322  Atoms  and  Chemical  Valence.        {^'"-  ^  May^^92'S: 
electrons.  This  is  clear  if  we  consider  two  cubes  with  electrons  at 
each  of  the  eight  corners.  When  the  cubes  are  placed  so  that  an 
edge  of  one  is  in  contact  with  an  edge  of  the  other  a  single  pair 
of  electrons  at  the  ends  of  the  common  edge  will  take  the  place  of 
four  electrons  in  the  original  cubes.  For  each  pair  of  electrons  held 
in  common  between  two  octets  there  is  a  decrease  of  two  in  the  total 
number  of  electrons  needed  to  form  the  octets. 
Let  e  represent  the  number  of  electrons  in  the  outside  shell  of 
the  atoms  that  combine  to  form  a  molecule.  Let  n  be  the  number 
of  octets  that  are  formed  from  these  e  electrons,  and  let  p  be  the 
number  of  pairs  of  electrons  which  the  octets  share  with  one  another. 
Since  every  pair  of  electrons  thus  shared  reduces  by  two  the  number 
of  electrons  required  to  form  the  molecules  it  follows  that  ^  =  8w  — 
2p  or  p  =  V2(8n  —  e). 
This  simple  equation  tells  us  in  each  case  how  many  pairs  of 
electrons  or  chemical  bonds  must  exist  in  any  given  molecule  be- 
tween the  octets  formed.  Hydrogen  nuclei,  however,  may  attach 
themselves  to  pairs  of  electrons  in  the  octets  which  are  not  already 
shared.  For  example,  in  the  formation  of  hydrogen  fluoride  from 
a  hydrogen  atom  and  a  fluorine  atom  there  are  8  electrons  in  the 
shells  (e  =  8) .  We  place  n  —  i  in  the  above  equation  and  find 
p  =  o.  In  other  words,  the  fluorine  atoms  do  not  share  electrons 
with  each  other.  The  hydrogen  nucleus  having  given  up  its  elec- 
tron to  the  fluorine  atoms  attaches  itself  to  one  of  the  pairs  of  elec- 
trons of  the  fluorine  octet,  and  thus  forms  a  molecule  having  a  rela- 
tively weak  external  field  of  force.  As  a  result,  hydrogen  fluoride 
is  a  liquid  of  low  boiling  point  instead  of  being  salt-like  in  charac- 
ter. 
The  equation  given  above  is  applicable  to  all  types  of  com- 
pounds. For  example,  if  we  apply  it  to  substances  such  as  sodium 
fluoride,  sulphur  fluoride,  or  potassium  fluosilicate,  which  were 
previously  considered,  we  find  in  each  case  p  =  o.  In  other  words, 
there  are  no  pairs  of  electrons  holding  the  atoms  of  these  compounds 
together.  On  the  other  hand,  if  we  consider  the  compound  N2H4, 
we  find  p  =  1.  Since  there  are  only  two  octets,  the  pair  of  elec- 
trons must  be  between  the  two  nitrogen  atoms  while  the  hydrogen 
nuclei  attach  themselves  to  pairs  of  electrons  of  the  nitrogen  octet. 
It  can  be  readily  shown  that  this  simple  theory  is  in  fact  identical 
with  the  accepted  valence  theory  of  organic  chemistry  and  leads 
to  the  same  structural  formulas  as  the  ordinary  theory  in  all  those 
