﻿Homogeneous 
  Gas 
  Reactions 
  at 
  Constant 
  Pressure. 
  437 
  

  

  Put 
  = 
  X, 
  the 
  fraction 
  of 
  A 
  changed. 
  The 
  volume 
  at 
  

   a 
  & 
  

  

  any 
  time 
  being 
  proportional 
  to 
  the 
  number 
  of 
  gas-molecules 
  

  

  present, 
  we 
  have 
  

  

  v 
  x 
  3a 
  + 
  (6— 
  a), 
  

  

  and 
  v 
  oc 
  3a(l 
  + 
  «X) 
  + 
  (6 
  — 
  a), 
  

  

  . 
  3a(l 
  + 
  aX)+(6-a)* 
  

   whence 
  v 
  = 
  v 
  9—7-77 
  — 
  V" 
  » 
  

  

  and 
  dv 
  _ 
  3at? 
  » 
  dX. 
  

  

  dt~ 
  3a+(6— 
  a) 
  TST" 
  

  

  Substituting 
  in 
  equation 
  (2) 
  gives 
  

  

  , 
  . 
  2 
  (l-X) 
  2 
  (--x) 
  

   \v 
  / 
  3aaX 
  

  

  dX 
  

  

  2a 
  + 
  b 
  

   or, 
  putting 
  - 
  = 
  p, 
  

  

  a 
  

  

  ?x 
  =/ 
  /ay 
  (i-x)v-x 
  ) 
  

  

  dt 
  \vj 
  Zee 
  -y 
  

  

  i 
  /n 
  2 
  i= 
  r 
  T 
  i!gL 
  & 
  . 
  . 
  (3) 
  

  

  VV 
  Jo 
  (i-x)^(^-X) 
  

  

  This 
  is 
  the 
  general 
  equation 
  for 
  B 
  in 
  excess. 
  

  

  * 
  If 
  in 
  addition 
  to 
  the 
  2« 
  molecules 
  of 
  A 
  and 
  the 
  b 
  molecules 
  of 
  B, 
  

   there 
  are 
  also 
  initially 
  present 
  na 
  molecules 
  of 
  an 
  inactive 
  gas, 
  then 
  

  

  _ 
  3fl(l+aX) 
  + 
  (6-g)-f-»a 
  

   V 
  ~ 
  V 
  ° 
  3a+{b-a)+?ia 
  

  

  so 
  that 
  

  

  .x 
  ,,f 
  (] 
  - 
  Xj 
  1^ 
  X 
  ). 
  

  

  dt 
  ~ 
  \vj 
  _3«aX 
  

  

  la+b+na 
  

   and 
  equation 
  (3) 
  becomes 
  

  

  P/«7, 
  il%. 
  S. 
  6. 
  Vol. 
  35. 
  No. 
  209. 
  il% 
  1918. 
  2 
  H 
  

  

  