185 



tl (.f, p) = Il (O, ƒ>„), 

 when fi(,i', p) is the molecular potential of the water in the solution 

 (in which .v is the molecular concentration of the dissolved substance, 

 p the pressure of equilibrium), and fi(0, p„) that of (he pure water 

 (in which the concentration of the dissolved substance is 0, the 

 pressure of equilibrium p„). 

 Now : 



f*(-«. P) = /(2') + pv^ + "'"'■ + ^ï' % (1 -•''•) 



and hence — as in dilute solutions Vj- (the molecular volume of the 

 water in the solution) can be equated to v„ ') (the molecular volume 

 of the pure water) : 



(p — p„)vi> = — ^^ W (1 — *') + «•'''^ 

 or 



RT 

 n=p-p, = [— %(l—.«) + «.»'), . . . . (1) 



when jr represents the "osmotic" pressure. In this « is tiie so-called 

 "influencing" coefficient in consequence of the interaction of the 

 molecules of the solvent and those of the dissolved substance. It is 

 known tliat « is represented by the expression ■) : 



" = by ' 



in which the numerator passes into (6,l/a,— h^V^a,y, when Hi^ =:^^rt^a, 

 can be put. 



Thesis III. All kinetic theories, therefore, which for non-diluted 

 solutions lead to expressions which remind directly of the equation 

 of state of gases and liquids (e.g. with v — b etc., and loit/iout /o(/(i- 

 rithmic member) must be rejected. (Therefore tiie theories of Wind, 

 Stern and others). 



Thesis IV. For very diluted solutions (I) passes into 



RT 



JX :=: a; , 



Van 't Hoff's well-known equation. Yet it is easy to see that the 

 deviations for non-diluted solutions are much slighter than those for 



1) v^ and v^ only dilfering in a (|uantity ol' the order x-, the difference can 

 always be thought included in the term ux-. 



2) See among others Z f. ph. Gh. 63 (1908;, p. 227— ;2"28 (Die Schraelz- und 

 Erstarrungskurven etc.). 



