The number of electrons to balance the equation
`NO_(3)^(-)+4H^(+)+e^(-)to2H_(2)O+NO`

Options

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

Answer

To balance the given redox reaction, we need to determine the number of electrons required. Let's break down the steps to find the solution.

### Step 1: Write the unbalanced equation
The unbalanced equation is:
\[ \text{NO}_3^{-} + 4\text{H}^{+} + e^{-} \rightarrow 2\text{H}_2\text{O} + \text{NO} \]

### Step 2: Determine the charges on both sides
- On the left side:
- The charge from \(\text{NO}_3^{-}\) is -1.
- The charge from \(4\text{H}^{+}\) is +4.
- Let \(X\) be the number of electrons (each electron has a charge of -1).

Therefore, the total charge on the left side is:
\[ -1 + 4 + X = 3 + X \]

- On the right side:
- Both \(\text{H}_2\text{O}\) and \(\text{NO}\) are neutral species, so the total charge is 0.

### Step 3: Set the charges equal to balance
To balance the charges, we set the total charge on the left side equal to the total charge on the right side:
\[ 3 + X = 0 \]

### Step 4: Solve for X
Now, we can solve for \(X\):
\[ X = 0 - 3 \]
\[ X = -3 \]

### Step 5: Determine the number of electrons
Since \(X\) represents the number of electrons and each electron has a charge of -1, we need 3 electrons to balance the equation.

### Final Answer
The number of electrons required to balance the equation is:
\[ \text{3 electrons} \]

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