50 



HYDROGEN ION CONCENTRATION 



rrr^-i [a— 1 



By substituting for [HS] its value in (1), namely, r , we 



obtain 



a 



k + [H+] 



(2) 



Thus this equation represents a as a function of [H+]. The 

 dissociation constant of the acid, k, appears in this equation as a 

 constant value characterizing the function, which will be here 

 designated as the parameter of this function. The function a = 



. - . is graphically represented by the curve in figure 2 which 



shows a hyperbola cutting the zero ordinate at a sharp angle. 



1 2 3 V 5 10 Kxio-'' 



Fig. 2. The degree of dissociation-(a)-curve of an acid whose dissociation 

 constant = 1 X 10~'. Abscissa — [H+], ordinate-a. 



This representation is not especially clear, and the highly practical 

 significance of this function rests on the fact that by means of a 

 simple logarithmic transformation of the abscissa a very compre- 

 hensible graphic form is obtained. Instead of the abscissa repre- 

 senting the [H+] in our new form it stands for pH, and the curve 

 shows a as a function of pH. 



pH is an antibatic function of [H+]; i.e., the pH curve falls with 

 the rising [H+] curve. 



Our function may then be written as 



k 



a = 



k + 10-PH 



(2b) 



and is represented graphically in figure 3 on page 51. 



