Balance the following redox reactions:

$C r O_{4}^{2 -} (a q) + S^{2 -} (a q) ⟶ C r {(O H)}_{3} (s) + S (s)$

2 C r O_{4}^{2 -} (a q) + {3 S}^{2 -} (a q) + {8 H}_{2} O (l) ⟶ 2 C r {(O H)}_{3} (s) + 3 S (s) + 10 {O H}^{-} (a q)

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3 C r O_{4}^{2 -} (a q) + {3 S}^{2 -} (a q) + {8 H}_{2} O (l) ⟶ 2 C r {(O H)}_{3} (s) + 3 S (s) + 10 {O H}^{-} (a q)

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3 C r O_{4}^{2 -} (a q) + {2 S}^{2 -} (a q) + {8 H}_{2} O (l) ⟶ 2 C r {(O H)}_{3} (s) + 3 S (s) + 10 {O H}^{-} (a q)

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2 C r O_{4}^{2 -} (a q) + {2 S}^{2 -} (a q) + {8 H}_{2} O (l) ⟶ 2 C r {(O H)}_{3} (s) + 3 S (s) + 10 {O H}^{-} (a q)

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Solution

The correct option is A $2 C r O_{4}^{2 -} (a q) + {3 S}^{2 -} (a q) + {8 H}_{2} O (l) ⟶ 2 C r {(O H)}_{3} (s) + 3 S (s) + 10 {O H}^{-} (a q)$
The unbalanced chemical equation is $C r O_{4}^{2 -} (a q) + S^{2 -} (a q) ⟶ C r {(O H)}_{3} (s) + S (s)$ .
All atoms other than H and O are balanced.
The oxidation number of Cr changes from +6 to +3. The change in the oxidation number is 3.
The oxidation number of S changes from -2 to 0. The change in the oxidation number is 2.
To balance the increase in the oxidation number with decrease in the oxidation number, multiply $C r O_{4}^{2 -}$ and $C r {(O H)}_{3}$ with 2 and multiply $S^{2 -}$ and S with 3.
$2 C r O_{4}^{2 -} (a q) + 3 S^{2 -} (a q) ⟶ 2 C r {(O H)}_{3} (s) + 3 S (s)$
To balance O atoms, add 2 water molecules on RHS.
$2 C r O_{4}^{2 -} (a q) + 3 S^{2 -} (a q) ⟶ 2 C r {(O H)}_{3} (s) + 3 S (s) + 2 H_{2} O$
To balance H atms, add 10 $H^{+}$ on LHS.
$2 C r O_{4}^{2 -} (a q) + 3 S^{2 -} (a q) + 10 H^{+} ⟶ 2 C r {(O H)}_{3} (s) + 3 S (s) + 2 H_{2} O (l)$
Since the reaction occurs in basic medium, add 10 hydroxide ions on either side.
$2 C r O_{4}^{2 -} (a q) + 3 S^{2 -} (a q) + 10 H^{+} + 10 O H^{-} ⟶ 2 C r {(O H)}_{3} (s) + 3 S (s) + 2 H_{2} O (l) + 10 O H^{-}$
On LHS, 10 hydrogen ions combine with 10 hydroxide ions to form 10 water molecules out of which 2 water molecules cancel with 2 water molecules on RHS.
$2 C r O_{4}^{2 -} (a q) + 3 S^{2 -} (a q) + 8 H_{2} O (l) ⟶ 2 C r {(O H)}_{3} (s) + 3 S (s)$
This is the balanced chemical equation.

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