44 HYDEOGEN ION CONCENTRATION 



from which 



fFT+i — ^ t^^J _ u [undissociated acid] 

 [S~] [acid ion] 



In such a mixture the concentration of the undissociated acid is- 

 virtually equal to the concentration of total free acetic acid, for the 

 latter is very slightly dissociated. The concentration of the anions 

 in this mixture is virtually equal to that of the sodium acetate, for 

 the latter is assumed to be completely dissociated, and the acetate 

 ions given off by the free acetic acid are negligible in quantity com- 

 pared to those given off by the salt. The expression given above 

 therefore becomes: 



[H+] = k X [^^^^ ^^^^'^^ ^^'^^^ (1) 



[Na— acetate] 



This expression is an approximation, since it is based on certain 

 assumptions which are not absolutely exact. But it is quite valid 

 for a great variety of cases with a very fair degree of accuracy. The 

 deviations found under certain conditions, which will be dwelt upon 

 later, are so small that they can well be used only as corrections for 

 the above approximation. 



For somewhat stronger acids, such as tartaric acid, in which the 

 dissociation of the free acid may not be disregarded, the concentra- 

 tion of the undissociated acid is not assumed to be equal to that of 

 the free acid [E] but is expressed as [E] — [H+]; and the concentra- 

 tion of the anions is not equal to that of the salt, for the free acid 

 yields also anions to the same extent as it does H-ions. Instead of 

 the above equation (1) we obtain: 



^ k([E] - [H^]) 



[Na-salt] + [H+] ^ ^ 



From this the following quadratic equation for [H+] is derived: 



vc 



^^^ ^ _ [N.-saltl+k _^ l/ UNa-saltl + k V ^ ^ ^^^ 



This is the first correction for the approximate formula. Prac- 

 tically, it is seldom of any significance. The second much more im- 

 portant correction has the purpose of rectifying the approximate 



