﻿Reactions 
  between 
  Two 
  Substances. 
  285 
  

  

  Now 
  let 
  the 
  substance 
  A 
  be 
  in 
  excess, 
  so 
  that 
  -=p>l. 
  

   We 
  have 
  

  

  Kt 
  dX 
  

  

  „=r 
  x 
  

  

  where 
  K 
  = 
  kb*. 
  _ 
  Jo 
  0-X) 
  3 
  (l-X)' 
  

  

  The 
  solution 
  is 
  

  

  A, 
  B, 
  C, 
  D 
  being 
  constants 
  depending 
  on 
  p. 
  

  

  p=l%. 
  ThenA=-64. 
  B=-16. 
  C= 
  --4. 
  D=64. 
  

  

  X 
  -2 
  -4 
  6 
  7 
  -8 
  10 
  

  

  Kt 
  -15 
  -47 
  1-51 
  3-01 
  11-49 
  oo 
  

  

  p=lh 
  ThenA=-8. 
  B=-4. 
  C=-2. 
  D=8. 
  

  

  X 
  -2 
  -5 
  -6 
  -7 
  -8 
  -9 
  1-0 
  

  

  K* 
  -082 
  -411 
  -602 
  115 
  215 
  4-76 
  oc 
  

  

  p 
  = 
  2. 
  TbenA=-l. 
  B=— 
  1. 
  0=-l. 
  D 
  = 
  l. 
  

  

  X 
  -3 
  -6 
  -8 
  -9 
  -95 
  -97 
  TO 
  

  

  Kt 
  -065 
  -216 
  -575 
  1-01 
  1*58 
  2-02 
  oc 
  

  

  The 
  graphs 
  for 
  these 
  are 
  shown 
  in 
  fig. 
  5. 
  

   There 
  is 
  yet 
  the 
  quadri-inolecular 
  reaction 
  of 
  the 
  type 
  

   2A 
  + 
  2B->1 
  or 
  more 
  resultants. 
  In 
  this 
  case 
  we 
  have 
  

  

  x 
  dX 
  

  

  (l-X)S(p-X)" 
  

  

  where 
  K 
  = 
  £a 
  3 
  and 
  p=- 
  >1. 
  

  

  r 
  a 
  

  

  The 
  solution 
  is 
  

  

  K 
  ,- 
  2 
  inept 
  1 
  -** 
  i 
  x 
  r 
  p+i-^x 
  _P+l\ 
  

  

  Ip-iy** 
  p-x 
  + 
  (p-l)»l(l-X)( 
  ? 
  -X) 
  p 
  J 
  

  

  X 
  -2 
  -4 
  -6 
  -7 
  -8 
  1-0 
  

  

  Kt 
  21 
  -70 
  22 
  4-7 
  117 
  oo 
  

  

  p=% 
  

  

  X 
  -1 
  -3 
  -5 
  75 
  -85 
  -9 
  1-0 
  

  

  Kt 
  -03 
  -129 
  -36 
  1*465 
  3*33 
  600 
  oo 
  

  

  p=3. 
  

   X 
  -5 
  8 
  -9 
  -95 
  10 
  

  

  Kt 
  -141 
  707 
  1-80 
  4-14 
  oc 
  

  

  The 
  general 
  curves 
  for 
  this 
  type 
  of 
  quadri-molecular 
  

   reaction 
  are 
  shown 
  in 
  fig. 
  6. 
  

  

  Phil. 
  Mag. 
  S. 
  6. 
  Vol. 
  35. 
  No. 
  207. 
  March 
  1918. 
  X 
  

  

  H. 
  

  

  