What is the value of $x$ and $y$ in order to balance following redox reaction? $\mathrm{xCuO}+\mathrm{yNH}_3…

What is the value of $x$ and $y$ in order to balance following redox reaction? $\mathrm{xCuO}+\mathrm{yNH}_3 \longrightarrow \mathrm{xCu}+\mathrm{N}_2+\mathrm{xH}_2 \mathrm{O}$
  1. $\mathrm{x}=2, \mathrm{y}=1$
  2. $\mathrm{x}=1, \mathrm{y}=2$
  3. $x=2, y=3$
  4. $x=2, y=3$

Solution

Reaction: $x \mathrm{CuO}+y \mathrm{NH}_3 \rightarrow x \mathrm{Cu}+\mathrm{N}_2+x \mathrm{H}_2 \mathrm{O}$. Step 1: Assign oxidation states: - Cu in CuO: +2 , reduced to 0 in Cu . - N in $\mathrm{NH}_3:-3$, oxidized to 0 in $\mathrm{N}_2$.
Step 2: Write half-reactions: 1. Reduction: $\mathrm{Cu}^{2+}+2 e^{-} \rightarrow \mathrm{Cu}$, - $x \mathrm{CuO}$ contributes $2 x$ electrons. 2. Oxidation: $2 \mathrm{NH}_3 \rightarrow \mathrm{~N}_2+6 e^{-}$, - Each $y \mathrm{NH}_3$ contributes $3 y$ electrons.
Step 3: Equate total electrons: $2 x=3 y \quad \Rightarrow \quad x=\frac{3 y}{2} .$
Step 4: Trial values to balance: Let $x=2: y=3$. Balanced Equation: $2 \mathrm{CuO}+3 \mathrm{NH}_3 \rightarrow 2 \mathrm{Cu}+\mathrm{N}_2+3 \mathrm{H}_2 \mathrm{O}$
Answer: $x=2, y=3$, Option 3.

Asked in: MHT CET 2024 (09 May Shift 1)

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