ELECTROLYTES AND THEIR ACTION 199 



For this reason they make useful standard mixtures for hydrogefr ion con- 

 centrations not far removed from neutrality, as we shall see later. 



The Bicarbonate System. Similar considerations may be applied to the 

 bicarbonate and carbon dioxide system. In actual dissociation the conditions 

 are not so complex, since we have to deal with a dibasic acid instead of a 

 tribasic one. On the other hand, there is a new complication added in the 

 escape of CO 9 as a gas. 



The equations of dissociation may be written thus, to correspond with those 

 of the phosphates : 



(3) 



(4) 



(5) 



(6) HCO 3 ' + H 2 O^H 2 CO 3 + OH'. 



Since carbonic acid, H 2 CO 3 , is a very weak acid, few hydrogen ions are formed 

 by equation (4). Sodium bicarbonate, as a weak base, produces few hydroxyl 

 ions, but as a sodium salt, produces a considerable number of HCO 3 ' ions. 

 Suppose that CO 2 is added to a mixture of bicarbonate and CO 9 .H CO 3 is 

 formed, and this increases the concentration of HCO 3 ' by dissociation. The 

 result of this will be increase of non-dissociated NaHCO 3 by throwing back 

 equation (3). 



The way in which these facts work in the maintenance of moderate changes 

 only in H' ion concentration will best be seen by taking a numerical example. 

 We must first, however, refer to the principle of isohydric solutions. This 

 states that, if two solutions have an ion in common and in the same concentration 

 in both, no change in the concentration of this ion will take place when the 

 solutions are mixed. 



The dissociation constant of H 2 CO 3 is 3 x 10~ 7 , hence 



(3xlO--)(H 2 C0 3 ) = (H-)(HC0 3 ') 5 



and that of H 2 PO 4 ' is 2 x 10~", according to Lawrence J. Henderson (1909, 

 p. 269), hence 



(2 x 10-') (H 2 P0 4 ') = (H-) (HP0 4 "). 



Suppose that H 2 CO 3 and NaHCO 3 are present together in a solution. From 

 the low value of the dissociation constant of the former we may assume that the 

 concentration of the non-dissociated H 9 CO 3 is almost exactly the same as that of 

 the dissolved CO 2 ; practically all the HCO 3 ' ions, therefore, come from the 

 strongly dissociated NaHCO 3 , and their concentration is proportional to it that 

 is, in decimolar concentration, about 0'8 of it, since this is the proportion 

 dissociated. The dissociation of NaH 2 PO 4 is also 0-8, and that of Na. 2 HPO 4 , 

 as regards H* ion, is 0'04. 



We may write the above equations thus : 



and, if the salts are in decimolar concentration : 



~ 0-8(NaHC0 3 ) ~ -04(Na 2 HPO 4 ) 



Hence, to obtain a hydrogen ion concentration of 1 x 10' 7 (i.e., neutrality at 

 24) 



(H 2 CQ 3 ) J_ (NaH,P0 4 ) 1 

 (NaHCO 3 )~3-75 Or (Na 2 HPO 4 ) 'J'5' 



an expression which gives the proportion of the constituents necessary for 

 neutrality in a solution containing all four, or either pair, since they are isohydric. 

 The absolute concentrations may vary so long as the ratios are kept constant, 

 and the latter can only change if dissociation constants change. 



For the sake of simplicity, we will take for further consideration the first 



