Balance the following redox reactions in acidic solutions:

$U O_{2} + {C r}_{2} O_{7}^{2 -} ⟶ U O_{2}^{2 +} + {C r}^{2 +} + H_{2} O$

3 U O_{2} + {C r}_{2} O_{7}^{2 -} + 14 H^{+} ⟶ 3 U O_{2}^{2 +} + {2 C r}^{2 +} + {7 H}_{2} O

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2 U O_{2} + {2 C r}_{2} O_{7}^{2 -} + 14 H^{+} ⟶ 3 U O_{2}^{2 +} + {2 C r}^{2 +} + {5 H}_{2} O

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3 U O_{2} + {2 C r}_{2} O_{7}^{2 -} + 14 H^{+} ⟶ 3 U O_{2}^{2 +} + {2 C r}^{2 +} + {5 H}_{2} O

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None of these

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Solution

The correct option is A $3 U O_{2} + {C r}_{2} O_{7}^{2 -} + 14 H^{+} ⟶ 3 U O_{2}^{2 +} + {2 C r}^{2 +} + {7 H}_{2} O$
The unbalanced chemical equation is as follows:
$U O_{2} + {C r}_{2} O_{7}^{2 -} ⟶ U O_{2}^{2 +} + {C r}^{3 +} + H_{2} O$
Balance all atoms except H and O.
$U O_{2} + {C r}_{2} O_{7}^{2 -} ⟶ U O_{2}^{2 +} + 2 {C r}^{3 +} + H_{2} O$
The oxidation number of U changes from +4 to +6. The change in the oxidation number is 2.
The oxidation number of Cr changes from +6 to +3. The change in the oxidation number per Cr atom is 3. Total change in the oxidation number for 2 Cr atoms is 6
To balance the increase in the oxidation number with decrease in oxidation number, multiply $U O_{2}$ and $U O_{2}^{2 +}$ with 3.
$3 U O_{2} + {C r}_{2} O_{7}^{2 -} ⟶ 3 U O_{2}^{2 +} + 2 {C r}^{3 +} + H_{2} O$
T
o balance O atoms, add 6 water molecules of RHS.
$3 U O_{2} + {C r}_{2} O_{7}^{2 -} ⟶ 3 U O_{2}^{2 +} + 2 {C r}^{3 +} + 7 H_{2} O$
To balance H atoms, add 14 $H^{+}$ on LHS
$3 U O_{2} + {C r}_{2} O_{7}^{2 -} + 14 H^{+} ⟶ 3 U O_{2}^{2 +} + 2 {C r}^{3 +} + 7 H_{2} O$
This is the balanced chemical equation.

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Similar questions

{C r}_{2} O_{7}^{2 -} + {F e}^{2 +} + H^{\oplus} ⟶ {C r}^{3 +} + {F e}^{3 +} + H_{2} O

6 {F e}^{2 +} + 14 H^{\oplus} + {C r}_{2} O_{7}^{2 -} ⟶ 6 {F e}^{3 +} + 2 {C r}^{3 +} + 7 H_{2} O

{C r}_{2} O_{7}^{2 -} + 14 H^{\oplus} + 6 l^{⊖} ⟶ 2 {C r}^{3 +} + 3 H_{2} O + 3 I_{2}

{C r}_{2} O_{7}^{2 -} (a q) + H {N O}_{2} (a q) ⟶ {C r}^{3 +} (a q) + {N O}_{3}^{-} (a q)

{C r}_{2} O_{7}^{2 +} (a q) + 14 H^{+} (a q) + 6 {F e}^{2 +} (a q) \to 6 {F e}^{3 +} (a q) + 2 {C r}^{3 +} (a q) + 7 H_{2} O (l)

{C r}_{2} O_{7}^{2 -} H^{+} - - \to C r

{C r}_{2} O_{7}^{2 -}

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