682 
second component, i.e. when 2, and a, are small, the above equa- 
tion may be simplitied, for in consequence of the small value of 
« we may then write: 
ie) i RT 
dx,*)/p.7T. 2, (1—«,) 
and when we neglect wz, by the side of 1, the coefficient of dz, 
becomes: 
When we now consider the equilibrium between a mixed crystal 
phase and a liquid, or between two mixed erystal phases at constant 
pressure, we get: 
il Vann 
(4,—7,) dT = — RT ——— dz, 
wv, 
and 7'(n, — 7,) being = — M, Q,, we get: 
ET 
MQ «, 
or 
(iig 
AT = —— x 
MQ (z, 1) 
This is RornMunp’s formula derived by another way. For the 
molecular lowering, i.e. for the lowering caused by 1 gr. mol. of 
the second component in 1000 gr. of the first the following equa- 
tion is obtained: 
NN OO 
de, 100005 z, 
From this it is seen that when the second phase is no mixed 
erystal, hence «, = O, this formula passes into that of Van 'r Horr. 
When we consider the lowering of the freezing point, brought 
about by addition of a second substance that forms mixed crystals 
with the first, only the second phase is a mixed crystal and the 
first a liquid. When we, however, direct our attention to a lowering 
of a transition point, the first phase is a mixed crystal, and in 
general the second will be so too, just as in the case of solidification. 
(Cf. the subjoined figure). 
It follows from the above relations that when we may treat 
diluted mixed crystal phases thermodynamically as diluted liquid 
solutions, the molecular size of the second substance present in the 
second phase in small concentration with regard to the molecular 
size of the same substance in the first phase, can be found from the 
