﻿C. 
  L. 
  Speyers 
  — 
  Boiling 
  Point 
  Curves. 
  

  

  343 
  

  

  observed 
  values 
  being 
  those 
  of 
  Thayer.* 
  The 
  agreement 
  is 
  

   fair 
  but 
  can 
  be 
  improved. 
  Referring 
  to 
  the 
  figures 
  of 
  a 
  pre- 
  

   ceding 
  paperf, 
  it 
  may 
  be 
  noticed 
  that 
  in 
  the 
  toluene 
  and 
  alco- 
  

   hol 
  mixture, 
  the 
  molecular 
  weight 
  of 
  each 
  solute 
  approaches 
  

   the 
  normal 
  value 
  when 
  the 
  mixture 
  is 
  dilute 
  with 
  respect 
  to 
  

   that 
  solute, 
  but 
  that 
  in 
  the 
  benzene 
  and 
  alcohol 
  mixture, 
  the 
  

   molecular 
  weight 
  of 
  each 
  solute 
  keeps 
  very 
  high 
  even 
  when 
  

   the 
  solution 
  is 
  dilute 
  with 
  respect 
  to 
  that 
  solute. 
  Moreover 
  

   that 
  two 
  observations 
  on 
  the 
  vapor 
  pressure 
  of 
  benzene 
  point 
  

   to 
  a 
  normal 
  molecular 
  weight 
  for 
  alcohol 
  in 
  dilute 
  solution, 
  but 
  

   since 
  these 
  observations 
  are 
  so 
  far 
  from 
  the 
  others, 
  at 
  the 
  time 
  

   of 
  writing 
  the 
  paper 
  they 
  could 
  not 
  be 
  given 
  any 
  weight. 
  

   !Xot 
  so 
  now. 
  Thayer's 
  data 
  point 
  very 
  directly 
  to 
  these 
  two 
  

   observations 
  being 
  much 
  nearer 
  the 
  truth 
  than 
  the 
  neighboring 
  

   ones. 
  Wherefore 
  it 
  seems 
  allowable 
  to 
  assume 
  that 
  the 
  molec- 
  

   ular 
  aggregation 
  of 
  ethyl 
  alcohol 
  in 
  benzene 
  is 
  about 
  the 
  same 
  

   as 
  in 
  toluene 
  and 
  that 
  the 
  molecular 
  aggregation 
  of 
  benzene 
  in 
  

   ethyl 
  alcohol 
  is 
  about 
  the 
  same 
  as 
  that 
  of 
  toluene 
  in 
  ethyl 
  

   alcohol. 
  Values 
  calculated 
  on 
  this 
  assumption 
  are 
  marked 
  by 
  

   1 
  in 
  fig. 
  4. 
  

  

  ^ 
  ■ 
  — 
  a 
  a 
  ©- 
  * 
  

  

  Giw 
  

  

  C 
  fi 
  H 
  fi 
  10 
  

  

  20 
  

  

  90C 
  2 
  H 
  5 
  OH 
  

  

  When 
  the 
  two 
  constituents 
  of 
  homogeneous 
  liquid 
  mixtures 
  

   have 
  normal 
  molecular 
  weights 
  for 
  all 
  concentrations, 
  the 
  boil- 
  

   ing 
  point 
  curves 
  will 
  be 
  straight 
  lines 
  when 
  

  

  dpi 
  

  

  dt 
  n 
  

  

  dp 
  x 
  

   It, 
  

  

  where 
  2\i 
  P» 
  denote 
  the 
  vapor 
  pressures 
  of 
  the 
  two 
  constituents 
  

   and 
  t„ 
  t„ 
  denote 
  the 
  corresponding 
  temperatures. 
  When 
  

  

  dp, 
  

   dt 
  n 
  

  

  dp 
  x 
  

  

  then 
  the 
  boiling 
  point 
  curve 
  is 
  convex 
  towards 
  the 
  axis 
  of 
  

   abscissae 
  provided 
  p 
  2 
  > 
  p 
  v 
  but 
  when 
  p^ 
  <p 
  iy 
  then 
  the 
  boiling 
  

   point 
  curve 
  is 
  concave 
  towards 
  this 
  axis. 
  

  

  In 
  no 
  case 
  should 
  a 
  mixture 
  have 
  a 
  minimum 
  boiling 
  point 
  

   when 
  both 
  constituents 
  have 
  normal 
  molecular 
  weights 
  at 
  all 
  

  

  * 
  Joura. 
  Phys. 
  Chem., 
  ii, 
  382, 
  1898. 
  

  

  f 
  Speyers, 
  Journ. 
  Am. 
  Chem. 
  Soc, 
  xxi, 
  282, 
  1898. 
  

  

  