﻿436 
  Dr. 
  G. 
  W. 
  Todd 
  on 
  Reaction- 
  Velocity 
  Curves 
  for 
  

  

  The 
  volume 
  after 
  a 
  time 
  t, 
  when 
  the 
  fraction 
  of 
  A 
  changed 
  

   is 
  X, 
  is 
  

  

  v 
  cc 
  2a(l 
  + 
  «X)4- 
  {b 
  — 
  a), 
  

   where 
  a 
  is 
  a 
  constant 
  for 
  the 
  particular 
  reaction. 
  

  

  If 
  the 
  volume 
  increases 
  a 
  is 
  positive, 
  if 
  the 
  volume 
  

   decreases 
  a 
  is 
  negative. 
  

  

  We 
  get 
  2g(i 
  + 
  a 
  ,X 
  )+(b-a)* 
  

  

  V 
  ~ 
  V 
  ° 
  2a+{b-a) 
  ' 
  ' 
  

   and 
  dv 
  __ 
  2av 
  ot 
  dX 
  

  

  ~di 
  ~ 
  2a-\r(b 
  — 
  a) 
  ' 
  ~dt 
  ' 
  

   . 
  Equation 
  (1) 
  now 
  becomes 
  

   a 
  dX 
  aX 
  2av 
  cx. 
  dX 
  

  

  v 
  dt 
  v 
  2 
  a 
  + 
  b 
  dt 
  

  

  -*J(i-x)g-x. 
  

  

  §=*.J 
  /( 
  1-X 
  Xp 
  -X), 
  

  

  which 
  is 
  independent 
  of 
  ex.. 
  Hence 
  a 
  volume-change 
  at 
  

  

  constant 
  pressure 
  does 
  not 
  affect 
  -^-, 
  so 
  that 
  the 
  general 
  

  

  curves 
  given 
  in 
  the 
  paper 
  previously 
  alluded 
  to 
  will 
  do 
  for 
  

   the 
  case 
  of 
  bi-molecular 
  reactions 
  at 
  constant 
  pressure 
  as 
  

   well 
  as 
  at 
  constant 
  volume. 
  

  

  Ter-molecular 
  Reactions. 
  

  

  Many 
  binary 
  gas-reactions 
  are 
  of 
  the 
  type 
  2 
  A 
  + 
  B->1 
  or 
  

   more 
  resultants. 
  Let 
  us 
  work 
  out 
  this 
  case 
  assuming 
  first 
  

   that 
  B 
  is 
  in 
  excess. 
  

  

  Let 
  2a 
  gm. 
  mols. 
  of 
  A 
  react 
  with 
  b 
  gm. 
  mols. 
  of 
  B. 
  

  

  At 
  time 
  t, 
  2x 
  gm. 
  mols. 
  of 
  A 
  and 
  x 
  gm. 
  mols. 
  of 
  B 
  will 
  

   be 
  changed. 
  

  

  Let 
  v 
  be 
  the 
  total 
  volume 
  at 
  time 
  t. 
  

  

  The 
  velocity 
  of 
  reaction 
  is 
  given 
  by 
  

  

  d(x\ 
  , 
  fa 
  — 
  x\ 
  2 
  fb—x\ 
  

  

  or 
  1 
  dx 
  x 
  dv 
  k 
  , 
  N 
  9/ 
  , 
  . 
  /ON 
  

  

  p-dt-?dt 
  = 
  ? 
  ( 
  - 
  a 
  —W- 
  M) 
  - 
  • 
  • 
  • 
  (2) 
  

   (N.B. 
  The 
  concentration 
  of 
  the 
  gas 
  A 
  has 
  been 
  taken 
  as 
  

   half 
  the 
  number 
  of 
  A 
  molecules 
  per 
  unit 
  volume.) 
  

  

  * 
  If 
  there 
  is 
  also 
  initially 
  present 
  m 
  molecules 
  of 
  an 
  inert 
  gas, 
  then 
  

  

  2a(l 
  + 
  aX 
  ) 
  + 
  ( 
  b-a)+m 
  

   dX 
  

  

  V 
  ~ 
  Vo 
  2a+(6-a)+m 
  ' 
  

  

  but 
  this 
  does 
  not 
  affect 
  the 
  final 
  expression 
  for 
  

  

  