If the balanced reaction is as given below, find the value of $x, y$ and $z$ .

$C u (N H_{3}) {_{4}}^{2 +} (a q) + S_{2} O {_{4}}^{2 -} (a q) + x O H^{-} \to y S O {_{3}}^{2 -} (a q) + C u (s)$ $+ z N H_{3} (a q) + 2 H_{2} O$

x = 4, y = 2, z = 4

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x = 3, y = 2, z = 3

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x = 4, y = 3, z = 4

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None of the above

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Solution

The correct option is A $x = 4, y = 2, z = 4$
The unbalanced chemical equation is,

$C u (N H_{3}) {_{4}}^{2 +} (a q) + S_{2} O {_{4}}^{2 -} (a q) \to S O {_{3}}^{2 -} (a q) + C u (s) + N H_{3} (a q)$

Balance $N$ and $S$ atoms.

$C u (N H_{3}) {_{4}}^{2 +} (a q) + S_{2} O {_{4}}^{2 -} (a q) \to 2 S O {_{3}}^{2 -} (a q) + C u (s) + 4 N H_{3} (a q)$

The oxidation number of $C u$ decreases from $+ 2$ to $0$ . Net decrease in the oxidation number is $2$ .
The oxidation number of $S$ atom increases from $+ 3$ to $+ 4$ . For $2 S$ atoms, the oxidation number increases by $2$ .
Thus, an increase in the oxidation number is balanced with a decrease in oxidation number.

To balance $O$ atoms, add $2$ water molecules on LHS.

$C u (N H_{3}) {_{4}}^{2 +} (a q) + S_{2} O {_{4}}^{2 -} (a q) + 2 H_{2} O (l) \to 2 S O {_{3}}^{2 -} (a q) + C u (s) + 4 N H_{3} (a q)$

To balance $H$ atoms, add $4$ protons on RHS.

$C u (N H_{3}) {_{4}}^{2 +} (a q) + S_{2} O {_{4}}^{2 -} (a q) + 2 H_{2} O (l) \to 2 S O {_{3}}^{2 -} (a q) + C u (s) + 4 N H_{3} (a q) + 4 H^{+} (a q)$

Since the reaction is in basic medium, add $4$ hydroxide ions on either side.

$C u (N H_{3}) {_{4}}^{2 +} (a q) + S_{2} O {_{4}}^{2 -} (a q) + 2 H_{2} O (l) + 4 O H^{-} (a q) \to 2 S O {_{3}}^{2 -} (a q) + C u (s) + 4 N H_{3} (a q) + 4 H^{+} (a q) + 4 O H^{-} (a q)$

On RHS, $4$ hydrogen ions combine with $4$ hydroxide ions to form $4$ water molecules out of which $2$ water molecules cancel with $2$ water molecules on LHS.

$C u (N H_{3}) {_{4}}^{2 +} (a q) + S_{2} O {_{4}}^{2 -} (a q) + 4 O H^{-} (a q) \to 2 S O {_{3}}^{2 -} (a q) + C u (s) + 4 N H_{3} (a q) + 2 H_{2} O (a q)$

This is the balanced chemical equation in basic medium.

The coefficients $x, y$ and $z$ are $4, 2$ and $4$ respectively.

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If the balanced reaction is as given below, find the value of $x, y$ and $z$ .

$C u (N H_{3}) {_{4}}^{2 +} (a q) + S_{2} O {_{4}}^{2 -} (a q) + x O H^{-} \to y S O {_{3}}^{2 -} (a q) + C u (s)$ $+ z N H_{3} (a q) + 2 H_{2} O$