120 



HYDKOGEN ION CONCENTRATION 



Oj9S 



is on the average greater than the mean distance between two 



oppositely charged ions which attract each other. Between two 



univalent ions there is a potential difference which may be expressed 



e- 

 as — , where e is the charge on the ion and r is the distance. The 



potential between two ions of the same charge is reverse in sign to 

 that existing between two ions oppositely charged, which is due to 

 repulsion in the first and to attraction in the latter case. If the mean 

 distance between any two neighboring identically charged ions were 

 equal to that between two oppositely charged ions, then the algebraic 

 sum of the individual potential differences would be equal to zero. 



But since these distances are not 

 equal, therefore the total poten- 

 tial is not = 0, and as a result 

 there is an average potential dif- 

 ference, in the sense that the 

 attraction exceeds the repulsion. 

 In such a solution, therefore, 

 there is stored a certain amount 

 of potential difference. This de- 

 duction is used by Milner in his 

 second paper to calculate the 

 effect of the ionic charge upon 

 the lowering of the freezing point 

 of a solution. As a result of very 

 complicated calculations he ob- 

 tained the curves shown in figure 

 15. This figure shows in the dotted curve how the molar lowering of 

 the freezing point should change with the concentration of an elec- 

 trolyte consisting of two univalent ions, assuming the usual mass 

 action law; while the solid line curve represents the results of Milner 's 

 calculations. The crosses indicate the values for KCl found by 

 freezing point determinations. With the exception of the lowest con- 

 centrations for which the experimental technic is uncertain and the 

 highest concentrations for which the accuracy of the calculations 

 becomes uncertain, the observed points agree quite well with the 

 calculated values. Bjerrum called the mutual effect of the ions in 

 regard to their osmotic pressure "the Milner effect." It is, therefore, 

 unnecessary to assume any measurably incomplete dissociation of 

 KCl in order to explain the course of its lowering of the freezing point. 



OSO 



0.05 

 Concentration 



Fig. 15 



(Taken from Bjerrum) 



