NON-DISSOCIABLE INORGANIC RADICAL 173 



ion and one casein ion, then applying the ordinary laws of dis- 

 sociation, since in the solution containing no KCI the total con- 

 centration of K ions must have been very nearly 0.01 and calling 

 A the concentration of protein ions in this solution, C the dissoci- 

 ation-constant of the caseinate and X the concentration of the 

 undissociated caseinate we have, very nearly: 



0.01 A = KX 



while the solution containing 0.04 N potassium (0.03 N KCI) we 

 have, very nearly, 



whence A = 2Q X, or the caseinate must, in the first solution, have 

 been ffths dissociated. Now it should be particularly observed 

 that this is most decidedly a minimal estimate of the degree of 

 dissociation of this salt, if the assumption upon which we have 

 proceeded is correct. For free casein is insoluble and 1 gram of 

 casein is just carried into solution by 11.4 X 10~^ equivalents 

 of base, whereas these solutions contained as we have seen nearly 

 nine times this amount of neutralized KOH, If we suppose that, 

 in reality, nine COOH groups in the casein molecule have been 

 neutralized by KOH in these solutions, so that the caseinate 

 yields nine K+ ions, then the above solution (i.e., that which 

 contained no KCI) must have been no less than ffffllfths 

 dissociated. Hence, at the very lowest estimate, if we assume 

 that it dissociates potassium ions, a solution of potassium casein- 

 ate containing 99 X 10~^ equivalents of potassium per gram of 

 caseinate must be |f ths dissociated. 



Upon dilution, therefore, its conductivity could only increase 

 by ^V^h, or 4 per cent and, moreover, no solution of potassium 

 caseinate could be possessed of a greater equivalent conductivity 

 than that of the above solution plus 4 per cent, i.e., about 90 X 10""* 

 at 30° C. 



But, as we shall see in succeeding chapters, the equivalent con- 

 ductivity of a 1 per cent solution of caseinate in 0.01 N KOH 

 increases very much more than 4 per cent on dilution, nor can 

 this increase, as we shall see, be attributed to hydrolytic dissocia- 

 tion. Moreover solutions of potassium caseinate can readily be 

 obtained which are acid to litmus and which possess an equivalent 



