In the reaction, $A s_{2} S_{3} + x N O_{3}^{-} + y H^{+} ⟶ 2 A s S O_{4} + z N O_{2} + a S + 2 H_{2} O$ Find the coeffieicnts x , y, z and a (Respectively)

10, 4, 10, 3

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5, 4, 5, 3

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4, 10, 3, 10

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None of these

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Solution

The correct option is A
10, 4, 10, 3

This is a very special case of redox reaction. Note that the given reaction involves two oxidations and one reduction.

a. Two oxidation half reactions are

i. $A s^{3 +}$ $⟶$ $A s O_{4}^{3 -}$

ii. $S^{2 -}$ $⟶ S$

First, balancing these two half reduction reactions:

i. $2 A s^{3 +} + 8 H_{2} O ⟶ A s O_{4}^{3 -} + 16 H^{+} + 4 e^{-}$

ii. $3 S^{2 -} ⟶ 3 S + 6 e^{-}$

Now add the two equations to get

$2 A s^{3 +} + 3 S^{2 -} + 8 H_{2} O ⟶ A s O_{4}^{3 -} + 3 S + 16 H^{+} + 10 e^{-}$ ...(i)

b. Reduction half reaction : $N O_{3}^{-} ⟶ N O_{2}$

Now let us balance the reduction half reaction and proceed as usual.

$N O_{3}$ + $2 H^{+}$ + $1 e^{-}$ $⟶$ $N O_{2}$ + $H_{2} O$ ...(ii)

Adding the two reactions (i) and 10 $\times$ (ii), we get

$A s_{2} S_{3} + 10 N O_{3}^{-} + 4 H^{+} ⟶ 2 A s O_{4}^{3 -} + 10 N O_{2} + 3 S + 2 H_{2} O$

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