﻿216 
  Dr. 
  S. 
  E. 
  Milner 
  on 
  the 
  Effect 
  of 
  

  

  the 
  equality 
  is 
  practically 
  complete 
  but 
  the 
  limit 
  of 
  experi- 
  

   mental 
  error 
  is 
  still 
  somewhat 
  wide 
  *. 
  

  

  (4) 
  fix 
  and 
  /3 
  2 
  both 
  vary 
  with 
  the 
  concentration 
  in 
  a 
  way 
  

   which 
  requires 
  to 
  be 
  accounted 
  for. 
  

  

  Tbe 
  original 
  theory 
  of 
  Arrhenius 
  of 
  course 
  explains 
  per- 
  

   fectly 
  the 
  equality 
  f3i 
  = 
  (3 
  2 
  by 
  identifying 
  each 
  of 
  them 
  with 
  

   ,/3 
  the 
  fraction 
  of 
  the 
  ions 
  associated. 
  The 
  variation 
  of 
  ft 
  

   with 
  the 
  concentration 
  (J 
  which 
  it 
  requires, 
  namely 
  

  

  fi^S-K, 
  (4) 
  

  

  is, 
  however, 
  quite 
  inconsistent 
  with 
  the 
  experimental 
  varia- 
  

   tion 
  of 
  fii 
  and 
  /3 
  2 
  . 
  Numerous 
  attempts 
  have 
  been 
  made 
  to 
  

   get 
  over 
  the 
  difficulty 
  by 
  modifications 
  in 
  the 
  mass 
  action 
  

   equation 
  (4), 
  but 
  this 
  procedure, 
  whether 
  the 
  modifications 
  

   have 
  a 
  theoretical 
  basis 
  or 
  are 
  purely 
  empirical, 
  will 
  be 
  

   found 
  to 
  increase 
  rather 
  than 
  diminish 
  the 
  difficulty 
  in 
  which 
  

   the 
  theory 
  is 
  involved. 
  For 
  the 
  law 
  (4) 
  is 
  a 
  thermodynamical 
  

   result 
  the 
  truth 
  of 
  which 
  is 
  independent 
  of 
  any 
  theory 
  of 
  

   the 
  mechanism, 
  and 
  rests 
  solely 
  on 
  the 
  assumption 
  that 
  the 
  

   osmotic 
  pressure 
  of 
  the 
  ions 
  and 
  the 
  molecules 
  obeys 
  the 
  law 
  

   for 
  perfect 
  gases. 
  If 
  the 
  phenomenon 
  is 
  one 
  of 
  pure 
  dis- 
  

   sociation 
  (and 
  no 
  successful 
  explanations 
  of 
  the 
  discrepancy 
  

   have 
  been 
  reached 
  on 
  other 
  lines), 
  the 
  fact 
  that 
  (4) 
  is 
  not 
  

   obeyed 
  is 
  conclusive 
  evidence 
  that 
  either 
  the 
  ions 
  or 
  the 
  

   molecules 
  do 
  not 
  obey 
  the 
  gas 
  law. 
  But 
  when 
  this 
  is 
  

   the 
  case, 
  the 
  experimental 
  quantity 
  fti 
  in 
  (1) 
  is 
  no 
  longer 
  

   the 
  same 
  as 
  j3 
  the 
  true 
  association. 
  /9j 
  will 
  in 
  fact 
  be 
  

   equal 
  to 
  j3 
  plus 
  the 
  additional 
  reduction 
  in 
  the 
  value 
  of 
  

   PV/RT 
  for 
  the 
  electrolyte 
  due 
  to 
  the 
  non-obedience 
  of 
  the 
  

   osmotic 
  pressure 
  to 
  the 
  gas 
  law, 
  and 
  calculation 
  shows 
  that, 
  

   as 
  far 
  as 
  can 
  be 
  estimated 
  from 
  the 
  experimental 
  curves, 
  the 
  

   last 
  term 
  is 
  many 
  times 
  greater 
  than 
  the 
  first. 
  Comparison 
  

   of 
  /3i 
  with 
  a 
  modified 
  mass-action 
  law 
  is 
  thus 
  invalid. 
  

  

  An 
  equally 
  great 
  objection 
  applies 
  to 
  any 
  attempt 
  to 
  

   represent 
  the 
  /3 
  2 
  of 
  the 
  conductivity 
  variation 
  by 
  means 
  

   of 
  a 
  modification 
  of 
  the 
  mass-action 
  law. 
  For 
  if 
  /3 
  2 
  is 
  

   actually 
  the 
  same 
  as 
  j8 
  the 
  true 
  association 
  it 
  must 
  be 
  

   different 
  from 
  f$ 
  u 
  which 
  is 
  not 
  the 
  same 
  as 
  ft 
  except 
  in 
  the 
  

   single 
  case 
  when 
  (4) 
  is 
  obeyed. 
  This 
  is, 
  however, 
  in 
  conflict 
  

   with 
  the 
  experimental 
  result 
  (3). 
  It 
  may 
  be 
  thought 
  that 
  

   the 
  differences 
  between 
  & 
  and 
  /3 
  2 
  thus 
  necessitated 
  are 
  small 
  

   second 
  order 
  ones 
  concerning 
  which 
  experiment 
  is 
  incon- 
  

   clusive, 
  but 
  this 
  is 
  not 
  the 
  case. 
  They 
  are 
  of 
  the 
  same 
  order 
  

  

  * 
  Cf. 
  A. 
  A. 
  Noyes 
  and 
  K. 
  G. 
  Falk, 
  Amer. 
  Chem. 
  Soc. 
  Journ. 
  xxxiv. 
  

   p. 
  485 
  (1912), 
  where 
  a 
  systematic 
  comparison 
  of 
  all 
  the 
  best 
  data 
  is 
  

   given. 
  

  

  