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

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Solution

${C r_{2} O_{7}}^{2 -} + I^{-} + H^{+} \to C r^{3 +} + I_{2} + H_{2} O$
$6 e^{-} + C r_{2}^{+ 12} O_{7}^{2 -} ⟶ 2 C r^{3 +}$ $R e d u c t i o n$
$2 I^{-} ⟶ I_{2} + 2 e^{-} \times 3$ $o x i d a t i o n$
Balancing the charges and adding both equations.
${C r_{2} O_{7}}^{2 -} + 6 I^{-} \to 2 C r^{3 +} + 3 I_{2}$
Balancing oxygen,
${C r_{2} O_{7}}^{2 -} + 6 I^{-} \to 2 C r^{3 +} + 3 I_{2} + 7 H_{2} O$
Balancing hydrogen,
$14 H^{+} + {C r_{2} O_{7}}^{2 -} + 6 I^{-} \to 2 C r^{3 +} + 3 I_{2} + 7 H_{2} O$

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