22 HYDROGEN ION CONCENTRATION 



If the [0H~] be graphically represented in a rectangular system of 

 coordinates as a function of [H+] then the hyperbola shown in 

 figure 1 is obtained. 



It is of interest to find out at what reaction the sum of H+ and 

 0H~ ions of a solution is at its minimum. An inspection of the above 

 figure shows that it occurs at the neutral reaction, [H+] = 10~'^. 



Mathematically this point can be derived in the following way: 

 Let the sought value [H+] + [0H~] be designated as u. Then 



u = [H+J + IOH-] 



Km 



u = [H+] + 



[H+] 



du k. 



d[H+] [H+]2 



Setting this derivative = 0, we obtain as the minimal condition 



[H+] = V^ 

 [H+] = IOH-] = Vk^ 



which represents the reaction of neutrality. That this value repre- 

 sents a minimum and not a maximum is shown by the fact that its 

 second derivative 



d[H+]2 [H+]2 



must always be positive. 



7. The hydrogen ion exponent and the pH scale 



The statement [H+] = 10"^ may also be expressed as log [H+] 

 = -7, or, -log [H+] = 7. S0renseni'' replaced the term log [H+] 

 by the symbol pH.^^ The acidic or basic property of a solution 



1^ S. P. L. Sorensen, Enzymstudien II. Biochem. Zeitschr. 21, 131 (1909). 



16 S0rensen's original symbol was PH"^; the present author uses ph for 

 -log[H+], and the symbol h for [H+]. In order to avoid adding to the already 

 confusing multiplicity of these symbols the form pH adopted by the Amer- 

 ican Society of Biological Chemists and the symbol [H+] now in current use 

 in this country will be adhered to in this translation to designate S0renson's 

 exponent and the molar concentration of hydrogen ions respectively. The 

 abbreviation "hydrion" for hydrogen ion will also be used. — Translator. 



