﻿Constitution of Aqueous Solutions. 11 



the simplest way to proceed is to find r for H by t/(X,KB3)^ 

 = 0-222 using for X 67-5, and to find r for OH by t/(\KB!> 

 = 0-05 with \ = 62-7. The results are 1/83 and 1*23. 

 Each H ion keeps 1'83 molecules of (H 2 0) 3 out of existence, 

 and each OH ion keeps 1*23 in existence. But as regards 

 the H ion of an acid, we have seen that it also breaks up 

 1*92H 2 into H and OH, and we ought to consider this H 2 

 derived from the (H 2 0) 2 into which (H 2 0) 3 is broken down 

 by the ion. So there is an extra change of volume due to 

 this ionization. The limiting volume of the H ion being 8 

 and of OH being 10, the mean volume of a gramme of 

 ionized H 2 is 18/18 or 1. Thus J(H 2 0) 2 in changing from 

 dihvdrol into the ions H and OH undergoes expansion 

 18(1-0-9179), so the ionization of 1*92 times ^(H 2 0) 2 causes 

 expansion 2'84. But the change of (H 2 0) 3 into [;(HnO) 2 

 involves a contraction 11*8. Hence the contraction due to 

 the ionization of H 2 caused bv the H ion is equivalent to 

 the forming of 2-81/1 1*8 or 0"24 molecules of (H 2 0) ? from 

 (H 2 0) 2 . Hence for the apparent value of r for the H ion we 

 have 1*83 due to itself, 1'92 x 1*83 due to the 192 ions of H 

 it liberates from H 2 diminished by 1'92 x T23 for the 

 contrary effect of the 1*92 ions of OH formed by it, and 

 then further diminished by the O'2-l just found. This gives 

 for the apparent value of r for H the value 2*74 to be 

 compared with the 2*66 obtained from the HN0 3 data. A 

 similar calculation for the OH ion gives for r the apparent 

 value 



- 1-86 x 1-23 + 0-86x1-83 + 0*86 x 0-136-1 x 18/11-8 



or — 0'53 to be compared with — 0'29 obtained from the 

 NaOH and KOH data. In both cases the agreement is 

 sufficient to confirm the conclusion reached from the apparent 

 ionic velocities of H and OH. 



From this investigation of the characteristic ions of acids 

 and alkalies w T e have obtained the following results : — That 

 the ionic velocities ascribed to H and OH are not the real 

 velocities of these ions, but the sum of the true velocities and 

 the velocities of the ions which these produce from H 2 0. In 

 u Ionization &c." (loc. cit.) I suggested that the large excep- 

 tional velocities of H and OH might be due to the fact that 

 these being the ions of H 2 might enter (H 2 0) 3 and (H 2 0) 2 

 at one end and liberate the corresponding ion at the other by 

 electric action, these ions thus appearing to have larger velo- 

 cities than the true ones. Here we have reached the more 

 definite conclusion that the exceptionally large velocities are 

 due to the ionization of H 2 by H and OH, whereby the 



