towards a Dynamical Theory of Solutions. Gl 



relation we can use the data of Otten from the Tahellen for 

 X at 18° C. for formic acid and propionic acid, using for 77 

 the values found by Tsakalotos at 20°, which in the case of 

 water differ by about 2 parts in 1000 from the mean of the 

 best experimental values at 18°. For formic acid 



(\97) i =0-3308-0-2386j9 1 .... (54) 



as shown by the comparison 



10% 955 2034 298 



3 3995 



5002 5996 7006 



8902 



9853 



10^)3 exp. ... 3346 2863 2599 2343 



2116 1884 1638 



1107 



572 



calc. ... 3080 2823 259 



7 2355 



2114 1877 1636 



1184 



957 



For propionic acid 











(\ v y = o- 



2217 — 



0-223 Pl , . . 





(55) 



the comparison being 











10% 1007 2001 



3004 



5004 7001 1 



5997 



10000 



10Vw;)3exp. ... 2190 1820 



1542 



1086 626 



347 



iso 



calc... 1992 1770 



1547 



1100 656 



185 



—13 



The case where pi = l doas not rightly enter into the 

 comparison, it is added for information only. 



For acetic acid with the data of Kohlrausch 



(Xiy) f =0-2'366-0-223|>„ . (56) 



and for butyric acid with the data of Otten 



(\ v y = 0'2'dW-0-2±5 1 ? 1 . . (57) 



For propionic acid (55) can be simplified to 



(\ v f = 0-225 p 2 , .... (58) 



and for butyric (57) to the same. Our essential theoretical 

 problem is to interpret the meaning of the simple form 



(\r))* = a] : '>2 hi a manner harmonious with the interpretation 

 of (53). It becomes (X^/\ ?; o ) 2 = a 6 p 2 6 /\<y7i 2 which may be 

 regarded as an approximation derived from 



(XVAo%) 2 =«Vp 6 (l-A'?/X„%)/A V J . . (59) 



in which \rj/\ 7j is small. It may be said that (53) in the 

 fatty acids holds from pi — nearly, to 0*1, 'and (58) from 

 0'2 to 0*8 or 0*9, a transition form being required for values 

 of ;?! between 0*1 and 0*2. When p l =0'2 J Xr}/\Vo ^$ a 

 value about 0*006 for formic acid and 0'002 for the others. 

 We can now interpret (59) and (53) together. 



If there are a double molecules per unit volume, of which 

 x are ionized, there are 2x ions of each sort uniformly 



