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4                  INTRODUCTION
                  proportion  here  is 7·81  to 6-30  =  1·239: 1, which  corresponds
                  equally  well  with  the  numbers  b:4  or  Il:9.  The  formula
                  C,H,  requires  93-75  p.c.  carbon  and  6·25  p.c.  hydrogen,  and
                  the  formula  C,H,,  93-62  p..  carbon  and  6-38  p.c.  hydrogen,
                  the  deviations  from  the  actual  numbers  found  being  in  both
                  cases  within the  limits of experimental  error.  Therefore other
                  considerations  must  be  taken  into  account here,  in  order  to
                  decide  between  the  two  formule.
                   The  formula derived  from  the  results of analyses  is termed
                  the Empirical Formula,  and  expresses the  simplest numerical
                  relationship  between  the  atoms  of  the elements present.  'The
                  actual molecular formula may be a multiple of this,  and has to
                  be  determined  according  to  special  principles.

                        Determination  of  Molecular  Weight
                  1,  By  CHEMICAL  METHODS.
                   Our  chemical  formulae  (e.g.  CH,O)  express  not merely  a
                  percentage relation,  but at the same time the smallest quantity
                 of  the  compound  which  is  capable  of  existing  as  such,  i.e.  a
                  molecule of it.  This molecule is  ideally no  longer divisible  by
                  mechanical means,  but only by chemical, and then into its con-
                 stituent atoms.  If  the formula CHO  were the  correct one for
                 acetic acid, then the amount of oxygen (or carbon) contained in
                 a molecule would be indivisible,  and  that of hydrogen divisible
                 only  by  2.  Since,  however,  it has  been  observed  that one-
                  fourth  of the  total  hydrogen  in acetic acid  is replaceable,  e.g.
                  by a metal,  with  the formation of a salt,  it is obvious that the
                 quantity  of hydrogen  in the  molecule must be  divisible  by 4,
                 and so  the formula must contain at least 4 atoms of hydrogen,
                 and  must therefore  be  (HO,,  or  some  multiple  of  it.  This
                  is,  in fact, the case.  Acetate of silver contains 64·67  p.c.  silver,
                 and therefore 35+33 p.c. of the acetate radical;  or,  to l atom of
                  silver =  108  parts  by  weight,  there are D8  parts by  weight of
                 the  acid  radical.  This  59,  together  with  1  atom  of  hydrogen
                  =1, makes the molecular weight of acetic acid 60,  =  2  x  30,
                  - 2x CH,O,  = C,H,0,
                   This  is  a  determination  of  molecular  weight by  chemical
                 means.  Such  determinations  are  carried  out in  the  case  of
                 acids generally by means of their silver salts;  these are usually
                 normal  salts,  are  easy  to  purify,  are  almost always  free  from
                  water  of  crystallization,  and  are  readily  analysed.  It  is,
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