﻿122 
  Hie 
  Ionic 
  and 
  Thermal 
  Coefficients 
  of 
  Nitric 
  Acid. 
  

  

  ratios 
  of 
  the 
  calculated 
  and 
  found 
  coefficients 
  of 
  expansion, 
  on 
  

   the 
  one 
  hand, 
  and 
  the 
  factor 
  of 
  ionic 
  dissociation, 
  on 
  the 
  other, 
  

   yet 
  such 
  a 
  general 
  result 
  as 
  that 
  given 
  above 
  would 
  follow 
  if 
  

   the 
  sums 
  of 
  the 
  coefficients 
  of 
  expansion 
  of 
  the 
  separated 
  ions, 
  

  

  namely, 
  H 
  and 
  N0 
  3 
  , 
  were 
  greater 
  than 
  that 
  of 
  the 
  undissociated 
  

   molecule 
  HN0 
  3 
  . 
  The 
  general 
  result 
  is, 
  however, 
  probably 
  

   complicated 
  by 
  the 
  affinity 
  of 
  the 
  acid 
  for 
  water 
  and 
  the 
  

   consequent 
  formation 
  of 
  either 
  hydrates 
  or 
  of 
  complex 
  mole- 
  

   cular 
  structures 
  (say 
  #), 
  each 
  of 
  which 
  would 
  have 
  its 
  par- 
  

   ticular 
  coefficient. 
  The 
  net 
  result 
  is 
  expressible 
  by 
  a 
  general 
  

   equation 
  : 
  

  

  K=2[*(H,)+ife'(N0 
  3 
  ) 
  + 
  ^ 
  / 
  (HN03)+^»...l. 
  . 
  (6) 
  

  

  A 
  further 
  point 
  of 
  interest 
  is 
  that 
  the 
  values 
  for 
  the 
  lower 
  

   temperature-limit 
  are 
  for 
  the 
  lower 
  percentage 
  concentrations 
  

   less 
  than 
  the 
  values 
  for 
  the 
  higher 
  temperature-limit, 
  yet 
  for 
  

   the 
  higher 
  percentage 
  concentration 
  this 
  relation 
  is 
  reversed 
  ; 
  

   the 
  reversal 
  takes 
  place 
  at 
  about 
  40 
  per 
  cent. 
  

  

  If 
  a 
  curve 
  be 
  drawn 
  in 
  which 
  the 
  mean 
  coefficients 
  for 
  

   either 
  limits 
  of 
  temperature 
  are 
  expressed 
  in 
  terms 
  of 
  per- 
  

   centages, 
  the 
  observational 
  results 
  are 
  found 
  to 
  lie 
  approxi- 
  

   mately 
  upon 
  four 
  straight 
  lines 
  — 
  namely, 
  firstly, 
  from 
  1 
  to 
  

   8 
  per 
  cent.; 
  secondly, 
  from 
  11 
  to 
  54 
  per 
  cent.; 
  thirdly, 
  from 
  

   54 
  to 
  70 
  per 
  cent. 
  ; 
  and, 
  fourthly, 
  from 
  70 
  to 
  93 
  per 
  cent. 
  ; 
  

   and 
  the 
  remainder 
  upon 
  an 
  irregular 
  curve. 
  

  

  With 
  regard 
  to 
  these 
  several 
  points, 
  it 
  may 
  be 
  noticed 
  that 
  

   the 
  54 
  per 
  cent, 
  corresponds 
  to 
  that 
  of 
  maximum 
  contraction 
  

   as 
  found 
  by 
  Kolb 
  and 
  ourselves, 
  while 
  the 
  irregularity 
  from 
  

   92 
  to 
  100 
  per 
  cent, 
  has 
  already 
  been 
  alluded 
  to. 
  The 
  

   behaviour 
  of 
  nitric 
  acid 
  as 
  regards 
  this 
  physical 
  property 
  is 
  

   so 
  far 
  different 
  from 
  sulphuric 
  acid, 
  which 
  has 
  been 
  com- 
  

   pletely 
  investigated 
  by 
  Pickering*, 
  in 
  that, 
  firstly, 
  the 
  

   variations 
  are 
  much 
  more 
  marked 
  ; 
  and, 
  secondly, 
  the 
  

   maximum 
  value 
  occurs 
  at 
  100 
  per 
  cent., 
  while 
  that 
  of 
  

   sulphuric 
  acid 
  is 
  at 
  about 
  86 
  per 
  cent., 
  from 
  which 
  point 
  

   the 
  value 
  of 
  the 
  coefficient 
  decreases 
  to 
  98 
  per 
  cent., 
  and 
  from 
  

   this 
  concentration 
  up 
  to 
  100 
  per 
  cent, 
  slightly 
  increases. 
  

  

  In 
  conclusion, 
  we 
  trust 
  that 
  we 
  may 
  be 
  allowed 
  to 
  raise 
  a 
  

   plea 
  for 
  the 
  more 
  complete 
  investigation 
  of 
  the 
  physical 
  pro- 
  

   perties 
  of 
  solutions 
  of 
  liquids 
  in 
  liquids 
  of 
  a 
  high 
  degree 
  of 
  

   concentration 
  as 
  regards 
  the 
  solute. 
  The 
  results 
  to 
  be 
  ob- 
  

   tained 
  will, 
  we 
  believe, 
  be 
  as 
  full 
  of 
  interest 
  as 
  those 
  already 
  

   obtained 
  with 
  solutions 
  of 
  a 
  high 
  degree 
  of 
  dilution 
  as 
  regards 
  

   the 
  solvent 
  water. 
  

  

  Oxford, 
  October 
  1901. 
  

  

  * 
  Journ. 
  Chem. 
  Soc. 
  1890, 
  p. 
  114. 
  

  

  