102 J. van't Hoff on the Function of Osmotic Pressure 



simply expressed, and require the same fractional coefficients 

 which Schlosing himself arrived at. 



Before proceeding to this investigation, it is necessary to 

 include cases where partially insoluble bodies are present : 

 this is easily done ; they may be included in the formulae 

 given above, remembering that such bodies exist in solution 

 up to its saturation-point, and are therefore present with 

 constant concentration. All concentrations depending on this 

 may, therefore, be removed from the first term of the above 

 equation to the second, without affecting the constancy of the 

 latter. Everything remains the same, except that in the first 

 term only the dissolved bodies need be considered. 



1. We shall first examine Gruldberg and Waage's observa- 

 tions. The first case they studied was that expressed by the 

 equation 



BaC0 3 + K 2 S0 4 ^BaS0 4 + K 2 C0 3 ; 

 and they found, according to their simplified formula, that 



log C K . 2 so 4 — log Ck 2 co 3 =K. 

 The relation given by our equation is almost identical, for, 

 for K 2 S0 4 , a=l and 2 = 2-11, and for K 2 C0 3 ,a = l and 2 = 2-26; 

 hence 



log Ck^o.-I'O? log Ck 2 co 3 = K. 

 A similar agreement exists with sodium carbonate, for then 

 the values of i for Na 2 S0 4 and Na 2 C0 3 are 1-91 and 2'18 

 respectively ; hence 



. log C Nail so 4 — 1*14 log Na,C0 3 = K. 



2. This result, expressed in what is almost a whole number, 

 cannot be expected in the above-mentioned experiment of 

 Schlosing (Comptes rendus, lxxiv. 1552 ; lxxv. 70). There 

 the subject of experiment was the solubility of calcium car- 

 bonate in water containing carbonic acid, and the state of 

 equilibrium is expressible by the following statement : — 



CaC0 3 + H 2 C0 3 ^Ca(HC0 3 ) 2 . 



We should expect that, as &==1 for carbon dioxide, that i 

 should = 2 56 for calcium hydrogen carbonate: — 



0*39 log Ch 2 C0 3 — log C C a(HC0 3 ) 2 =K ; 



and Schlosing found : — 



0-37866 log C H2 co 3 -log C Ca(H co 3 ) =K. 



Similar experiments w T ith barium are equally satisfactory ; 

 the value of i for barium hydrogen carbonate is 2*66, and the 

 following results are calculated : — 



0-376 log Ch.CO, — log C B a(HC0 3 ^ = K. 



