﻿344 
  C. 
  L. 
  Speyers 
  — 
  Boiling 
  Point 
  Curves. 
  

  

  concentrations. 
  Only 
  when 
  one 
  or 
  both 
  constituents 
  have 
  

   abnormal 
  molecular 
  weights 
  in 
  a 
  mixture, 
  can 
  the 
  mixture 
  

   have 
  a 
  minimum 
  boiling 
  point. 
  But 
  even 
  then 
  the 
  mixture 
  

   need 
  not 
  have 
  a 
  minimum 
  boiling 
  point. 
  For 
  when 
  the 
  vapor 
  

   pressures 
  of 
  the 
  two 
  pure 
  constituents 
  are 
  very 
  different 
  then, 
  

   if 
  the 
  constituent 
  with 
  higher 
  vapor 
  pressure 
  is 
  the 
  associated 
  

   one, 
  the 
  vapor 
  pressure 
  of 
  the 
  other 
  constituent 
  may 
  not 
  be 
  

   high 
  enough 
  at 
  any 
  concentration 
  to 
  prevail 
  over 
  the 
  diminish- 
  

   ing 
  vapor 
  pressure 
  of 
  the 
  associated 
  constituent. 
  On 
  the 
  

   other 
  hand, 
  when 
  the 
  constituent 
  with 
  lower 
  vapor 
  pressure 
  is 
  

   the 
  associated 
  one, 
  then 
  a 
  minimum 
  boiling 
  point 
  is 
  to 
  be 
  

   expected 
  even 
  though 
  the 
  vapor 
  pressures 
  of 
  the 
  two 
  pure 
  con- 
  

   stituents 
  may 
  be 
  very 
  different. 
  Yet 
  it 
  is 
  possible 
  in 
  this 
  case 
  

   also 
  that 
  the 
  mixture 
  should 
  have 
  no 
  minimum 
  boiling 
  point. 
  

  

  When 
  the 
  two 
  constituents 
  are 
  both 
  associated, 
  then 
  the 
  

   mixture 
  should 
  have 
  a 
  minimum 
  boiling 
  point 
  in 
  general, 
  but 
  

   not 
  always, 
  for 
  it 
  is 
  possible 
  for 
  the 
  associating 
  powers 
  of 
  the 
  

   two 
  constituents 
  to 
  be 
  alike, 
  in 
  which 
  case 
  a 
  change 
  in 
  

   concentration 
  would 
  make 
  no 
  difference 
  in 
  the 
  numerical 
  value 
  

   of 
  n/ip—j?') 
  and 
  equation 
  1 
  would 
  still 
  remain 
  the 
  equation 
  to 
  

   a 
  straight 
  line. 
  

  

  Equation 
  1 
  thus 
  accounts 
  for 
  the 
  boiling 
  point 
  curves 
  of 
  

   every 
  mixture 
  for 
  which 
  the 
  partial 
  pressures 
  of 
  the 
  con- 
  

   stituents 
  are 
  known 
  at 
  some 
  one 
  temperature 
  not 
  very 
  far 
  

   from 
  the 
  boiling 
  temperature 
  of 
  the 
  mixture 
  under 
  considera- 
  

   tion. 
  

  

  Eutgers 
  College, 
  Feb. 
  3d, 
  1900. 
  

  

  