42 HYDROGEN ION CONCENTRATION 



But since the concentrations of the undissociated acids, [Si] and 

 [S2], in the case of weak acids are virtually equal to those of the total 

 acids, or to [Ai] and [A2] respectively, the above expression becomes 

 for practical purposes: 



[H+] = VkiAi + k,A3 (5) 



For example if we take a solution containing one mole of acetic 

 acid per liter (ki = 2 X 10~^) and one mole of carbonic acid (ka 

 = 3 X 10~^), then its hydrion concentration is 



[H+] = V2 X 10-5 + 3 X 10-7 



which is practically equal to that of a one molar acetic acid solu- 

 tion without carbonic acid, where 



[H+] = -v/2 X 10-s 



Even the hydrion concentration of a solution of one molar CO2 

 + 0.1 molar acetic acid solution, 



[H+] = Vo.l X 2 X 10-5 + 3 X 10-' = 4.5 X 10-^ 



is practically the same as that of a pure 0.1 M acetic solution where 

 [H+] = 4.48 X 10~^ This illustrates the fact that the stronger 

 acid suppresses the dissociation of a weaker acid. 



Many years ago Arrhenius-^ established the law which states: 

 When isohydric solutions (solutions of the same [H'^]) of different acids 

 are mixed, the [H+] is not changed on mixing. This law may be 

 easily derived from the data given above in this section. Let Ai 

 and A2 be the concentrations of the two acids whose dissociation 

 constants are ki and k2. The concentrations Ai and A2 are so 

 chosen that the [H+] of the two solutions is the same. This con- 

 dition is fulfilled when (see (la) on p. 40) ki X Ai = k2 X A2, 

 and then of course [H+] = V ki X Ai = Vk2 X A2. Let us now 

 mix m volumes of the first solution with n volumes of the second. 



Then the concentration of the first acid in the mixture is ; — Ai, 



m + n 



n 



and the concentration of the second is ; — A2. According 



m + n 



to (5) above the hydrion concentration of the mixture is: 



-V' 



[H+] = t/ki • — ^ Ai 4- kj 



m + n ' m + n 



■^ Sv. Arrhenius, Zeitschr. f. physikal. Chem. 2, 284 (1888). 



