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Lewis Acids and Bases  165
       more  strongly  bonded  to A than  it is  to B.  In this book we  shall maintain  the



       distinction between the two definitions and shall follow the usual convention that
       the unmodified  term acid will refer to a Bransted acid, while Lewis acids will be
       specified as such.
       Strengths of Lewis Acids and Bases
       Because the  Lewis acid-base  concept  is  an extremely  useful  one in  chemistry,
       quantitative  relationships  of  the  types  discussed  in  the  previous  sections  for
       Bransted acids and bases would be helpful. The task of classifying the Lewis acids
       and bases according to some criterion of strength has nevertheless proved to be a
       difficult one, and methods being developed still yield largely qualitative results.
       Brsnsted acid-base  reactions  always involve transfer of a proton;  this common
       feature  allows  meaningful  quantitative  comparisons  of  strengths  to  be  made.
       Different Lewis acid-base  reactions,  on the other hand, do not necessarily have
       any feature in common, and the result is that the term "strength"  does not have a
       well-defined meaning.
           The problem may be illustrated by  a simple example.l1° Suppose that we
       wish  to compare the "coordinating  power  " of two Lewis bases, say an amine,
       NR,,  and a  phosphine,  PR,.  We might do this  by  comparing the equilibrium



                                           K '
                                   A + B'       AB'                       (3.63)
       constants for Reactions 3.62 and 3.63 of the two bases, B and B',  with the same
       Lewis acid, for example BF,.  Quantitative data are not always available; but it is
       often  possible  to  make  qualitative  decisions  about  orders  of  reactivity.  The
       information  we have shows that the nitrogen base should be judged  to have the
       greater  coordinating  power,  since  the  equilibrium  constant  is  greater  for  the
       formation of nitrogen base complex.111 A similar qualitative result is found with
       H+ as the reference acid.l12 If, on the other hand, the equilibrium constants for a
       nitrogen  and a phosphorus  base with Ag+ are measured,  it is found  that  with
       respect to this Lewis acid the phosphine has much greater coordinating  power
       than  does  the  amine.  A  similar  situation  arises with  another  set  of  bases,  the
       halide ions. If H + is taken as the reference acid, fluoride is the most effective base
       in solution, followed by chloride, bromide, and iodide. With silver ion, however,
       the order is exactly reversed; iodide forms the most stable complex and fluoride
       the least stable.l13

       Hard and Soft Lewis Acids and Bases
       Despite the apparent chaos of the picture presented  by these results, it is possible
       to find some qualitative relationships that are useful. Schwarzenbach,l14 and also

       110 S. Ahrland, J. Chatt, and N.  R. Davies, Quart. Reu.  (London), 12, 265 (1958).
       111 W. A. G. Graham and F. G. A. Stone, J. Znorg.  Nucelar Chem., 3, 164 (1956).
       112 See Table 3.13 for solution data and Table 3.18 for gas-phase data.
       113 See note  110.
       114 (a) G. Schwarzenbach, Experientia,  Suppl.,  5,  162 (1956); (b) G.  Schwarzenbach, Aduan.  Znorg.
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