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Redox Reactions

Question
CBSEENCH11006774

Balance the following equation by half reaction method in acidic medium:
MnO subscript 4 superscript minus space plus space Br to the power of minus space space space rightwards arrow space space space Mn to the power of 2 plus end exponent space plus space Br squared

Solution
(i) Write the oxidation and reduction half-reactions by observing the changes in oxidation numbers and write these separately.
                                      -1              0
oxidation half reaction:      Br-   rightwards arrow     Br2
Reduction half-reaction:
      plus 7
MnO subscript 4 superscript minus space space space space rightwards arrow space space space space space Mn to the power of 2 plus end exponent
2. Balancing the oxidation half reaction.
(i) Balance Br atoms by multiplying Br- by 2.
              2 Br to the power of minus space space rightwards arrow space space space Br subscript 2
(ii) Add 2 electrons towards R.H.S. in order to balance the charges on bromine atoms.
                   2 Br to the power of minus space space space rightwards arrow space space space space stack Br subscript 2 space plus space 2 straight e to the power of minus with left parenthesis Balanced space oxidation space half space rection right parenthesis below
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. 
                      plus 7
MnO subscript 4 superscript minus space space space rightwards arrow space 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 charge on manganese atoms. 
              MnO subscript 4 superscript minus plus space 5 straight e to the power of minus space space rightwards arrow space space Mn to the power of 2 plus end exponent
(iii) Balance H atoms by adding 8H+ 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 rightwards arrow space space space Mn to the power of 2 plus end exponent space plus space 4 straight H subscript 2 straight O
space space space space space space space space space space space space space space space space space space space space space space space space space space space space left parenthesis Balanced space reduction space half space reaction right parenthesis
4. Multiply balanced oxidation half-reaction by 5 and balanced reduction half-reaction by 2 to equate electrons and add both the half reactions.
space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space 0
space space space space space space space space 2 Br to the power of minus space space space rightwards arrow space space Br subscript 2 space plus space 2 straight e to the power of minus right square bracket space cross times space 5
MnO subscript 4 superscript minus space plus space 5 straight e space plus space 8 straight H to the power of plus space space rightwards arrow space 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
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
10 Br to the power of minus space plus space 2 MnO subscript 4 superscript minus space plus space 16 straight H to the power of plus space space rightwards arrow space space space 5 Br subscript 2 space plus space 2 Mn to the power of 2 plus end exponent 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
This is a balanced redox equation.