated 
substances, whether closely related or not; indeed, chemical relationship seems to 
be much more important than the state of molecular aggregation, for the relation 
is true for methyl and ethyl alcohol, while it is altogether untrue for benzene and 
hexane. 
The boiling-point of a mixture of closely related liquids may be ascertained 
from the vapour pressures of the components, but not so simply as in the case of 
non-miscible liquids, because the boiling-point depends on the composition of the 
liquid, 
» Where 2, 
