( 779 ) 
Ov | ay 07¢ 
d == SS 1 — LI == Lt Zed Ye (hoe 
u, | v u le ap | 7 v Gan | dT v (33) (2) 
Equating of this expression for the first and the second phase, 
and joining the terms with dp, d7, and de we get equation 
(1). When, however, we do not perform these operations, but keep 
to equation (2), we immediately find the law of van ’r Horr. For 
we now reason as follows. The compressed dilute solution is in 
equilibrium with the solvent under normal pressure; so the thermo- 
dynamic potential of the solvent, which can freely move through 
the membrane, must be the same in the solution and in the pure 
solvent. And so the modification in the thermodynamic potential 
brought about on one hand by the increase of pressure, on the other 
by the addition of the dissolved substance, must be equal to zero, 
mid 50, as dl = 0: 
Aon 7 076 7 
Dede ih =S x 
0a PT P ‘ On? OT 
| | A RETRO 
Now for an exceedingly dilute solution «{ = | = ——-; in the 
Oa? pT la 
first member of the equation we can neglect the term with w, and 
we need not make a difference between the v of the solution and 
that of the solvent, and so we get: 
BL 
v dp = as da *), 
11h 
follows from (2). 
the law of van ’r Horr. 
2 Now when we consider the osmotic phenomenon, the thought of 
introducing the idea ‘osmotic temperature’ as analogy of the osmo- 
tic pressure, naturally suggests itself, and this has repeatedly been 
done *). The reasoning is then as follows. The equilibrium through 
the semipermeable membrane is disturbed when on one side a sub- 
stance is dissolved, because then the number of particles of the sol- 
vent per unit of volume decreases. So if we want to reach a state 
in which an equal number of particles move from the left towards 
the right and from the right towards the left we must either raise 
the pressure of the solution, in consequence of which more solvent 
molecules are forced out, or its temperature, so that the number of 
outgoing molecules will be increased by the greater velocity. Now 
the increase of temperature which must be given to the solution 
1) Cf. Théorie Moléculaire § 18. 
°) Cf. e.g. van Laar, These Proc. IX, p. 61. 
