Balance the following chemical equation:
`Pb(NO_(3))_(2(s))overset("Heat")(to)PbO_((s))+NO_(2(g))+O_(2(g))`

Options

A. `Pb(NO_(3))_(2(s))toPbO_((s))+2NO_(2(g))+1/2O_(2(g))`
B. `Pb(NO_(3))_(2)to2PBo_((s))+NO_(2(g))+2O_(2(g))`
C. `2Pb(NO_(3))_(2)to5PbO_((s))+3NO_(2(g))+5O_(2(g))`
D. `Pb(NO_(3))_(2)to2PbO_((s))+NO_(2(g))+O_(2(g))`

Explanation

To balance the chemical equation \( \text{Pb(NO}_3)_2(s) \overset{\text{Heat}}{\rightarrow} \text{PbO}(s) + \text{NO}_2(g) + \text{O}_2(g) \), we will follow these steps:

### Step 1: Write the unbalanced equation
The unbalanced equation is:
\[ \text{Pb(NO}_3)_2(s) \rightarrow \text{PbO}(s) + \text{NO}_2(g) + \text{O}_2(g) \]

### Step 2: Count the number of atoms of each element on both sides
- **Reactants**:
- Lead (Pb): 1
- Nitrogen (N): 2 (from 2 NO3)
- Oxygen (O): 6 (from 2 NO3)

- **Products**:
- Lead (Pb): 1 (from PbO)
- Nitrogen (N): 1 (from NO2)
- Oxygen (O): 1 (from PbO) + 2 (from 2 NO2) + 2 (from O2) = 5

### Step 3: Balance the nitrogen atoms
Since there are 2 nitrogen atoms in the reactants and only 1 in the products, we need to place a coefficient of 2 in front of NO2:
\[ \text{Pb(NO}_3)_2(s) \rightarrow \text{PbO}(s) + 2 \text{NO}_2(g) + \text{O}_2(g) \]

### Step 4: Recount the atoms after balancing nitrogen
- **Reactants**:
- Pb: 1
- N: 2
- O: 6

- **Products**:
- Pb: 1
- N: 2 (from 2 NO2)
- O: 1 (from PbO) + 4 (from 2 NO2) + 2 (from O2) = 7

### Step 5: Balance the oxygen atoms
Now we have 6 oxygen atoms in the reactants and 7 in the products. To balance the oxygen, we can adjust the O2. We need 1 more oxygen atom in the products, so we can place a coefficient of \( \frac{1}{2} \) in front of O2:
\[ \text{Pb(NO}_3)_2(s) \rightarrow \text{PbO}(s) + 2 \text{NO}_2(g) + \frac{1}{2} \text{O}_2(g) \]

### Step 6: Final check for balance
- **Reactants**:
- Pb: 1
- N: 2
- O: 6

- **Products**:
- Pb: 1
- N: 2
- O: 1 (from PbO) + 4 (from 2 NO2) + 1 (from \( \frac{1}{2} \) O2) = 6

Now, all elements are balanced.

### Final Balanced Equation
\[ \text{Pb(NO}_3)_2(s) \rightarrow \text{PbO}(s) + 2 \text{NO}_2(g) + \frac{1}{2} \text{O}_2(g) \]