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108                 Basic physical chemistry
              for  N  ;   for H S(g):  + 1  for H and therefore  - 2 for S.  For the atoms on
                         2
              the right side of the reaction the oxidation numbers are for NO(g):  - 2
              for  oxygen  and  therefore  + 2  for  N  ;   for  S  the oxidation  number is  O ;
              and  fo  r   H20(1):  + 1  fo  r   H  and  - 2  fo  r   oxygen.  Hence,  the  reaction
              decreases the oxidation number for nitrogen (from  + 5  to  + 2) ;  there­
              fore nitrogen is reduced .  The oxidation number of sulfur, on the other
              hand,  is  increased  (from  - 2  to O);  therefore  sulfur is oxidized .  The
              oxidation numbers of the hydrogen and oxygen remain unchanged .
                (b)  The  oxidation  numbers  of  the  atoms  on  the  left  side  of  the
              reaction  are  + 2 for Cu,  + 1  for H  ,   and  - 2  for oxygen.  On the  right
              side  of the  reaction  they  are  0  for Cu, 0  for oxygen,  and  + 1  for H  .
              Hence,  the  reaction decreases the oxidation number of  u   (from  + 2
                                                                C
              to 0) ; therefore copper is  reduced .  The  oxidation number of oxygen is
              increased (from  - 2 to O) ; therefore oxygen  s   oxidized.
                                                     i


                          6.3  Balancing oxidation-reduction  reactions
              A  balanced chemical equation must have  the  same  number and  types
              of atoms  on  both  sides  of the  equation ,  and  the  sum of the  electric
              charges  must be the same for the reactants as for the products of the
              reaction.  If all  the reactants and products are known,  the equation for
              a  redox  reaction  may  be balanced by  the half-reaction  method.  (An­
              other method,  called the oxidation-number method, may also be used ,
              but for our purposes knowledge of one method is  sufficient .)
                The  half-reaction  method  involves application  of the  following  se­
                        p
              quential ste s .
                                t
              Step  1 .   Write down  h e   overall unbalanced equation for the reaction.
                   2
              Step  .   Write down the unbalanced  equations  for the oxidation half­
                     reaction  and  for  the  reduction  half-reaction  (species  should
                     not  be  written  as  free  atoms  or  ions  unless  they  exist  in
                     these forms).
                                                s
              Step  3.  For  each  of the  half-reaction ,   first  balance  the  atoms  that
                      undergo  oxidation  and  reduction.  Then  balance  atoms  other
                      than  oxygen  and  hydrogen.  Finally, balance  the  oxygen  and
                                   s
                      hydrogen  atom .   [In  neutral  or  acidic  solutions ,  H20  and
                      H + (aq)  may  be  added  to  balance  the  oxygen  and  hydrogen
                            3
                      atoms.  The oxygen atoms are balanced first .  For each excess
                      oxygen atom on one side of the equation, balance is achieved
                      by adding one H 20 to the other side.  Then H + (aq)  is used to
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