734 ACTIVITY COEFFICIENT OF THE HYDROGEN ION 



from the pH, taking the value for the dissociation constant of water 

 at 40°C. as 2.8 X 10~^^. The rate is directly proportional in this 

 range to the hydroxyl ion concentration as determined by the hydro- 

 gen electrode. It is not possible to compare the hydroxyl ion con- 

 centration as determined by the conductivity since the alkali so- 

 lutions contained some carbonate. The constant is not so good 

 here as in the acid solution since the reaction in strong alkali is ex- 

 tremely rapid. It will be noticed that the proportionality factor 

 for the hydroxyl ion is 4700 whereas that for the hydrogen ion was 

 150; i.e., the hydroxyl ions hydrolyze about 30 times more rapidly 

 than hydrogen ions at the same concentration. It is not possible 

 to say whether this difference is due to the hydrogen and hydroxyl 

 ions or to the difference in the ease of hydrolysis of the gelatin-acid 

 salt and the alkali gelatin. 



V. Influence of Hydrogen and Hydroxyl Ions in Low Concentration. 



It has been shown above that the velocity of hydrolysis in the acid 

 range may be calculated from the equation 



Velocityjj = 150 Cjj 



and in strongly alkaline solutions from the equation 



Velocity OH = 4700 Cqh 



Combining these two equations we would calculate that (in round 

 numbers) the velocity at any Cjj =150 (Ch + 30 Cqh)- This is the 

 same type of equation found by Wijs- to represent the influence 

 of the concentration of hydrogen and hydroxyl ions on the rate of 

 hydrolysis of methyl acetate. The formula predicts that the rate 

 of hydrolysis is a minimum when the Cjj = 30 Cqjj or at 40°C. at 

 about pH 6.0. (The mathematical proof of this statement is that 

 the first derivative of the above expression is zero at the point where 

 Cjj = 30 Cqhj 3-nd would be equal to approximately 3 X 10~^; i.e, 

 it would take nearly 30 years to cause an increase of 3 per cent in 

 the formol titration of a gelatin solution at 40°C.) It was found, 

 however, that the hydrolysis actually occurred at pH 6.0, about 



^- Vv'ijs, J. J. A., Z. physik. Chenu, 1893, xii, 514. 



