22 Mr. W. Sutherland on Ionization in Solutions 



our theoretical equation when v 1 = v 2 = l may be written 

 X=X — j\ (2n)*, showing the variation of X to be propor- 

 tional to A , whereas Kohlrausch finds it nearly proportional 

 to X Y . He also, in his latest paper (1904), makes X linear 

 in ri*. It seems to me that these discrepancies between 

 theory and experiment are probably due to the neglected, 

 variation of the conductivity of water caused by the presence 

 of solute. It offers a likely clue to the law of the ionization 

 of H 2 by solutes. But although this nicety of theory seems 

 at present to be lost in experiment, because of uncertainty 

 about the ionization of H 2 0, the experiments of Kohl- 

 rausch substantiate it in another way. On the average, the 

 chlorides and nitrates of K, Na, and Li give approximately 

 X=X — 120(v 1 7i) 7 for monovalent ion with monovalent, that 

 is, with v i — v 2 = n i = n 2 = l. According to the result for all 

 solutions of NaCl at the beginning of this section, the co- 

 efficient 120 should be replaced by 4-035 X = 440. This 

 discrepancy seems to arise from the same cause as those just 

 mentioned. It requires special investigation, though it 

 affects all solutions in a similar manner. 



For the oxalate and sulphate of K and the nitrates of Ba 

 and Sr, that is for two monovalent ions along with a divalent, 

 when v 2 = v ] /2 = n 2 /2 = 7i 1 = l or vice versa, the coefficient of 

 (Viw)* has the values 270, 390, 360, and 340, the mean being 

 340. For MgS0 4 and ZnSQ 4 , according to the data of 1904 

 due to Kohlrausch and Grriineisen, the coefficient is 1490 and 

 1600, mean 1550. Here we have divalent ion with divalent 

 ion, and v l = Vo=2n 1 = 2n (2 = 2. Now, from the theoretical 

 relation (23), if for the moment we assume A 01 and A 02 to 

 have the same constant value for all ions, we deduce that the 

 coefficients of (v^i)^ in these three cases ought to stand to 

 one another as 2* : 2(3/2)* : 4, or as 1'26 : 2*29 : 4 ; whereas 

 the 120, 340, and 1550 just given from experiment with very 

 dilute solutions are more nearly as 1*2 : 34 : 15'5. From 

 strong solutions at the beginning of this section the ratios 

 are 4'03 : 7'3 : 3 L'55, or 1*2 : 2'2 : 9'5. 



We can bring the theory into harmony with experiment 

 if we go back to Section 2 and take T the time of relaxation 

 in f to be proportional to (vi + Vq) 2 , or to the square of the 

 mean valency of the solute whose motion is being studied. 

 The effective force keeping a solute completely ionized 

 appears to vary inversely as the square of the mean valency 

 of the solute it is acting upon. So in (4), (9), and (13) 

 C should be treated as proportional to (v x + v 2 ) 2 ; and therefore 

 in (23), if j is to be treated as an absolute constant, a factor 



