﻿282 
  Dr. 
  G. 
  W. 
  Todd 
  on 
  the 
  Velocity 
  of 
  

  

  The 
  maximum 
  value 
  of 
  X 
  = 
  l. 
  Giving 
  X 
  values 
  up 
  to 
  1 
  

   we 
  get 
  

  

  X 
  -1 
  2 
  3 
  -4 
  -5 
  -6 
  -7 
  8 
  9 
  l'O 
  

  

  Kt 
  -111 
  -250 
  -428 
  -666 
  1-00 
  T50 
  2-33 
  4-00 
  9'00 
  oo 
  

  

  These 
  are 
  plotted 
  on 
  fig. 
  1 
  (/j>=1), 
  and 
  the 
  curve 
  will 
  

   apply 
  to 
  any 
  bi-molecular 
  reaction 
  in 
  which 
  the 
  initial 
  

   concentrations 
  are 
  equal. 
  7 
  

  

  Take 
  (ii.) 
  one 
  of 
  the 
  substances 
  in 
  excess, 
  say 
  - 
  =/>, 
  

   where 
  p>l. 
  Then 
  we 
  have 
  a 
  

  

  "-^'{■^£=?}- 
  

  

  

  p=V5. 
  

  

  

  

  X 
  .. 
  

  

  . 
  -1 
  

  

  •2 
  

  

  •3 
  -4 
  -5 
  -6 
  

  

  Xt.. 
  

  

  . 
  -071 
  

   p=2. 
  

  

  •159 
  

  

  •267 
  -401 
  -572 
  -808 
  

  

  X 
  .. 
  

  

  . 
  -1 
  

  

  •2 
  

  

  •3 
  '4 
  -5 
  -6 
  

  

  Kt.. 
  

  

  . 
  -054 
  

   p=3. 
  

  

  •117 
  

  

  •194 
  -288 
  -405 
  -559 
  

  

  X 
  .. 
  

  

  . 
  1 
  

  

  •2 
  

  

  •3 
  -4 
  -5 
  -6 
  -7 
  

  

  K*.. 
  

  

  . 
  -036 
  

  

  •077 
  

  

  •126 
  -183 
  255 
  344 
  S 
  

  

  •8 
  9 
  95 
  1-0 
  

  

  l 
  1-16 
  1-69 
  2-77 
  8-66 
  00 
  

  

  •7 
  8 
  9 
  -95 
  1-0 
  

  

  •771 
  110 
  1-70 
  2-32 
  00 
  

  

  •94 
  -97 
  1-0 
  

  

  These 
  are 
  plotted 
  on 
  fig. 
  1 
  (PI. 
  IX.), 
  and 
  the 
  curves 
  will 
  

   apply 
  to 
  any 
  bi-molecular 
  reaction 
  of 
  the 
  type 
  A 
  + 
  B-^l 
  

   or 
  more 
  resultants. 
  

  

  Ter-molecular 
  Reaction, 
  

  

  Let 
  the 
  reaction 
  be 
  represented 
  by 
  2A 
  + 
  B->1 
  or 
  more 
  

   resultants, 
  then 
  the 
  velocity 
  of 
  reaction 
  is 
  given 
  by 
  

  

  \ 
  aJ 
  \a 
  a) 
  

   Bringing 
  to 
  the 
  same 
  notation 
  as 
  before 
  gives 
  

  

  '"-Jo 
  (l-X)'(p-X)' 
  

   where 
  K=&a 
  2 
  . 
  

  

  Take 
  (i.) 
  equal 
  initial 
  concentrations, 
  i. 
  e. 
  p 
  = 
  l, 
  then 
  

  

  which 
  gives 
  

  

  ^ 
  f* 
  dX 
  _1 
  (2-X)X 
  

   ^-J 
  (1-X)»-S 
  (1-X)" 
  

  

  X 
  -1 
  2 
  -3 
  -4 
  -5 
  6 
  -7 
  -8 
  9 
  1-0 
  

  

  Kt 
  -117 
  -281 
  -520 
  -889 
  1-50 
  2-63 
  606 
  120 
  50 
  co 
  

  

  