﻿Interionic 
  Force 
  in 
  Electrolytes. 
  359 
  

  

  when 
  interionic 
  force 
  is 
  present, 
  the 
  average 
  amount 
  of 
  the 
  

   property 
  which 
  is 
  capable 
  of 
  being 
  transferred 
  from 
  a 
  position 
  

   in 
  which 
  the 
  mutual 
  energy 
  of 
  its 
  ion 
  is 
  $ 
  1 
  to 
  a 
  position 
  of 
  

   zero 
  mutual 
  energy, 
  is 
  

  

  (10) 
  

  

  iw 
  JPi/** 
  

  

  mv 
  . 
  e 
  

  

  This 
  quantity 
  represents 
  the 
  contribution 
  to 
  the 
  external 
  

   pY 
  made 
  by 
  the 
  ion 
  when 
  it 
  forms 
  part 
  of 
  a 
  group. 
  The 
  

   summation 
  of 
  it 
  for 
  each 
  ion 
  in 
  the 
  electrolyte 
  would 
  give 
  

   the 
  external 
  pY 
  or, 
  strictly 
  speaking, 
  its 
  instantaneous 
  

   value 
  in 
  the 
  view 
  observed. 
  The 
  external 
  pressure 
  of 
  a 
  

   system 
  of 
  ions 
  subject 
  to 
  interionic 
  force 
  determined 
  in 
  this 
  

   way 
  is 
  a 
  perfectly 
  definite 
  thing 
  everywhere 
  in 
  equilibrium 
  

   throughout 
  the 
  volume. 
  It 
  is 
  identical 
  with 
  the 
  pressure 
  of 
  

   the 
  free 
  ions 
  as 
  defined 
  above. 
  Superposed 
  on 
  it 
  in 
  the 
  

   interior 
  of 
  groups 
  is 
  the 
  internal 
  pressure 
  (got 
  by 
  summing 
  

   \mv 
  i 
  (l 
  — 
  e 
  Plk11 
  ) 
  for 
  each 
  ion), 
  which 
  is 
  exerted 
  against 
  the 
  

   mutual 
  forces 
  and 
  is 
  not 
  effective 
  on 
  the 
  walls. 
  

  

  A 
  comparison 
  of 
  the 
  result 
  (10) 
  for 
  the 
  contribution 
  of 
  

   an 
  ion 
  to 
  the 
  external 
  pY 
  when 
  it 
  is 
  in 
  a 
  position 
  of 
  mutual 
  

   energy 
  with 
  others 
  with 
  that 
  (8) 
  for 
  the 
  mobility 
  of 
  the 
  ion 
  

   in 
  the 
  same 
  circumstances, 
  shows 
  that 
  both 
  are 
  affected 
  

   by 
  the 
  mutual 
  energy 
  in 
  exactly 
  the 
  same 
  way. 
  Suppose 
  

   now 
  we 
  follow 
  in 
  imagination 
  the 
  history 
  of 
  an 
  individual 
  

   ion 
  in 
  an 
  electrolyte 
  for 
  a 
  long 
  time. 
  We 
  shall 
  observe 
  that 
  

   its 
  state 
  as 
  regards 
  the 
  mutual 
  energy 
  (f) 
  1 
  which 
  it 
  possesses 
  

   with 
  other 
  ions 
  is 
  continually 
  varying. 
  If 
  we 
  take 
  the 
  average 
  

   value 
  over 
  a 
  sufficiently 
  long 
  time 
  of 
  the 
  quantities 
  

  

  «</ 
  l/CT 
  and 
  CT./' 
  /M 
  , 
  

  

  we 
  shall 
  get 
  in 
  the 
  first 
  instance 
  the 
  average 
  value 
  of 
  the 
  

   mobility 
  u 
  x 
  of 
  the 
  ion 
  (which 
  is 
  of 
  course 
  the 
  same 
  as 
  

   that 
  u 
  of 
  any 
  other 
  ion 
  of 
  the 
  same 
  kind, 
  but 
  u 
  differs 
  if 
  

   the 
  kind 
  differs), 
  and 
  in 
  the 
  second 
  instance 
  a 
  quantity 
  

   which, 
  when 
  multiplied 
  by 
  the 
  total 
  number 
  N 
  of 
  ions 
  in 
  the 
  

   electrolyte 
  (combined 
  or 
  not) 
  gives 
  the 
  product 
  pY 
  of 
  the 
  

   pressure 
  of 
  the 
  free 
  ions 
  into 
  the 
  volume. 
  It 
  is 
  clear 
  that, 
  

   whatever 
  the 
  effect 
  of 
  (pi 
  may 
  be 
  on 
  the 
  actual 
  values, 
  we 
  

   shall 
  always 
  have 
  

  

  ^ 
  = 
  FW 
  =const 
  (11 
  > 
  

  

  Hence 
  in 
  an 
  electrolyte, 
  while 
  alterations 
  with 
  the 
  concen- 
  

   tration 
  of 
  u 
  and 
  pY 
  may, 
  and 
  indeed 
  will, 
  be 
  produced 
  as 
  

   the 
  result 
  of 
  the 
  presence 
  of 
  interionic 
  forces, 
  the 
  alterations 
  

   will 
  always 
  be 
  such 
  that 
  the 
  ratio 
  of 
  u 
  to 
  p 
  Y 
  remains 
  

   unaffected. 
  

  

  2 
  2 
  

  

  