`Pb(NO_3)_2 + Fe_2(SO_4)_3 to Fe(NO_3)_3+ PbSO_4 `
Coefficients of lead sulphate and ferric nitrate in the balanced equation of the above reaction are

Options

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

Explanation

To balance the chemical equation \( \text{Pb(NO}_3\text{)}_2 + \text{Fe}_2(\text{SO}_4)_3 \rightarrow \text{Fe(NO}_3\text{)}_3 + \text{PbSO}_4 \), we will follow these steps:

### Step 1: Write the unbalanced equation
The unbalanced equation is:
\[ \text{Pb(NO}_3\text{)}_2 + \text{Fe}_2(\text{SO}_4)_3 \rightarrow \text{Fe(NO}_3\text{)}_3 + \text{PbSO}_4 \]

### Step 2: Count the number of each type of atom on both sides
- **Left side:**
- Pb: 1
- N: 2
- O: 6 (from \( \text{NO}_3 \)) + 12 (from \( \text{SO}_4 \)) = 18
- Fe: 2
- S: 3

- **Right side:**
- Pb: 1
- N: 3
- O: 3 (from \( \text{NO}_3 \)) + 4 (from \( \text{SO}_4 \)) = 7
- Fe: 1
- S: 1

### Step 3: Balance the iron (Fe) atoms
To balance the iron atoms, we need 2 iron atoms on the right side. We can do this by placing a coefficient of 2 in front of \( \text{Fe(NO}_3\text{)}_3 \):
\[ \text{Pb(NO}_3\text{)}_2 + \text{Fe}_2(\text{SO}_4)_3 \rightarrow 2\text{Fe(NO}_3\text{)}_3 + \text{PbSO}_4 \]

### Step 4: Recount the atoms
- **Left side:**
- Pb: 1
- N: 2
- O: 18
- Fe: 2
- S: 3

- **Right side:**
- Pb: 1
- N: 6 (from \( 2 \times \text{Fe(NO}_3\text{)}_3 \))
- O: 6 (from \( 2 \times \text{NO}_3 \)) + 4 (from \( \text{SO}_4 \)) = 10
- Fe: 2
- S: 1

### Step 5: Balance the lead (Pb) and sulfate (SO₄) groups
Since we have 1 lead on both sides, we can balance the sulfate by placing a coefficient of 3 in front of \( \text{PbSO}_4 \):
\[ \text{Pb(NO}_3\text{)}_2 + \text{Fe}_2(\text{SO}_4)_3 \rightarrow 2\text{Fe(NO}_3\text{)}_3 + 3\text{PbSO}_4 \]

### Step 6: Final recount of atoms
- **Left side:**
- Pb: 3
- N: 2
- O: 18
- Fe: 2
- S: 3

- **Right side:**
- Pb: 3
- N: 6
- O: 18 (6 from \( 2 \times \text{NO}_3 \) + 12 from \( 3 \times \text{SO}_4 \))
- Fe: 2
- S: 3

### Step 7: Adjust the coefficients for nitrate
To balance the nitrogen, we need to adjust the coefficient in front of \( \text{Pb(NO}_3\text{)}_2 \) to 3:
\[ 3\text{Pb(NO}_3\text{)}_2 + \text{Fe}_2(\text{SO}_4)_3 \rightarrow 2\text{Fe(NO}_3\text{)}_3 + 3\text{PbSO}_4 \]

### Final Balanced Equation
The final balanced equation is:
\[ 3\text{Pb(NO}_3\text{)}_2 + \text{Fe}_2(\text{SO}_4)_3 \rightarrow 2\text{Fe(NO}_3\text{)}_3 + 3\text{PbSO}_4 \]

### Coefficients of Lead Sulfate and Ferric Nitrate
From the balanced equation:
- Coefficient of Lead Sulfate (\( \text{PbSO}_4 \)) = 3
- Coefficient of Ferric Nitrate (\( \text{Fe(NO}_3\text{)}_3 \)) = 2