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Redox Reactions

Question
CBSEENCH11006776

Write correctly balanced half reaction and the overall equations for the skeleton equation:
          MnO subscript 4 superscript minus space plus space straight H subscript 2 straight C subscript 2 straight O subscript 4 space space rightwards arrow space space space stack Mn to the power of 2 plus end exponent space plus space CO subscript 2 with left parenthesis in space acid space solution right parenthesis below

Solution
1. Write the oxidation and reduction half-reactions by observing the changes in oxidation number and write these separately.
                                        +3            +4 
Oxidation half reaction:        straight C subscript 2 straight H subscript 4 straight O subscript 2 space space rightwards arrow space space CO subscript 2

Reduction half reaction:     +7                +2
                                      MnO subscript 4 superscript minus space space space space rightwards arrow space space space Mn to the power of plus 2 end exponent
2. Balancing the oxidation half reaction.
 (i) Balance C atoms by multiplying CO2 by 2.
                   +3                     +4
                    straight C subscript 2 straight H subscript 4 straight O subscript 2 space space rightwards arrow space space space 2 CO subscript 2
(ii) Add 2 electrons towards R.H.S. in order to balance charges on carbon atoms.
                   straight C subscript 2 straight H subscript 2 straight H subscript 4 space space space rightwards arrow space space space 2 CO subscript 2 space plus space 2 straight e to the power of minus
(iii) Balance H atoms by adding two H+ (reaction occurs in the acidic medium) towards R.H.S.
straight C subscript 2 straight H subscript 2 straight O subscript 4 space rightwards arrow space space 2 CO subscript 2 space plus space 2 straight e to the power of minus space plus space 2 straight H to the power of plus
space space space space space space space space space left parenthesis Balanced space oxidation space half space reaction right parenthesis
3. Balancing the reduction half reaction.
   (i) Balancing of Mn is not required as the number of each Mn is one on both the sides.
                   +7
                  MnO subscript 4 superscript minus space space space rightwards arrow space space space space Mn to the power of 2 plus end exponent
(ii) Add 5 electrons towards L.H.S. in order to balance the charges on manganese atoms. 
                       MnO subscript 4 superscript minus space plus space 5 straight e to the power of minus space space space rightwards arrow space space space Mn to the power of 2 plus end exponent
(iii) Balance H atoms by adding eight H+ towards
L.H.S.
        MnO subscript 4 superscript minus space plus space 5 straight e to the power of minus space plus space 8 straight H to the power of plus space space space rightwards arrow space space space MN to the power of 2 plus end exponent space plus space 4 straight H subscript 2 straight O
                                      (Balanced reduction half reaction)
4. Multiply balanced oxidation half reaction by 5 and balanced reduction half reaction by 2 to equate the electrons and add both the half reactions. 
                              straight C subscript 2 straight H subscript 2 straight O subscript 4 space space space rightwards arrow space space space 2 CO subscript 2 space plus space 2 straight e to the power of minus space plus space 2 straight H to the power of plus right square bracket space cross times space 5
minus negative negative negative negative negative negative negative negative negative negative negative negative negative negative negative negative negative negative
MnO subscript 4 superscript minus space plus space 5 straight e to the power of minus space plus space 8 straight H to the power of plus space space space rightwards arrow space space space Mn to the power of 2 plus end exponent space plus space 2 straight H subscript 2 straight O right square bracket space cross times space 2
space space space 2 MnO subscript 4 superscript minus space plus space 5 straight C subscript 2 straight H subscript 2 straight O subscript 4 space plus space 6 straight H to the power of plus space space space rightwards arrow space space space space 2 Mn to the power of 2 plus end exponent space plus space 10 CO subscript 2 space plus space 8 straight H subscript 2 straight O
minus negative negative negative negative negative negative negative negative negative negative negative negative negative negative negative negative negative negative negative negative negative negative negative negative negative negative negative negative
This space is space the space balanced space redox space equation. space