﻿Ionic 
  Velocities*, 
  and 
  Atomic 
  Sizes. 
  169 
  

  

  ion 
  we 
  may 
  take 
  K 
  as 
  of 
  the 
  order 
  2, 
  while 
  K 
  is 
  80, 
  and 
  

   therefore 
  (1— 
  K 
  /K)//D 
  is 
  of 
  the 
  order 
  1/14; 
  for 
  m=-'01, 
  

   this 
  expression 
  will 
  be 
  1/140, 
  for 
  w 
  = 
  '001 
  it 
  will 
  be 
  1/1400. 
  

   For 
  dilute 
  solutions 
  it 
  is 
  therefore 
  negligible, 
  but 
  for 
  solutions 
  

   of 
  the 
  order 
  m 
  = 
  *01 
  it 
  cannot 
  safely 
  be 
  neglected, 
  especially 
  

   in 
  the 
  study 
  of 
  formula? 
  where 
  1— 
  •'% 
  plays 
  an 
  important 
  

   part, 
  for 
  though 
  the 
  error 
  in 
  i 
  may 
  be 
  relatively 
  small, 
  that 
  

   in 
  1 
  — 
  / 
  may 
  be 
  relatively 
  large. 
  In 
  the 
  case 
  of 
  an 
  ion 
  for 
  

   which 
  K 
  is 
  larger, 
  say 
  20 
  instead 
  of 
  2, 
  then 
  the 
  effect 
  of 
  

   dielectric 
  capacity 
  becomes 
  less 
  important. 
  But 
  this 
  line 
  

   of 
  thought 
  does 
  not 
  lead 
  direct 
  to 
  the 
  explanation 
  of 
  the 
  

   diverse 
  behaviour 
  discovered 
  by 
  Ostwald 
  for 
  weak 
  acids 
  and 
  

   ordinary 
  binary 
  electrolytes 
  ; 
  because 
  if 
  a 
  large 
  value 
  of 
  K 
  

   secures 
  that 
  i 
  measured 
  in 
  the 
  usual 
  way 
  is 
  nearly 
  correct 
  

   for 
  CH 
  3 
  COO 
  in 
  acetic 
  acid, 
  it 
  ought 
  also 
  to 
  act 
  in 
  the 
  same 
  

   way 
  for 
  sodium 
  acetate, 
  and 
  so 
  bring 
  this 
  electrolyte 
  under 
  

   Ostwald's 
  law 
  for 
  weak 
  acids 
  like 
  acetic, 
  whereas 
  sodium 
  

   acetate 
  ranges 
  itself 
  with 
  the 
  ordinary 
  binary 
  electrolytes. 
  

   It 
  seems 
  to 
  me 
  that 
  the 
  following 
  is 
  a 
  probable 
  explanation 
  

   why 
  Ostwald's 
  formula 
  applies 
  to 
  weak 
  acids. 
  Many 
  of 
  these 
  

   acids 
  are 
  known 
  to 
  polymerize. 
  Acetic 
  acid 
  is 
  probably 
  

   (CH 
  3 
  COOH) 
  2 
  , 
  and 
  when 
  dissolved 
  in 
  water 
  is 
  partly 
  dis- 
  

   sociated 
  into 
  CH3COOH, 
  which 
  is 
  practically 
  all 
  ionized 
  into 
  

   CH-COO 
  and 
  H 
  at 
  the 
  dilutions 
  of 
  Ostwald's 
  experiments. 
  The 
  

   conductivity 
  measurements 
  of 
  Ostwald 
  thus 
  give 
  him 
  the 
  

   amount 
  of 
  (CH 
  3 
  COOH) 
  2 
  which 
  has 
  been 
  dissociated 
  into 
  

   CH3COOH, 
  and 
  his 
  law 
  for 
  acetic 
  acid 
  is 
  probably 
  the 
  ex- 
  

   pression 
  for 
  equilibrium 
  between 
  di-acetic 
  acicl 
  and 
  the 
  

   products 
  of 
  its 
  dissociation, 
  namely, 
  mono-acetic 
  acid. 
  A 
  

   similar 
  explanation 
  will 
  apply 
  to 
  all 
  his 
  cases 
  of 
  weak 
  acids. 
  

   In 
  the 
  case 
  of 
  acetates 
  like 
  that 
  of 
  sodium, 
  we 
  must 
  consider 
  

   that 
  the 
  polymerization 
  is 
  not 
  so 
  stable 
  in 
  the 
  presence 
  of 
  

   water 
  as 
  that 
  of 
  acetic 
  acid, 
  and 
  that 
  in 
  dilute 
  solutions 
  the 
  

   di-acetate 
  is 
  practically 
  all 
  dissociated 
  into 
  mono-acetate, 
  

   in 
  which 
  form 
  the 
  acetate 
  is 
  usually 
  assumed 
  to 
  be 
  present 
  in 
  

   aqueous 
  solutions, 
  and, 
  finally, 
  that 
  with 
  the 
  acetates 
  it 
  is 
  

   really 
  the 
  dissociation 
  into 
  CH 
  3 
  COO, 
  and 
  Na 
  or 
  K 
  that 
  we 
  

   investigate 
  by 
  means 
  of 
  conductivities, 
  and 
  not 
  as 
  in 
  acetic 
  

   acid 
  the 
  relative 
  amounts 
  of 
  diacetate 
  and 
  monoacetate. 
  

  

  As 
  it 
  has 
  been 
  shown 
  that 
  we 
  must 
  have 
  an 
  experimental 
  

   investigation 
  of 
  dielectric 
  capacity 
  in 
  solutions 
  before 
  we 
  

   can 
  determine 
  ionizations 
  satisfactorily, 
  I 
  do 
  not 
  propose 
  to 
  

   dwell 
  at 
  length 
  on 
  the 
  wealth 
  of 
  existing 
  data, 
  but 
  a 
  brief 
  

   discussion 
  of 
  a 
  few 
  typical 
  solutions 
  is 
  necessary. 
  The 
  

   solutions 
  chosen 
  are 
  those 
  of 
  NaCl, 
  BaCl 
  2 
  , 
  CaCl 
  2 
  , 
  (NH 
  4 
  ) 
  2 
  S0 
  4 
  , 
  

   and 
  ZnS0 
  4 
  . 
  For 
  solutions 
  of 
  NaCl 
  we 
  have 
  the 
  latest 
  

  

  