490 The Origin of the Theory of Solutions, 



The general result of the investigation has been the experi- 

 mental confirmation of the theoretically predicted presence of 

 a minimum in the velocity. What takes place here ? The 

 H- and OH-ions in the water cause the saponification; the 

 acid which is formed undergoes electrolytic dissociation with 

 the production of H-ions. 



The equilibrium 4- — 



H + OTT -^— » H 2 Q ; 



which takes place between the H- and OH-ions on the one 

 hand and the water on the other, necessitates a diminution 

 in the number of hydroxy] ions on the appearance of new 

 hydrogen ions. The hydroxyl ions, however, saponify very 

 rapidly, and from the velocity of saponification by bases it is 

 calculated that they saponify 1400 times more rapidly than 

 hydrogen ions. Hence there must be a decrease in the velocity 

 caused by the disappearance of OH-ions, followed by an 

 increase in the velocity due to the increased production of 

 H-ions; in other words, there must be a minimum velocity. 



If C represents the concentration of the ester, and H and 

 C OH the concentrations of the ions, we have mathematically: — 



Telocity = KC(C H + 1400 C OH ) 



and H OH -="A. 



The change of velocity is 



dC R + U0OdC QW 



the minimum velocity 



rZC H =~1400dC OH 

 and C oh^°h = ~ C H rfC OH 5 



hence O nn = 5_. 



0H 1400 



The minimum therefore occurs when there are 1400 H-ions 

 and one OH-ion present in the solution. 



This is represented graphically in fig. 6. After about two 

 hours the velocity sinks to about -£§ of its initial value. At 

 this stage, two sets of experiments showed that a minimum 

 actually existed. 



A third experiment, performed with the greatest care, was 

 therefore made in order to determine accurately the minimum 

 velocity, and from this to calculate the electrolytic dissociation 

 of water. The result which was obtained was 0*071 X 10~ per 



