Section 97. Ionization of the Substances. 273 



gen) ; and it may reasonably be assumed that the same is true at 18 and 

 the intermediate temperatures. 



With the help of this principle, the secondary ionization of the sulphuric 

 acid that is, the ratio of the sulphate-ion concentration to the total sul- 

 phuric acid concentration can be calculated for the more dilute solu- 

 tions and for the lower temperatures by means of the relation 



Cso 4 Ch Ch.>so4 1 



~c~ ~ ~c + c 



where C represents the total molal concentration of the sulphuric acid, 

 and the other symbols, the molal concentrations of the separate substances 

 as indicated by the subscripts. This relation follows at once from a com- 

 bination of the equations, C = Ch^so 4 + Chso 4 + Cso 4 and Cn = Chso 4 + 

 2 Cso 4 , the latter of which is an expression of the fact that hydrogen-ion is 

 produced by the two chemical reactions H.,S0 4 H + -f- HS0 4 ~ and 

 H 2 S0 4 = 2 H + + S0 4 =. 



We have first made a preliminary calculation of the ratio Cso 4 /C by 

 the above expression by using for Cu/C twice the mean of the pairs of 

 values given in table 114 of the ratio of the hydrogen-ion concentration to 

 the total hydrogen-concentration, and by taking for Ch 2 so 4 /C the values 

 of the corresponding ratio for hydrochloric acid as derived from ionization 

 data given in table 41, Part V. We have then on the basis of this result, 

 which shows the approximate proportion of sulphate-ion and hydrosul- 

 phate-ion in the solution, interpolated a more correct value of the hydro- 

 gen-ion concentration between the two limiting values given in tables 114 

 and 115, which, it will be remembered, were obtained under the two 

 limiting assumptions that the acid dissociates only into H + and SO^f and 

 that it dissociates only into H + and HS0 4 ~.* Then new, final values of 

 the concentrations of the sulphate-ion and hydrosulphate-ion were obtained 

 by repeating the calculation. 



The values derived through these considerations are all brought together 

 in table 118. It will be understood, of course, that they are only rough 

 approximations. The concentrations are milli-formula-weights per liter, 

 in accordance with the formula represented by the subscripts. The symbol 

 C represents the total concentration of the acid in milli-formula-weights 

 of H 2 S0 4 per liter. But in calculating the values of the ionization-con- 

 stant given in the last column, the concentrations are all expressed in 

 formula-weights (not milli-formula-weights) per liter. 



*Designating these two limiting values (multiplied by 2) by C H /C and C H /C, 

 respectively, it can be readily shown by formulating the exact conductance equations 

 that we get for the true value of C/C: 



Cjl Ch 1 ChSQ4 ( Ch~Ch \ Ch 2CsQ4 / Ch~~Ch \ 



c : : c c V c " / c ~ c V c ' /' 



