﻿Interionic 
  Force 
  in 
  Electrolytes. 
  215 
  

  

  theory, 
  but 
  to 
  any 
  theory 
  of 
  dissociation 
  in 
  which 
  the 
  

   reduction 
  of 
  the 
  molecular 
  conductivity 
  is 
  ascribed 
  solely 
  

   to 
  a 
  reduction 
  in 
  the 
  number 
  of 
  the 
  free 
  ions, 
  instead 
  of 
  to 
  

   a 
  direct 
  effect 
  produced 
  by 
  the 
  interionic 
  forces 
  on 
  their 
  

   mobilities. 
  In 
  considering 
  it 
  we 
  will 
  confine 
  attention 
  to 
  

   dilute 
  solutions 
  of 
  strong 
  binary 
  electrolytes 
  in 
  water, 
  

   where 
  the 
  essential 
  facts 
  to 
  be 
  explained 
  by 
  any 
  theory 
  are 
  

   these 
  : 
  — 
  

  

  (1) 
  The 
  molecular 
  lowering 
  of 
  the 
  freezing-point 
  t 
  is 
  

   found 
  to 
  be 
  nearly, 
  but 
  not 
  quite, 
  twice 
  as 
  great 
  as 
  the 
  theo- 
  

   retical 
  value 
  t 
  valid 
  for 
  a 
  non-electrolyte. 
  Let 
  us 
  express 
  

   this 
  fact 
  thus 
  : 
  

  

  I-«2-A. 
  ...... 
  (1) 
  

  

  & 
  is 
  in 
  the 
  first 
  place 
  a 
  purely 
  experimental 
  quantity, 
  

   but 
  by 
  strict 
  thermodynamic 
  reasoning 
  it 
  can 
  be 
  identified 
  

  

  with 
  the 
  reduction 
  in 
  the 
  value 
  of 
  p^ 
  for 
  the 
  electrolyte 
  

  

  below 
  the 
  value 
  which 
  would 
  apply 
  to 
  an 
  electrolyte 
  com- 
  

   pletely 
  dissociated 
  and 
  obeying 
  the 
  gas 
  law. 
  In 
  the 
  theory 
  

   of 
  Arrhenius 
  it 
  is 
  further 
  identified 
  with 
  the 
  fraction 
  of 
  the 
  

   whole 
  number 
  of 
  ions 
  which, 
  as 
  the 
  concentration 
  is 
  increased 
  

   from 
  zero, 
  have 
  associated 
  into 
  molecules. 
  Equation 
  (1) 
  is 
  

   usually 
  written 
  with 
  the 
  symbol 
  7 
  for 
  the 
  fraction 
  of 
  mole- 
  

   cules 
  dissociated, 
  but 
  for 
  the 
  present 
  purpose 
  the 
  vise 
  of 
  

   £i( 
  = 
  l 
  — 
  7) 
  in 
  the 
  equation 
  is 
  more 
  convenient. 
  We 
  are 
  

   dealing 
  with 
  strong 
  electrolytes 
  where 
  at 
  the 
  most 
  there 
  

   are 
  only 
  small 
  departures 
  from 
  complete 
  dissociation, 
  and 
  

   of 
  these 
  according 
  to 
  the 
  theory 
  ^ 
  forms 
  the 
  direct 
  

   measure. 
  

  

  (2) 
  The 
  molecular 
  conductivity 
  X 
  diminishes 
  with 
  increase 
  

   in 
  the 
  concentration, 
  or 
  we 
  may 
  write,, 
  if 
  X 
  is 
  its 
  extrapolated 
  

   value 
  at 
  zero 
  concentration, 
  

  

  £=-i-a 
  (2) 
  

  

  y@ 
  2 
  can 
  not 
  be 
  identified 
  thermodynamically 
  with 
  anything, 
  

   but 
  on 
  the 
  theory 
  it 
  also 
  represents 
  the 
  fraction 
  of 
  the 
  ions 
  

   associated. 
  

  

  (3) 
  &= 
  fi 
  2 
  approximately 
  (3) 
  

  

  Much 
  work 
  has 
  been 
  done 
  in 
  testing 
  the 
  extent 
  of 
  the 
  

   agreement, 
  the 
  general 
  result 
  of 
  which 
  seems 
  to 
  be 
  that 
  

  

  