﻿Interionic 
  Force 
  in 
  Electrolytes. 
  217 
  

  

  of 
  magnitude 
  as 
  those 
  which 
  occur 
  in 
  the 
  comparison 
  of" 
  j3 
  2 
  

   with 
  the 
  unmodified 
  mass-action 
  law. 
  The 
  point 
  may 
  be 
  

   illustrated 
  by 
  a 
  brief 
  consideration 
  of 
  one 
  of 
  the 
  most 
  recent 
  

   positions 
  reached 
  in 
  the 
  development 
  of 
  the 
  original 
  theory. 
  

  

  Kraus 
  and 
  Bray 
  * 
  have 
  found 
  as 
  a 
  result 
  of 
  a 
  detailed 
  

   examination 
  of 
  a 
  great 
  many 
  solutions 
  in 
  various 
  solvents, 
  

   that 
  the 
  variation 
  of 
  X 
  can 
  be 
  closely 
  represented 
  by 
  the 
  

   empirical 
  formula 
  

  

  o/ 
  2 
  C 
  

  

  ^ 
  = 
  K 
  + 
  D(C 
  7 
  )-, 
  

  

  where 
  7= 
  — 
  ( 
  = 
  1 
  — 
  # 
  2 
  ), 
  and 
  K 
  and 
  D 
  are 
  constants. 
  

  

  According 
  to 
  this 
  formula 
  the 
  law 
  of 
  mass 
  action 
  (4) 
  is 
  

   obeyed 
  when 
  the 
  concentration 
  is 
  sufficiently 
  small, 
  the 
  

   term 
  D(Cy) 
  w 
  being 
  ultimately 
  negligible. 
  As 
  the 
  solution 
  

   becomes 
  more 
  concentrated 
  the 
  mass-action 
  u 
  constant 
  " 
  K 
  

   becomes 
  increased 
  by 
  a 
  term 
  depending 
  on 
  the 
  concen- 
  

   tration 
  of 
  the 
  ions. 
  They 
  conclude 
  from 
  their 
  examination 
  

   that 
  in 
  all 
  cases 
  the 
  conductivity 
  ratio 
  X/\ 
  is 
  a 
  true 
  measure 
  

   of 
  the 
  ionization, 
  and 
  that 
  the 
  simple 
  law 
  of 
  mass 
  action 
  

   applies 
  if 
  the 
  solution 
  is 
  made 
  sufficiently 
  dilute. 
  This 
  view 
  

   has 
  been 
  mentioned 
  with 
  approval 
  by 
  Arrhenius 
  f 
  , 
  who, 
  

   however, 
  lays 
  stress 
  on 
  the 
  fact 
  that 
  the 
  fundamental 
  

   difficulty 
  of 
  the 
  failure 
  of 
  the 
  strict 
  mass-action 
  law 
  is 
  still 
  

   unremoved 
  by 
  the 
  use 
  of 
  an 
  empirical 
  equation. 
  Curve 
  I., 
  

   fig. 
  1, 
  shows 
  the 
  agreement 
  of 
  the 
  equation 
  

  

  -2^= 
  -080 
  + 
  2-707(Cy)' 
  673 
  , 
  7 
  = 
  

   1 
  — 
  7 
  

  

  128-3' 
  

  

  with 
  experiment 
  in 
  aqueous 
  solutions 
  of 
  KC1 
  (the 
  constants 
  

   are 
  given 
  by 
  Kraus 
  and 
  Bray, 
  and 
  the 
  experimental 
  numbers 
  

   by 
  Noyes 
  and 
  Falk, 
  loc. 
  cit.). 
  The 
  curve 
  represents 
  well 
  

   the 
  conductivities 
  over 
  a 
  wide 
  range 
  except 
  at 
  the 
  lowest 
  

  

  concentrations. 
  Now 
  assuming 
  that 
  — 
  represents 
  the 
  true 
  

  

  A 
  

  

  ionization, 
  it 
  is 
  a 
  simple 
  matter 
  to 
  apply 
  the 
  general 
  differ- 
  

   ential 
  equation 
  of 
  mass 
  action 
  which 
  is 
  applicable 
  in 
  all 
  

   circumstances, 
  to 
  determine 
  the 
  variation 
  of 
  the 
  molecular 
  

   freezing-point 
  lowering 
  with 
  the 
  concentration 
  which 
  is 
  

   thermodynamically 
  necessitated 
  by 
  this 
  assumption 
  J. 
  The 
  

  

  * 
  Amer. 
  Chem. 
  Soc. 
  Journ. 
  xxxv. 
  p. 
  1315 
  (1913). 
  

   t 
  Chem. 
  Soc. 
  Journ. 
  cv. 
  p. 
  1414 
  (1914). 
  

   X 
  See 
  Appendix. 
  

  

  