﻿of 
  a 
  Heterogeneous 
  Reaction. 
  459 
  

  

  ■•\ 
  In 
  short, 
  no 
  adequate 
  comparison 
  between 
  reaction 
  veloci- 
  

   ties 
  and 
  rates 
  of 
  diffusion 
  can 
  be 
  made 
  in 
  the 
  present 
  case 
  with- 
  

   out 
  a 
  knowledge 
  of 
  the 
  value 
  of 
  the 
  diffusion 
  coefficient 
  of 
  

   iodine 
  in 
  0'5-normal 
  potassium 
  iodide 
  at 
  several 
  of 
  the 
  tempera- 
  

   tures 
  involved. 
  The 
  value 
  of 
  this 
  coefficient 
  at 
  25° 
  has 
  already 
  

   been 
  measured 
  by 
  Edgar 
  and 
  Diggs,* 
  but 
  at 
  other 
  tempera- 
  

   tures 
  its 
  value 
  is 
  unknown. 
  The 
  most 
  that 
  can 
  be 
  said 
  at 
  the 
  

   present 
  time 
  is 
  that 
  the 
  observed 
  changes 
  in 
  the 
  reaction 
  veloc- 
  

   ity 
  with 
  the 
  temperature 
  are 
  of 
  very 
  nearly 
  the 
  order 
  of 
  mag- 
  

   nitude 
  which 
  would 
  be 
  expected 
  from 
  the 
  usual 
  value 
  of 
  the 
  

   temperature 
  coefficient 
  of 
  diffusion. 
  

  

  We 
  have 
  still 
  to 
  consider 
  the 
  significance 
  of 
  the 
  observed 
  

   proportionality 
  between 
  the 
  reaction 
  velocity 
  and 
  the 
  product 
  

   of 
  the 
  fluidity 
  by 
  the 
  absolute 
  temperature, 
  which 
  is 
  indicated 
  

   by 
  the 
  constancy 
  of 
  K/$T. 
  No 
  doubt 
  in 
  many 
  cases 
  the 
  diffu- 
  

   sion 
  coefficient 
  of 
  a 
  dissolved 
  substance 
  is 
  proportional, 
  over 
  a 
  

   fairly 
  wide 
  range 
  of 
  temperature, 
  to 
  the 
  product 
  cj>T. 
  This 
  

   should 
  be 
  at 
  least 
  approximately 
  true 
  in 
  cases 
  in 
  which 
  the 
  

   diffusion 
  formula 
  of 
  Einstein 
  

  

  B 
  RT 
  , 
  

  

  is 
  applicable, 
  since 
  in 
  this 
  formula 
  R 
  and 
  i\^are 
  constants, 
  and 
  

   the 
  value 
  of 
  P, 
  the 
  molecular 
  radius, 
  can 
  generally 
  be 
  con- 
  

   sidered 
  as 
  constant 
  for 
  the 
  same 
  kind 
  of 
  molecule 
  at 
  different 
  

   and 
  not 
  too 
  widely 
  separated 
  temperatures. 
  Hence, 
  D 
  must 
  be 
  

   proportional 
  to 
  the 
  absolute 
  temperature 
  divided 
  by 
  the 
  vis- 
  

   cosity 
  77, 
  or 
  D 
  00 
  (j)T. 
  

  

  The 
  Einstein 
  formula 
  is 
  strictly 
  valid 
  only 
  when 
  the 
  mole- 
  

   cules 
  of 
  the 
  solute 
  are 
  not 
  dissociated 
  and 
  are 
  large 
  compared 
  

   with 
  those 
  of 
  the 
  solvent,f 
  but 
  dissociation, 
  if 
  nearly 
  complete, 
  

   would 
  not 
  necessarily 
  interfere 
  with 
  the 
  proportionality 
  be- 
  

   tween 
  D 
  and 
  <fiT. 
  There 
  is, 
  however, 
  one 
  limitation 
  which 
  

   may 
  be 
  important. 
  P 
  is 
  the 
  radius, 
  not 
  of 
  the 
  molecule 
  of 
  

   solute 
  itself, 
  but 
  of 
  the 
  diffusing 
  particle, 
  which 
  in 
  many 
  cases 
  

   includes 
  an 
  attached 
  or 
  entrained 
  group 
  of 
  molecules 
  of 
  the 
  

   solvent. 
  Whether 
  P 
  in 
  such 
  a 
  case 
  would 
  vary 
  with 
  the 
  tem- 
  

   perature 
  or 
  not, 
  would 
  depend 
  upon 
  the 
  nature 
  of 
  this 
  attach- 
  

   ment, 
  but 
  its 
  variation 
  might 
  often 
  be 
  appreciable, 
  especially 
  

   over 
  wide 
  temperature 
  intervals. 
  

  

  If 
  we 
  assume 
  that 
  the 
  rate 
  of 
  diffusion 
  of 
  iodine, 
  under 
  the 
  

   conditions 
  of 
  the 
  experiments 
  in 
  Table 
  II, 
  is 
  proportional 
  to 
  

   the 
  product 
  (j>T, 
  it 
  follows 
  from 
  the 
  constancy 
  of 
  K/$T 
  that 
  

   the 
  reaction 
  velocity 
  is 
  closely 
  proportional 
  to 
  the 
  diffusion 
  

  

  * 
  Loc. 
  cit. 
  

  

  f 
  Einstein, 
  Ann. 
  der 
  Physik 
  (4), 
  xix, 
  289, 
  1906. 
  

  

  