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 standard heats of formation for the reactants and products.

### 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 Heats of Formation**:
The heat of formation (\( \Delta H_f \)) values given are:
- For \( \text{SO}_2 \): \( \Delta H_f = -298.2 \, \text{kJ/mol} \)
- For \( \text{SO}_3 \): \( \Delta H_f = -98.2 \, \text{kJ/mol} \)

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

4. **Calculate the Heat of Reaction**:
- For the products, we have:
\[ \Delta H_f \, (\text{SO}_3) = -98.2 \, \text{kJ/mol} \]
- For the reactants, we have:
\[ \Delta H_f \, (\text{SO}_2) + \Delta H_f \, \left(\frac{1}{2} \text{O}_2\right) = -298.2 \, \text{kJ/mol} + 0 \, \text{kJ/mol} \quad (\text{since } O_2 \text{ is in its elemental form}) \]

Therefore, the heat of reaction calculation becomes:
\[ \Delta H_{reaction} = \left(-98.2 \, \text{kJ/mol}\right) - \left(-298.2 \, \text{kJ/mol}\right) \]
Simplifying this gives:
\[ \Delta H_{reaction} = -98.2 + 298.2 = 200 \, \text{kJ/mol} \]

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