Section (jy. Ionization of the Substances. 275 



if it were alone present at such a concentration that its ions are at a con- 

 centration equal to that of the common ion in the mixture, we determine 



the ratios K2 ^ ^, and -^ * by reference to the ioniza- 



C.K2SO4 + Cso 4 C-KHSO4 + Chso 4 



tion values given in table 27, Part IV, and in table 12, Part II, for potas- 

 sium sulphate and for potassium chloride, respectively, at the same concen- 

 tration of the total potassium.* In a similar way we obtained the ratio 

 Ch 2 so 4 /(Ch 2 so 4 + Chso 4 ) by determining from the data given in table 118 

 the value of this ratio for sulphuric acid when present alone in a solution 

 in which the hydrogen-ion concentration is the same as that in the solution 

 of the acid-salt under consideration. From these ratios and the prelimi- 

 nary values of Cso 4 and Chso 4 , final values of Ck 2 so 4 , Ckhso 4 , and Ch 2 so 4 

 are calculated. From these Ck is also obtained by means of the equation 

 Ck +Ckhso 4 + 2 Ckso 4 = C, where C is the molal concentration of the 

 potassium hydrogen sulphate. It follows now from the two equations, 



Ch -f- Chso 4 -j- Ckhso 4 -f- 2 Ch 2 so 4 C 

 and Cso 4 + Chso 4 + Ckhso 4 -f- Ch 2 so 4 -f- Ck 2 .so 4 = C, 

 that Cso 4 = Ch + Ch 2 so 4 Ck 2 so 4 

 and Chso 4 = C Ch 2 Ch 2 so 4 Ckhso 4 . 

 We have then calculated final values of Ch by the following equation, 

 which expresses the molal conductance A of the salt in terms of the 

 equivalent conductances and molal concentrations of the separate ions, 

 CA = CkAk + ChAh -f- Chso 4 Ahso 4 + 2 C S o 4 Aso 4 . In this equation all the 

 quantities except C H are known or can be expressed in terms of Ch and 

 known quantities with the help of the two preceding equations. The 

 equation then becomes 



c c 



-~-(Ah + A S o 4 -f- Aso 4 Ahso 4 ) = A -~ (A K + Ahso 4 ) + 



2(CkoSo 4 Ch 2 so 4 ) / . . s 



r - ( Aso 4 Ahso 4 j 



From the values of Ch/C so obtained we have finally calculated Cso 4 /C 



Whether one considers the ionization at the same concentration of the potassium- 

 ion or of the total potassium makes no substantial difference. 



