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Redox Reactions

Question
CBSEENCH11006767

Balance the following equation by oxidation number method:
left enclose CrO subscript 4 right parenthesis to the power of 2 minus end exponent space plus space space left parenthesis SO subscript 3 right parenthesis to the power of 2 minus end exponent space space space rightwards arrow space space end enclose open vertical bar Cr left parenthesis OH right parenthesis subscript 4 close vertical bar to the power of 1 minus end exponent space plus space left parenthesis SO subscript 4 right parenthesis to the power of 2 minus end exponent
(in alkaline medium)




Solution

(i) The skeleton equation along with oxidation number of each atom is
stack Cr with plus 6 on top space stack straight O subscript 4 superscript 2 minus end superscript with negative 2 on top space with Cr equals plus 6 below plus stack straight S with plus 4 on top space stack straight O subscript 3 superscript 2 minus end superscript with negative 2 on top with straight S equals plus 4 below space rightwards arrow stack left square bracket Cr with plus 3 on top space left parenthesis straight O with negative 2 on top space straight H with plus 1 on top right parenthesis subscript 4 right square bracket to the power of negative 1 end exponent with Cr equals plus 3 below space plus space stack straight S with plus 6 on top stack straight O subscript 4 superscript 2 minus end superscript with negative 2 on top with straight S equals plus 6 below
 
(ii) Noting the changein O.N. of above atoms,
       Increase      S = +4 to +6 i..e 2  
       Decrease     Cr =  +6   to  +3   i.e.  3
(iii) Equalise the increase/decrease in O.N. by
multiplying Cr subscript 2 straight O subscript 4 superscript 2 minus end superscript space by space 2 space and space left parenthesis SO subscript 3 right parenthesis to the power of 2 minus end exponent space by space 3.
   2 left parenthesis CrO subscript 4 right parenthesis to the power of 2 minus end exponent space plus space 3 left parenthesis SO subscript 3 right parenthesis to the power of 2 minus end exponent space space rightwards arrow space space space open square brackets Cr left parenthesis OH right parenthesis subscript 4 close square brackets to the power of minus space plus space left parenthesis SO subscript 4 right parenthesis to the power of 2 minus end exponent
(iv) Balance Cr atoms by multiplying [Cr(OH)4]- by 2 and balance S atoms by multiplying (SO4)2- by 3.
         2 left parenthesis CrO subscript 4 right parenthesis to the power of 2 minus end exponent space plus space 3 left parenthesis SO subscript 3 right parenthesis to the power of 2 minus end exponent space space space rightwards arrow space space space space 2 open square brackets Cr left parenthesis OH right parenthesis subscript 4 close square brackets to the power of minus space plus space left parenthesis 3 SO subscript 4 right parenthesis to the power of 2 minus end exponent
(v) Balance O atoms by adding three H2O molecules on the reactant side. 
              2 left parenthesis CrO subscript 4 right parenthesis to the power of 2 minus end exponent space plus space 3 left parenthesis SO subscript 3 right parenthesis to the power of 2 minus end exponent space plus space 3 straight H subscript 2 straight O space space rightwards arrow space space space 2 open square brackets Cr left parenthesis OH right parenthesis subscript 4 close square brackets to the power of minus space plus space 3 left parenthesis SO subscript 4 right parenthesis to the power of 2 minus end exponent
(vi) Balance the H atoms
      Net charge on LHS = -4 - 6 = -10
      Net charge on RHS = -2 -6 = -8
therefore  adding two OH-(basic medium) on RHS and adding 2 water molecules on the reactant side. 
         2 left parenthesis CrO subscript 4 right parenthesis to the power of 2 minus end exponent space plus space 3 left parenthesis SO subscript 3 right parenthesis to the power of 2 minus end exponent space plus space 5 straight H subscript 2 straight O space rightwards arrow space space space 2 open square brackets Cr left parenthesis OH right parenthesis subscript 4 close square brackets to the power of minus space plus space 3 left parenthesis SO subscript 4 right parenthesis to the power of 2 minus end exponent space plus space 2 OH to the power of minus