Calculate the heat of reaction for the following reaction `SO_2+1/2O_2rarrSO_3`. Given the value of heat of formation of `SO_2 and SO_3` are –298.2 kJ and – 98.2 kJ .

Options

A. `-200 kJ`
B. `-356.2 kJ`
C. `+200 kJ`
D. `-396.2 kJ`

Answer

To calculate the heat of reaction for the given reaction \( \text{SO}_2 + \frac{1}{2} \text{O}_2 \rightarrow \text{SO}_3 \), we will use the heat of formation values provided for \( \text{SO}_2 \) and \( \text{SO}_3 \).

### Step-by-Step Solution:

1. **Identify the Reaction**:
The reaction we are considering is:
\[ \text{SO}_2 + \frac{1}{2} \text{O}_2 \rightarrow \text{SO}_3 \]

2. **Write the Heat of Formation Values**:
- The heat of formation of \( \text{SO}_2 \) is \( \Delta H_f (\text{SO}_2) = -298.2 \, \text{kJ/mol} \)
- The heat of formation of \( \text{SO}_3 \) is \( \Delta H_f (\text{SO}_3) = -98.2 \, \text{kJ/mol} \)

3. **Use the Formula for Heat of Reaction**:
The heat of reaction (\( \Delta H_r \)) can be calculated using the formula:
\[ \Delta H_r = \Delta H_f (\text{products}) - \Delta H_f (\text{reactants}) \]

4. **Substitute the Values**:
Here, the product is \( \text{SO}_3 \) and the reactants are \( \text{SO}_2 \) and \( \frac{1}{2} \text{O}_2 \). Since \( \text{O}_2 \) is in its elemental form, its heat of formation is zero. Thus:
\[ \Delta H_r = \Delta H_f (\text{SO}_3) - [\Delta H_f (\text{SO}_2) + \Delta H_f \left(\frac{1}{2} \text{O}_2\right)] \]
\[ \Delta H_r = (-98.2 \, \text{kJ/mol}) - [(-298.2 \, \text{kJ/mol}) + 0] \]

5. **Calculate**:
\[ \Delta H_r = -98.2 \, \text{kJ/mol} + 298.2 \, \text{kJ/mol} \]
\[ \Delta H_r = 200 \, \text{kJ/mol} \]

6. **Final Answer**:
The heat of reaction for the given reaction is:
\[ \Delta H_r = +200 \, \text{kJ/mol} \]