103 
relation used there. We find for this), when the vapour pressure 
of the second component may be neglected which is certainly the 
case here: 
dl 
CT — (1 Pe —=& el 
da 
=p, (l—a)y 
So everywhere, where the exponent of e is positive, the vapour 
pressure line lies below the straight line which would represent the 
vapour pressure when the law of van ’t Horr held for all concen- 
trations. When this exponent is negative the real vapour pressure 
lies below this straight line. If we now apply van per Waats’s formula 
for p., and if we assume as above 6,—10006,, b,, = 22,45,, 
a, = 1004,, a,, = 20a, we get: y= 10-4 fora = 0.5 and y = 0.25 
for «= 0.2. So we really see the same course as given under a, 5, 
and c°). But on these suppositions the region of unmixing is not so 
narrow as is required in d. For y becomes = 2.5 for c— 0.1, 
and as for absolutely stable states the vapour pressure in the mixture 
cannot be greater than the sum of the vapour pressures of the com- 
ponents *), we must be in the region of unmixing already here. 
If, however, we take a,=1000a, and a,,=25a,, we get 
p—p,(l— a)e 
Vt form As and. oe 1.99 for a= 0.01. If 7 is still greater 
a 
than 100, we may even find much narrower regions of unmixing. 
b. 
Thus e.g, y = 0.95 for c= 0.01 with ; — 1000 and the correspond- 
) 
1 
b 
ing —*= 166, while a, is put =10000a, and a,,=105a,. That 
) 
1 
there exists still a region of unmixing, however, appears from the 
value y = 1,04 for « = 0.001. If a,, is taken somewhat greater still, 
the region of unmixing disappears. 
1) Compare the second volume of the Lehrbuch der Thermodynamik, which will 
shortly appear, p. 178. 
2) That a point of inflection must occur follows from the fact that the vapour- 
pressure line is turned convex downward at first, and then concave downward in 
the region of unmixing, as it has a maximum there. No general rule can, however, 
be derived as to whether this point of inflection will still lie in the absolutely 
stable, or in the metastable region. In virtue of the very slight breadth of the 
plait, however, which leads us to expect that we are already quite close to the 
maximum of ihe vapour-pressure line on the verge of unmixing it may be consi- 
dered as exceedingly probable that the point of inflection still falls in the absolutely 
stable region. 
8) Cf. the footnote p. 111. 
_ 
