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  LI. 
  A 
  Method 
  of 
  obtaining 
  General 
  Reaction- 
  Velocity 
  Curves 
  

   for 
  complete 
  Homogeneous 
  Gas 
  Reactions 
  at 
  Constant 
  

   Pressure. 
  By 
  George 
  W. 
  Todd, 
  D.Sc. 
  {Birm.), 
  B.A. 
  

  

  (Camb.) 
  *. 
  

  

  THE 
  writer 
  has 
  already 
  worked 
  out 
  general 
  curves 
  for 
  

   homogeneous 
  complete 
  reactions 
  between 
  two 
  sub- 
  

   stances 
  when 
  the 
  volume 
  o£ 
  the 
  reaction 
  space 
  remains 
  

   constant 
  t- 
  In 
  many 
  binary 
  gas 
  reactions 
  a 
  continuous 
  

   change 
  of 
  volume 
  takes 
  place 
  during 
  the 
  reaction 
  at 
  constant 
  

   pressure. 
  The 
  concentrations 
  of 
  the 
  reacting 
  gases 
  therefore 
  

   not 
  only 
  depend 
  on 
  the 
  amounts 
  transformed 
  but 
  also 
  on 
  the 
  

   volume 
  of 
  the 
  products. 
  Since 
  many 
  technical 
  gas-reactions 
  

   take 
  place 
  at 
  constant 
  pressure, 
  sets 
  of 
  general 
  curves 
  for 
  

   such 
  reactions 
  should 
  prove 
  of 
  great 
  value. 
  The 
  paper 
  gives 
  

   a 
  method 
  of 
  obtaining 
  the 
  curves. 
  

  

  Bi-molecular 
  Reactions. 
  

  

  Take 
  a 
  reaction 
  of 
  the 
  type 
  A-fB->l 
  or 
  more 
  resultants. 
  

   The 
  resultants 
  need 
  not 
  necessarily 
  be 
  gaseous. 
  We 
  will 
  

   assume 
  that 
  B 
  is 
  in 
  excess. 
  

  

  Let 
  a 
  <rm. 
  mols. 
  of 
  A 
  react 
  with 
  b 
  gm. 
  mols. 
  of 
  B. 
  

  

  Let 
  x 
  gm. 
  mols. 
  of 
  either 
  reactant 
  be 
  changed 
  in 
  time 
  t. 
  

  

  Let 
  v 
  be 
  the 
  the 
  total 
  volume 
  of 
  reactants 
  and 
  resultants. 
  

  

  The 
  velocity 
  of 
  the 
  reaction 
  is 
  given 
  by 
  

  

  d 
  (x\ 
  _, 
  a 
  — 
  x 
  b—x 
  

   dt\v) 
  ~ 
  " 
  '~v~ 
  ' 
  v 
  ' 
  

  

  where 
  k= 
  velocity 
  constant, 
  or 
  

  

  1 
  dx 
  x 
  dv 
  h 
  

  

  Put 
  - 
  =X, 
  i. 
  e. 
  the 
  fraction 
  of 
  A 
  chano-ed. 
  

   a 
  ' 
  8 
  

  

  If 
  the 
  pressure 
  is 
  maintained 
  constant 
  throughout 
  the 
  

   reaction, 
  then 
  the 
  volume 
  at 
  any 
  time 
  will 
  be 
  proportional 
  

   to 
  the 
  number 
  of 
  gas 
  molecules 
  present. 
  

  

  The 
  initial 
  volume 
  when 
  £=0 
  is 
  

  

  r 
  oc 
  2a 
  + 
  (b 
  — 
  a), 
  

   (b—a) 
  is 
  the 
  excess 
  of 
  B 
  present. 
  

  

  * 
  Communicated 
  by 
  the 
  Author, 
  

   t 
  Phil. 
  Mag. 
  vol. 
  xxxv. 
  p. 
  281. 
  

  

  