40 HYDROGEN ION CONCENTRATION 



the unionized part is [SH] = [A] — [H+]. From which it follows 

 that 



fH+]= 



[A] - IH+] 



k 



■V' 



[H+] = l/- + kA - - 



For weak acids this formula is simplified in the following manner: 



When the dissociation constant of the acid is very small then its 

 ionization is naturally very slight, less than one per cent, for example. 

 It can then be said with a fair degree of accuracy that the con- 

 centration of the undissociated acid is equal to that of the total 

 acid, or, [HS] = [A]. Hence it follows that 



[H+] = Vk X [A] (la) 



The [H+] is, therefore, proportional to the square root of the 

 concentration of the total acid. The analogous rule holds for the 

 case of a weak base where 



[0H-] = Vk X [B] 

 where [B] is the concentration of the total base. By substituting 

 for [0H-] its value as ^-77:^ the relation becomes 



IH+] = 



Vk X [B] 



For the weakest acids whose dissociation constants are of the 

 order of magnitude of that of water, as well as for moderately 

 strong acids in extremely low concentrations the above formulas 

 do not hold. For in these cases the H-ions yielded by the water 

 cannot be ignored in relation to those of the acid. In such cases the 

 [H+] is determined in the following way: Here also as above, be- 

 cause of the very slight degree of dissociation [HS] = [A] and 



[A] 

 Further, in accord with the law of electro-neutrality which 



