2 68 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 
aLme. 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 0° C, by calculation on the above data, should 
be 379 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 Arrheuius, 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 a the 
number of active, and /, the number of ions into which a molecule can 
111 i~ Jc li 
be dissociated, then the dissociation coefficient i = — — -— 
in -j- n 
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, i = l-\-(k-l)a can be obtained 
by measurement of conductivity of solution, i can obviously also be 
obtained from measurements of osmotic pressure. 
This coefficient will necessarily he 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 + -00367/ 1 - i atmospheres, 
in 
where 22-35 atmospheres is the pressure exerted by the gramme- 
molecule of gas in volume of 1 litre at D V., 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 him. 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 Ztsehr.f. physikal. Chem., Leipzig, 1SS7, Bd. i. S. 631. 
