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Redox Reactions

Question
CBSEENCH11006764

Balance the following,chemical equation by oxidation number method:

Mn to the power of 2 plus end exponent space plus space straight S subscript 2 straight O subscript 8 superscript 2 minus end superscript space space space space rightwards arrow space space space space stack MnO subscript 4 superscript minus space plus space HSO subscript 4 superscript minus with left parenthesis acidic space medium right parenthesis below


Solution
(i)The skeleton equation along with oxidation number each atom is:
space space straight O. straight N space increases space by space 5 space per space atom

stack Mn to the power of 2 plus end exponent with Mn equals plus 2 below and plus 2 on top space space plus stack stack left square bracket straight S subscript 2 with plus 7 on top space stack straight O subscript 8 with negative 2 on top with straight S equals plus 7 below right square bracket to the power of 2 minus end exponent space rightwards arrow space stack Mn with plus 7 on top space straight O with negative 2 on top to the power of negative space end exponent with Mn space equals plus 7 below space space space plus space stack straight H with plus 1 on top straight S with plus 6 on top space stack straight O subscript 4 superscript minus with negative 2 on top with straight S equals space plus 6 below

ii right parenthesis space Equalise space the space increase space divided by decrease space in space straight O. straight N. space multiply
space Mn to the power of 2 plus end exponent by space 2 space and space 5 straight S subscript 2 straight O subscript 8 superscript 2 minus end superscript space by space 5 comma
2 Mn to the power of 2 plus end exponent space plus space space 5 straight S subscript 2 straight O subscript 8 superscript 2 minus end superscript space rightwards arrow space MnO subscript 4 superscript minus space plus HSO subscript 4 superscript minus

iii right parenthesis space Balance space straight O space atoms comma space by space adding space eight space straight H subscript 2 straight O space molecules space
on space the space reactant space side comma
2 Mn to the power of 2 plus end exponent space plus 5 straight S subscript 2 straight O subscript 8 superscript 2 minus end superscript space space plus 8 straight H subscript 2 straight O space rightwards arrow space 2 MnO subscript 4 superscript minus space plus space 10 HSO subscript 4 superscript minus
Balance space the space straight H space atoms comma
Net space charge space on space LHS space equals plus 4 minus 10 space equals negative 6
Net space charge space on space RHS space equals negative 2 minus 10 space equals negative 12
Adding space six space straight H to the power of plus space on space RHS comma
2 Mn to the power of 2 plus end exponent space plus 5 straight S subscript 2 straight O subscript 8 superscript 2 minus end superscript space plus 8 straight H subscript 2 straight O space rightwards arrow space
space space space space space space space space space space space space space space space space space 2 MnO subscript 4 superscript minus space plus space 10 space HSO subscript 4 superscript minus space plus 6 straight H to the power of plus