Balance the following equations by oxidation number method.
${C r_{2} O_{7}}^{2 -} + H N O_{2} + H^{+} \to C r^{3 +} + {N O_{3}}^{-} + H_{2} O$

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Solution

${C r_{2} O_{7}}^{2 -} + H N O_{2} + H^{+} \to C r^{3 +} + {N O_{3}}^{-} + H_{2} O$
$6 e^{-} + C r_{2}^{+ 12} O_{7}^{2 -} ⟶ 2 C r^{3 +}$ $R e d u c t i o n$
$H N^{+ 3} O_{2} ⟶ N^{+ 5} O_{3}^{-} + 2 e^{-} \times 3$ $O x i d a t i o n$
Balancing the charges and adding the equations,
$C r_{2} O_{7}^{2 -} + 3 H N O_{2} ⟶ 2 C r^{3 +} + 3 N O_{3}^{-}$
Balancing oxygen,
$C r_{2} O_{7}^{2 -} + 3 H N O_{2} ⟶ 2 C r^{3 +} + 3 N O_{3}^{-} + 4 H_{2} O$
Balancing hydrogen,
$5 H^{+} + C r_{2} O_{7}^{2 -} + 3 H N O_{2} ⟶ 2 C r^{3 +} + 3 N O_{3}^{-} + 4 H_{2} O$

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H^{+}

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