HETEROGENEOUS EQUILIBRIA 265 



electrolyte. For thallous chloride in the presence of potassium chloride 

 the following results are obtained: 



TABLE CV. 



VALUE OF THE UN-IONIZED FRACTION AND OF THE ION PRODUCT FOB 



THALLOUS CHLORIDE IN WATER AT 25, IN THE PRESENCE OF 



POTASSIUM CHLORIDE, ASSUMING EQUATION 52. 



C of KC1 25 50 100 200 



S u 0.001755 0.001746 0.001734 0.001703 0.001586 



P-X10 4 . 2.052 2.039 2.011 1.973 1.808 



i 



The calculations are based upon A values identical with those of 

 Bray and Winninghoff. 27 Taking into account the uncertainties in the 

 values of A , as well as in the values of the solubilities themselves, it- 

 appears from an inspection of the above table that, assuming the equi- 

 librium in the mixture to be governed by Equation 52, the concentration 

 of the un-ionized fraction in the mixture, as well as the value of the ion 

 product, remains substantially constant up to a concentration of approxi- 

 mately 0.1 N potassium chloride. For example, in the presence of 0.1 N 

 potassium chloride, the concentration of the un-ionized fraction as cal- 

 culated is 0.001703 as against 0.001755 for a solution of thallous chloride 

 in water alone. This represents an increase of only 1.9 per cent. Simi- 

 larly, the ion product over the same concentration interval varies ondy 

 4 per cent. The increase in the value of the ion product and the de- 

 crease in the concentration of the un-ionized fraction of a binary salt, 

 on addition of a second electrolyte with a common ion, is therefore 

 primarily a consequence of the form of the function assumed as govern- 

 ing the equilibrium in the mixture. The manner in which P and C vary 



% u 



on the addition of a second electrolyte remains uncertain so long as the 

 law governing the equilibria in mixtures remains unknown. 



If the value of the ion product and the concentration of the un-ionized 

 fraction remain constant, the solubility of the salt is given by the 

 equation: 



KS 

 (70) S = S u 



where S is the solubility of the salt at any concentration, S u is the con- 

 centration of the un-ionized fraction, which is independent of concentra- 

 tion, 20^ is the concentration of the common ion, and K^ is a constant 



for the mixture whose value may be determined from the ioniza- 



27 Bray and Winninghoff, loc. cit. 



