Maximum number of moles of electrons taken up by one mole of `NO_(3)^(-)` when it is reduced to :

Options

A. `NH_3`
B. `NH_2OH`
C. `NO`
D. `NO_2`

Explanation

To determine the maximum number of moles of electrons taken up by one mole of \( \text{NO}_3^{-} \) when it is reduced to various compounds, we need to analyze the change in oxidation state of nitrogen in \( \text{NO}_3^{-} \) and the products given in the options. Here’s a step-by-step solution:

### Step 1: Determine the oxidation state of nitrogen in \( \text{NO}_3^{-} \)

1. **Set up the equation for oxidation state**:
Let the oxidation state of nitrogen be \( x \).
\[ x + 3(-2) = -1 \]
This accounts for the three oxygen atoms, each with an oxidation state of -2, and the overall charge of the ion is -1.

2. **Solve for \( x \)**:
\[ x - 6 = -1 \implies x = +5 \]
Thus, the oxidation state of nitrogen in \( \text{NO}_3^{-} \) is +5.

### Step 2: Analyze the reduction to each product

Now, we will analyze the oxidation state of nitrogen in each of the given products and calculate the change in oxidation state.

#### Option A: Reduction to \( \text{NH}_3 \)

1. **Oxidation state of nitrogen in \( \text{NH}_3 \)**:
\[ x + 3(+1) = 0 \implies x = -3 \]

2. **Change in oxidation state**:
\[ \Delta = -3 - (+5) = -8 \]
The change in oxidation state is 8.

#### Option B: Reduction to \( \text{NH}_2\text{OH} \)

1. **Oxidation state of nitrogen in \( \text{NH}_2\text{OH} \)**:
\[ x + 2(+1) - 2 + 1 = 0 \implies x = -1 \]

2. **Change in oxidation state**:
\[ \Delta = -1 - (+5) = -6 \]
The change in oxidation state is 6.

#### Option C: Reduction to \( \text{NO} \)

1. **Oxidation state of nitrogen in \( \text{NO} \)**:
\[ x + (-2) = 0 \implies x = +2 \]

2. **Change in oxidation state**:
\[ \Delta = +2 - (+5) = -3 \]
The change in oxidation state is 3.

#### Option D: Reduction to \( \text{NO}_2 \)

1. **Oxidation state of nitrogen in \( \text{NO}_2 \)**:
\[ x + 2(-2) = 0 \implies x = +4 \]

2. **Change in oxidation state**:
\[ \Delta = +4 - (+5) = -1 \]
The change in oxidation state is 1.

### Step 3: Conclusion

The maximum number of moles of electrons taken up by one mole of \( \text{NO}_3^{-} \) occurs when it is reduced to \( \text{NH}_3 \), which corresponds to a change of 8 moles of electrons.

**Final Answer**: The maximum number of moles of electrons taken up by one mole of \( \text{NO}_3^{-} \) when reduced to \( \text{NH}_3 \) is **8 moles**.

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