﻿Rhythmic 
  Precipitation. 
  

  

  19 
  

  

  Considering 
  the 
  formation 
  of 
  bands 
  of 
  silver 
  chromate 
  in 
  

   outward 
  diffusion 
  of 
  silver, 
  if 
  the 
  concentrations 
  for 
  precipita- 
  

   tion 
  are 
  A 
  for 
  the 
  silver 
  ions 
  and 
  C 
  for 
  the 
  chromat-ions 
  and 
  

   X 
  for 
  the 
  silver 
  chromate, 
  then 
  for 
  equilibrium 
  

  

  A 
  .C„ 
  = 
  k.X 
  (1) 
  

  

  k 
  will 
  vary 
  with 
  temperature. 
  

  

  Consider 
  a 
  space 
  into 
  which 
  diffusion 
  is 
  taking 
  place, 
  just 
  in 
  

   front 
  of 
  a 
  band 
  of 
  precipitate 
  which 
  is 
  newly 
  formed. 
  The 
  

  

  Fig. 
  9. 
  

  

  jT 
  ^A 
  ,' 
  m 
  — 
  «- 
  

  

  / 
  / 
  y 
  ^*^5 
  . 
  . 
  

  

  — 
  Jy- 
  — 
  - 
  *L^^L—^ 
  : 
  

  

  If 
  >'S 
  -'' 
  S 
  

  

  m 
  a 
  3 
  nOj 
  

  

  N 
  A 
  9 
  /V0 
  3 
  

  

  - 
  N 
  K 
  2 
  G0 
  4 
  

  

  N 
  PKNOJ, 
  

  

  To 
  ** 
  L 
  U 
  * 
  

  

  < 
  

   10 
  

  

  Ikr 
  2 
  I 
  4 
  S 
  6 
  

  

  Time 
  

  

  Fig. 
  9. 
  Simple 
  diffusion 
  (no 
  reaction). 
  

  

  silver 
  ions 
  are 
  " 
  dominant" 
  and 
  the 
  chromat-ions 
  in 
  excess 
  of 
  

   saturation 
  of 
  silver 
  chromate 
  have 
  been 
  removed 
  from 
  a 
  cer- 
  

   tain 
  space 
  on 
  each 
  side 
  of 
  the 
  band. 
  The 
  silver 
  ions 
  being 
  

   "dominant" 
  the 
  value 
  A 
  is 
  large 
  compared 
  with 
  C 
  , 
  so 
  that 
  

   the 
  silver 
  ions 
  may 
  be 
  regarded 
  as 
  starting 
  their 
  diffusion 
  from 
  

   the 
  precipitate 
  band 
  (or 
  perhaps 
  some 
  plane 
  outside 
  it), 
  while 
  

   the 
  chromat-ions 
  begin 
  their 
  diffusion 
  from 
  some 
  plane 
  at 
  a 
  dis- 
  

   tance 
  D 
  outside 
  the 
  band. 
  (See 
  fig. 
  5.) 
  It 
  should 
  be 
  noted 
  

   that 
  in 
  keeping 
  with 
  the 
  generally 
  accepted 
  conception 
  regard- 
  

   ing 
  aqueous 
  solutions 
  the 
  reagents 
  involved 
  will 
  diffuse 
  partly 
  

   as 
  molecules 
  and 
  partly 
  as 
  ions. 
  When 
  silver 
  ions 
  are 
  referred 
  

   to 
  it 
  is 
  understood 
  that 
  each 
  of 
  these 
  is 
  associated 
  with 
  an 
  

   oppositely 
  charged 
  nitrat-ion 
  the 
  two 
  charges 
  neutralizing 
  each 
  

   other. 
  For 
  the 
  purposes 
  of 
  discussion 
  of 
  the 
  reaction 
  with 
  the 
  

  

  