﻿Conductivity 
  of 
  Aqueous 
  Solutions. 
  1 
  53 
  

  

  the 
  relation 
  between 
  ionization 
  and 
  regional 
  dilution 
  in 
  a 
  

   complex 
  solution 
  is 
  the 
  same 
  as 
  between 
  ionization 
  and 
  

   dilution 
  in 
  a 
  simple 
  solution. 
  

  

  Finally, 
  from 
  the 
  nature 
  of 
  the 
  process 
  of 
  double 
  decom- 
  

   position, 
  if 
  ni 
  and 
  n 
  2 
  are 
  the 
  numbers 
  of 
  gramme-equivalents 
  

   of 
  1 
  and 
  2 
  added 
  to 
  water 
  in 
  preparing 
  the 
  solution, 
  we 
  have 
  

   the 
  equations 
  : 
  

  

  w^Nx 
  + 
  Ng, 
  rc 
  2 
  =N 
  2 
  + 
  N 
  4 
  , 
  and 
  N 
  3 
  = 
  N 
  i 
  . 
  . 
  . 
  (e) 
  

  

  We 
  have 
  thus 
  twelve 
  equations 
  for 
  determining 
  the 
  four 
  

   a's, 
  the 
  four 
  V's, 
  and 
  the 
  four 
  N's 
  involved 
  in 
  them. 
  

  

  The 
  functions, 
  /, 
  are 
  too 
  complex 
  to 
  admit 
  of 
  an 
  algebraical 
  

   solution 
  of 
  these 
  equations. 
  Were 
  it 
  possible 
  to 
  measure 
  con- 
  

   ductivity 
  with 
  sufficient 
  exactness, 
  however, 
  it 
  would 
  be 
  

   possible 
  to 
  solve 
  them 
  by 
  a 
  partially 
  graphical 
  process. 
  For 
  

   this 
  purpose, 
  reducing 
  equations 
  (6), 
  (c), 
  and 
  (e) 
  to 
  two, 
  we 
  

   should 
  have 
  

  

  N 
  3 
  =(«-V 
  1 
  n 
  1 
  -V 
  2 
  n 
  2 
  )/(V 
  3 
  + 
  V 
  4 
  -V,-V 
  2 
  ), 
  . 
  . 
  (1) 
  

   N 
  3 
  2 
  (V 
  3 
  V4/ViV 
  2 
  -l) 
  + 
  N 
  3 
  (n 
  1 
  + 
  n 
  i! 
  ) 
  = 
  n 
  l 
  H 
  2 
  . 
  ... 
  (2) 
  

  

  We 
  may 
  apply 
  equations 
  (d) 
  by 
  drawing 
  curves 
  which 
  give 
  

   the 
  relation 
  of 
  concentration 
  of 
  ions 
  to 
  dilution 
  for 
  simple 
  

   solutions 
  of 
  the 
  electrolytes. 
  We 
  may 
  then 
  apply 
  equations 
  

   (a) 
  by 
  reading 
  off 
  from 
  these 
  curves 
  the 
  dilutions 
  (V 
  l5 
  V 
  2 
  , 
  &c.) 
  

   of 
  simple 
  solutions 
  having 
  what 
  we 
  may 
  guess 
  at 
  as 
  being 
  the 
  

   concentration 
  of 
  ions 
  of 
  the 
  complex 
  solution. 
  We 
  may 
  then 
  

   determine 
  N 
  3 
  from 
  (1) 
  and 
  see 
  if 
  this 
  value 
  is, 
  first, 
  a 
  possible 
  

   value, 
  and, 
  if 
  so, 
  secondly, 
  one 
  that 
  will 
  satisfy 
  (2). 
  If, 
  

   though 
  a 
  possible 
  value, 
  it 
  will 
  not 
  satisfy 
  (2), 
  we 
  must 
  make 
  

   another, 
  and 
  this 
  time 
  a 
  more 
  intelligent, 
  guess, 
  and 
  so 
  on, 
  

   until 
  a 
  value 
  of 
  the 
  concentration 
  of 
  ions 
  has 
  been 
  selected 
  

   giving 
  values 
  of 
  Y 
  l9 
  Y 
  2 
  , 
  &c. 
  which 
  will 
  satisfy 
  both 
  (1) 
  and 
  

   (2), 
  when, 
  N 
  3 
  being 
  thus 
  determined, 
  N,, 
  N 
  2 
  , 
  and 
  N 
  4 
  may 
  be 
  

   found, 
  and 
  all 
  the 
  data 
  required 
  for 
  calculation 
  are 
  known. 
  

  

  We 
  have 
  tried 
  this 
  method 
  but 
  without 
  a 
  satisfactory 
  

   result. 
  The 
  denominator 
  in 
  expression 
  (1) 
  is 
  a 
  small 
  quantity, 
  

   and 
  even 
  when 
  the 
  curves 
  referred 
  to 
  above 
  are 
  drawn 
  with 
  

   the 
  best 
  available 
  data 
  as 
  to 
  conductivity, 
  it 
  is 
  affected 
  by 
  too 
  

   large 
  an 
  error. 
  

  

  It 
  is 
  possible, 
  however, 
  by 
  the 
  aid 
  of 
  the 
  above 
  equations 
  

   to 
  determine 
  the 
  constitution 
  of 
  a 
  complex 
  solution 
  with 
  a 
  

   known 
  concentration 
  of 
  ions 
  and 
  therefore 
  a 
  calculable 
  con- 
  

   ductivity, 
  to 
  prepare 
  the 
  solution, 
  and 
  measure 
  its 
  conductivity, 
  

   and 
  thus 
  to 
  apply 
  a 
  somewhat 
  severe 
  test 
  to 
  the 
  dissociation 
  

   theory 
  as 
  a 
  working 
  hypothesis. 
  

  

  For 
  this 
  purpose 
  select 
  a 
  low 
  value 
  of 
  the 
  concentration 
  of 
  

  

  