The number of electrons required to balance the following equation are :
`NO_(3)^(-)+4H^(+)rarr2H_(2)O+NO`

Options

A. 5
B. 4
C. 3
D. 2

Answer

To determine the number of electrons required to balance the given redox reaction:

**Reaction:**
\[ \text{NO}_3^{-} + 4\text{H}^{+} \rightarrow 2\text{H}_2\text{O} + \text{NO} \]

### Step-by-Step Solution:

1. **Identify the Charges on Both Sides:**
- On the **reactant side**:
- Charge from \(\text{NO}_3^{-}\) is \(-1\).
- Charge from \(4\text{H}^{+}\) is \(4 \times (+1) = +4\).
- Total charge on the reactant side:
\[ -1 + 4 = +3 \]

- On the **product side**:
- \(\text{H}_2\text{O}\) is neutral (0 charge).
- \(\text{NO}\) is also neutral (0 charge).
- Total charge on the product side:
\[ 0 + 0 = 0 \]

2. **Calculate the Difference in Charge:**
- The total charge on the reactant side is \(+3\) and on the product side is \(0\).
- To balance the charges, we need to add electrons to the reactant side.

3. **Determine the Number of Electrons Needed:**
- Each electron has a charge of \(-1\).
- To balance the \(+3\) charge on the reactant side, we need \(3\) electrons:
\[ +3 + (-3) = 0 \]

4. **Rewrite the Balanced Equation:**
- Including the electrons, the balanced equation becomes:
\[ \text{NO}_3^{-} + 4\text{H}^{+} + 3\text{e}^{-} \rightarrow 2\text{H}_2\text{O} + \text{NO} \]

### Conclusion:
The number of electrons required to balance the equation is **3**.