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Redox Reactions

Question
CBSEENCH11006766

Balance the following equation by oxidation number method:
Fe to the power of 2 plus end exponent space plus space Cr subscript 2 straight O subscript 7 superscript 2 minus end superscript space plus space straight H to the power of plus space space rightwards arrow space space Fe to the power of 3 plus end exponent space plus space 2 Cr to the power of 3 plus end exponent space plus space 3 straight H subscript 2 straight O

Solution

(i) The skeleton equation along with oxidation number of each atom is
stack stack Fe to the power of 2 plus end exponent with plus 2 on top with Fe equals plus 2 below space plus stack stack Cr subscript 2 with plus 6 on top space stack straight O subscript 7 superscript negative 2 end superscript with negative 2 on top space with Cr space equals plus 6 below plus stack straight H to the power of plus with plus 1 on top space rightwards arrow stack space stack Fe to the power of 3 plus end exponent with 3 plus on top with Fe space equals plus 3 below space plus stack stack 2 Cr to the power of 3 plus end exponent with plus 3 on top with Cr space equals plus 3 below space plus stack 3 straight H subscript 2 with plus 1 on top straight O with negative 2 on top
Total O.N. of Cr = +12
Total O.N of Cr = +6
(ii) Noting the change in O.N. of above atoms,
    Increase     Fe = +2  to  +3 to i.e.  1
  Decrease      Cr = +12  to  +6 i.e. 6
(iii) Equalise the increase/decrease in O.N. by multiplying Fe2+ by 6,
              6 Fe to the power of 2 plus end exponent space plus space Cr subscript 2 straight O subscript 7 superscript 2 minus end superscript space plus space straight H to the power of plus space space space rightwards arrow space space space space 6 Fe to the power of 3 plus end exponent space plus space 2 Cr to the power of 3 plus end exponent space plus space 3 straight H subscript 2 straight O
(iv) Balance Fe atoms by multiply Fe3+ by 6.
   6 Fe to the power of 2 plus end exponent space plus space Cr subscript 2 straight O subscript 7 superscript 2 minus end superscript space plus space straight H to the power of plus space space space rightwards arrow space space space space 6 Fe to the power of 3 plus end exponent space plus space 2 Cr to the power of 3 plus end exponent space plus space 3 straight H subscript 2 straight O
(v) Balance the hydrogen atoms
   Net charge on LHS = +12 -2 + 1 = +11
   Net charge on RHS = +18 + 6 = +24
  So difference  = 24 - 11 = 13
Therefore adding thirteen H+ LHS,
6 Fe to the power of 2 plus end exponent space plus space Cr subscript 2 straight O subscript 7 superscript 2 minus end superscript space plus space 14 straight H to the power of plus space rightwards arrow space space space 6 Fe to the power of 3 plus end exponent space plus space 2 Cr to the power of 3 plus end exponent space plus space 3 straight H subscript 2 straight O    
(vi) Balance O atoms and four more H2O molecules on RHS, the balanced equation is
6 Fe to the power of 2 plus end exponent space plus space Cr subscript 2 straight O subscript 7 superscript 2 minus end superscript space plus space 14 straight H to the power of plus space space rightwards arrow space space 6 Fe to the power of 3 plus end exponent space plus space 2 Cr to the power of 3 plus end exponent space plus space 7 straight H subscript 2 straight O