268 DIFFUSION, OSMOSIS, AND FILTRATION. 



It is, however, by no means the fact that, in the case of all sub- 

 stances in aqueous solution, agreement exists between the observed 

 osmotic pressure and that directly calculated on the above hypothesis 

 alone. In many cases the pressures observed in solution are far higher 

 than those calculated from the concentration in gramme-molecules per 

 unit volume. Thus the osmotic pressure of a 1 per cent, aqueous solu- 

 tion of common salt at C., by calculation on the above data, should 

 be 3*79 atmospheres, but actual measurement shows it to be over 7 

 atmospheres. 



This phenomenon, common to all solutions of electrolytes, is 

 accounted for on the hypothesis of Arrhenius, 1 that the dissociated ions 

 of an electrolyte in solution are capable of exerting pressure as well as 

 the undissociated molecules. The osmotic pressure of solutions of 

 electrolytes is then raised above the simple molecular value by the 

 coefficient expressing the extent to which the molecules are dissociated 

 in passing into solution (dissociation coefficient). 



This coefficient gives the ratio of the observed osmotic pressure of a 

 solution to the pressure calculated on the assumption that no dissocia- 

 tion of molecules occurs in passing into solution. It may be deter- 

 mined for a substance at a particular dilution most accurately, by 

 measurement of the electrical conductivity of the solution. 



If m is the number of inactive molecules in the solution, and n the 

 number of active, and k the number of ions into which a molecule can 



be dissociated, then the dissociation coefficient i = : 



m-rn 



Since the " activity co-efficient " a = ^ is measurable by the 



m + n 



ratio of the molecular conductivity of the solution to the limiting value 

 it approaches by increased dilution, & = !+(/;- 1) can be obtained 

 by measurement of conductivity of solution, i can obviously also be 

 obtained from measurements of osmotic pressure. 



This coefficient will necessarily be of very different value for 

 different classes of electrolytes, since the possible number of ions is 

 variable. Thus sodium chloride has 2, potassium sulphate 3, 

 potassium ferrocyanide 5 ions. 



Hence as a formula may be given 



P = 22-35 (1 + -003670- * atmospheres, 



m 



where 22 - 35 atmospheres is the pressure exerted by the gramme- 

 molecule of gas in volume of 1 litre at C 1 ., c the number of grammes 

 of the substance per litre, m its molecular weight, and i its dissociation 

 coefficient at the concentration c. 



As regards the practical estimation of the osmotic pressure of a 

 solution, the direct measurement by a semipermeable membrane is not 

 only tedious, and limited to cases where the dissolved substance has no 

 chemical action on the film, but seldom practicable, on account of the 

 difficulty in constructing membranes, to which the term may be strictly 

 applied. Obviously, unless the membrane is really impermeable to the 

 dissolved substance, the values on account of the " leakage " of dissolved 

 substance must be below the real amount. 



1 Ztschr.f. physikal. Chem., Leipzig, 1887, Bd. i. S. 631. 



