Theory of Electrolytic Dissociation. 283 



it may be, as soon as the solution becomes so dilute that, 

 except for an inappreciable fraction of the time 7 these spheres 

 of influence do not in general intersect each other, any 

 further addition of solvent Avill only increase the separation 

 of the spheres of action; it cannot change the internal 

 condition of one of these spheres or affect the interaction 

 between the solute particles and their surrounding solvent. 

 The change of available energy produced by the entry of 

 solvent must then simply be that due to the dilution of the 

 solute particles, and cannot depend on any interaction between 

 solute and solvent. The rate of change of available energy 

 with dilution, that is, the osmotic pressure, must consequently 

 be independent of the nature of the solvent, and will there- 

 fore have the same value if no solvent be present. Thus, in 

 cases where this is possible, that is, tor volatile solutes, it 

 follows that the osmotic pressure must be equal to the 

 gaseous pressure corresponding to the same concentration. 

 We thus theoreticallv establish the gaseous laws for the 

 osmotic pressure of volatile solutes, and, since volatility is 

 probably only a matter of degree, it seems reasonable to 

 extend this result to non- volatile bodies. Whether this 

 extension be regarded as theoretically valid or not, there is 

 abundant experimental evidence that it is practically justified, 

 since the osmotic pressure of solutions of such substances as 

 cane-sugar is well known to have the gaseous value. 



When in solutions of electrolytes we examine the osmotic 

 pressure or the correlated effects such as the depressions of 

 the freezing-point, abnormally great values are obtained, 

 and, by the course of reasoning given above, it follows that 

 a number of solute particles greater than that indicated by 

 the chemical formula must exist in the solution ; that is, that 

 dissociation must have occurred. To connect this result with 

 the migratory independence of the ions of electrolysis, it is 

 necessary to show that for solutions so dilute that the solute 

 particles are beyond each other's sphere of influence, the 

 number of ions indicated by the electrical behaviour is the 

 same as the number of independent particles required to pro- 

 duce the observed osmotic effects. Thus for a dilute solution 

 of potassium chloride, which yields two electrical ions, potas- 

 sium and chlorine, the depression of the freezing-point should 

 be twice as great as for a solution of cane-sugar of equivalent 

 molecular concentration. For bodies yielding three tons* 

 such as sulphuric acid or barium chloride, the freezing-point 

 depression should similarly be three times the normal value. 

 When the concentration of the solution is increased, the 

 spheres of influence of the solute particles will intersect, and 



