The values of heat of formation of `SO_(2)` and `SO_(3)` are - 298.2 kJ and - 98.2 kJ. The heat of reaction of the following reaction will be `SO_(2)(g)+(1)/(2)O_(2)(g)to SO_(3)(g)`

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 \( SO_2(g) + \frac{1}{2}O_2(g) \rightarrow SO_3(g) \), we will use the heat of formation values provided for \( SO_2 \) and \( SO_3 \).

### Step-by-Step Solution:

1. **Identify the heat of formation values**:
- Heat of formation of \( SO_2 \) (ΔH_f°) = -298.2 kJ/mol
- Heat of formation of \( SO_3 \) (ΔH_f°) = -98.2 kJ/mol
- Heat of formation of \( O_2 \) (ΔH_f°) = 0 kJ/mol (since it's a standard state element)

2. **Write the formula for heat of reaction**:
The heat of reaction (ΔH_rxn) can be calculated using the formula:
\[ \Delta H_{rxn} = \Delta H_f^{\text{products}} - \Delta H_f^{\text{reactants}} \]

3. **Substitute the values into the formula**:
For the reaction \( SO_2(g) + \frac{1}{2}O_2(g) \rightarrow SO_3(g) \):
- Products: \( SO_3 \)
- Reactants: \( SO_2 \) and \( O_2 \)

Therefore, we can substitute the values:
\[ \Delta H_{rxn} = \Delta H_f^{SO_3} - \left( \Delta H_f^{SO_2} + \Delta H_f^{O_2} \right) \]
\[ \Delta H_{rxn} = (-98.2 \text{ kJ/mol}) - \left( -298.2 \text{ kJ/mol} + 0 \text{ kJ/mol} \right) \]

4. **Calculate the heat of reaction**:
\[ \Delta H_{rxn} = -98.2 \text{ kJ/mol} - (-298.2 \text{ kJ/mol}) \]
\[ \Delta H_{rxn} = -98.2 + 298.2 \]
\[ \Delta H_{rxn} = 200 \text{ kJ/mol} \]

5. **Final answer**:
The heat of reaction for the given reaction is \( 200 \text{ kJ} \).