320 PHYSICAL CHEMISTRY 



hand, the divergence of the observed values from the requirement of 

 the Mass- Action Law amounts to many per cent. 



It seems appropriate at once to supplement these principles in 

 regard to the form of the concentration function by a statement of two 

 general rules which have been found to express the magnitude of the 

 ionization of salts of different types. These rules, unlike the preced- 

 ing principles, are only crude approximations; but, nevertheless, 

 they prove of some assistance in rough applications of the ionic the- 

 ory, and undoubtedly possess an important theoretical significance 

 not yet recognized. They may be stated as follows: (1) the decrease 

 of ionization with increasing concentration is roughly constant in the 

 case of different salts of the same type; and (2) the un-ionized fraction 

 at any definite molal concentration is roughly proportional to the pro- 

 duct of the valences of the two ions in the case of salts of different types. 

 Thus, at 0.1 normal concentration the mean value of the degree of 

 ionization for 17 uni-univalent salts measured at 18 is 83.3 per cent, 

 the average deviation of the separate values from this mean is 2.1 

 per cent, and the maximum deviation of any of them is 5.4 per cent, 

 of the mean value; while for fourteen uni-bivalent salts the mean 

 value is 69.8 per cent, the average deviation 5 per cent of this, and 

 the maximum deviation about 10 per cent of it. The un-ionized 

 fraction in -^ molal solution is 13^ per cent for these univalent salts; 

 30 per cent, or about twice as great, for the uni-bivalent salts; and 

 60 per cent, or about four times as great, for the three bi-bivalent salts 

 investigated (zinc, magnesium, and copper sulphates). The salts of 

 mercury and cadmium are pronounced exceptions to the rule. 



Far more extensive material for testing these rules is furnished by 

 the measurements made at 25 between the concentrations of ^ and 

 T oVf norma l- I n the case of the uni-univalent salts, data exist at this 

 temperature and these concentrations for thirty-six inorganic salts, 

 about sixty-five sodium salts of organic acids, and about an equal 

 number of hydrochlorates of organic bases. A consideration of all 

 these data shows that, with only three or four exceptions not of 

 a pronounced character, the values of the degree of ionization of all 

 these salts in ^~ normal solution lie between the limits of 84 and 90 per 

 cent and are fairly uniformly distributed throughout this range of 

 6 percent. For sixty-seven uni-bivalent salts the corresponding limits 

 of the ionization values are 72 and 81 per cent, while for only four 

 such salts do the values lie beyond these limits. For the six uni-tri- 

 valent salts investigated the range is from 67 to 76 per cent; for the 

 three uni-quadrivalent salts from 59 to 63 per cent, and for twelve 

 bi-bivalent salts from 49 to 63 per cent, while three such salts show 

 more considerable variations. The values of the un-ionized fraction 

 corresponding to the mean of these two limits for the different types 

 of salts at the same equivalent concentration increase somewhat 



