346 TRANSACTIONS OP SECTION A. 



any integer from 2 upwards. The most probable value of ' n ' for water at ordinary 

 temperatures is 3. While the greater part of any quantity of water consists of (H 2 0) 3 

 it is probable that the actual state at any temperature is one of equilibrium between 

 varying amounts of (H 2 0) 3 , (H 2 0) 2 , and H 2 0. At the moment of dissociation the 

 single molecule produced is unsaturated and tends to produce dissociation of other 

 water or salt molecules within reach. This seems the proper explanation of the 

 ionisation of solutes. The state of equilibrium existing in water can itself be repre- 

 sented by Ostwald's law derived from the work of Guldberg and Waage, thus 



= Km> (1) 



(1 — aw)Vw 



The symbols have the meanings usually assigned to ' o ' and ' V.' The law for the 

 Bolute only, assumed in the same state and occupying the same volume as it actually 

 does in the solution, will be 



(Y- a ^)V = K ' 2 > 



The addition of salt to the solvent will necessarily destroy the state of equilibrium 

 represented by (1) and (2). 



The change in equilibrium of water may be proportional to either, (a) the amount 

 of salt added, or (6) the amount of dissociated salt added. 



The change in the value of K for the solute will necessarily be proportional to the 

 amount of dissociated water, as only single molecules, i.e. H 2 0, are able to attach to 

 themselves the ions from the solute. We may thus put, taking (a) above 



1 a 



Kw = K'io =z and K = K' = . 



V Vw 



As aw will be Email, put 1 — aw = 1 ; remembering also that Vw is sensibly constant, 

 we can immediately obtain 



v K' /„, Vw ., 1 



Vw V V a/V (1 -a)V 



whence 



= B. 



(1 - ")n/V 



This is Rudol phi's law. 



If the assumption (b) above is used then the change in Kw will be given by 



Kw = K'w L 



and by the same process as above the final result is 



This is van't HofPs equation. 



The above equations are thus obtained from theoretical considerations of the law 

 of mass action for both solvent and solute. The assumption in the theory outlined 

 that is most open to doubt is that involved in equation (1) namely, that water dis- 

 sociates into two parts. 



The most probable value of ' n ' being 3, it is possible that the state of equilibrium 

 is one between (H 2 0) 8 and three molecules, H 2 0. Applying the mass-action law 

 to this case and proceeding as above there results, in place of Rudolphi's equation, 



(1 - a)V* 

 and in place of van't Hoff's equation, 



"=E. 



(1 - a)V' 



These two equations do not hold for dilute solutions, so that it seems correct to 

 consider the products of dissociation to be di-hydrol and mono-hydrol at ordinary 



