In the redox reaction, `x KMnO_(4) + NH_(3) rarr y KNO_(3) + MnO_(2) + MnO_(2) + KOH + H_(2)O`, x and y are

Options

A. `x = 4, y = 6`
B. `x = 3, y = 8`
C. `x = 8, y = 6`
D. `x = 8, y = 3`

Explanation

To solve the redox reaction \( x \text{KMnO}_4 + \text{NH}_3 \rightarrow y \text{KNO}_3 + \text{MnO}_2 + \text{KOH} + \text{H}_2\text{O} \) and find the values of \( x \) and \( y \), we will follow these steps:

### Step 1: Identify Oxidation States
- In \( \text{KMnO}_4 \), manganese (Mn) has an oxidation state of +7.
- In \( \text{MnO}_2 \), manganese has an oxidation state of +4.
- In \( \text{NH}_3 \), nitrogen (N) has an oxidation state of -3.
- In \( \text{KNO}_3 \), nitrogen has an oxidation state of +5.

### Step 2: Determine Changes in Oxidation States
- For manganese: The change in oxidation state from +7 to +4 is a reduction of 3.
- For nitrogen: The change in oxidation state from -3 to +5 is an oxidation of 8.

### Step 3: Set Up the Stoichiometric Coefficients
To balance the changes in oxidation states, we can use the method of cross-multiplication:
- Let \( x \) be the coefficient for \( \text{KMnO}_4 \) and \( y \) be the coefficient for \( \text{KNO}_3 \).
- The ratio of the changes in oxidation states gives us:
\[ \frac{x}{y} = \frac{8}{3} \]
- This implies:
\[ 8 \text{KMnO}_4 + 3 \text{NH}_3 \rightarrow 8 \text{KNO}_3 + \text{MnO}_2 + \text{KOH} + \text{H}_2\text{O} \]

### Step 4: Balance the Reaction
Now we will balance the entire reaction:
- For potassium (K), we have 8 from \( \text{KMnO}_4 \) and need 8 in the products.
- For nitrogen (N), we have 3 from \( \text{NH}_3 \) and need 3 in \( \text{KNO}_3 \).
- For oxygen (O), we will balance the remaining oxygen atoms from \( \text{H}_2\text{O} \).

### Step 5: Write the Final Balanced Equation
After balancing all components, we arrive at the balanced equation:
\[ 8 \text{KMnO}_4 + 3 \text{NH}_3 \rightarrow 3 \text{KNO}_3 + 4 \text{MnO}_2 + 5 \text{KOH} + 4 \text{H}_2\text{O} \]

### Step 6: Identify Values of \( x \) and \( y \)
From the balanced equation:
- \( x = 8 \)
- \( y = 3 \)

### Final Answer
Thus, the values of \( x \) and \( y \) are:
- \( x = 8 \)
- \( y = 3 \)

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