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 solve the problem, we need to calculate the heat of reaction (ΔH_R) for the following reaction:

\[ \text{SO}_2(g) + \frac{1}{2} \text{O}_2(g) \rightarrow \text{SO}_3(g) \]

### Step 1: Write down the heat of formation values
The heat of formation values given are:
- ΔH_f(SO₂) = -298.2 kJ/mol
- ΔH_f(SO₃) = -98.2 kJ/mol

### Step 2: Understand the concept of heat of reaction
The heat of reaction (ΔH_R) can be calculated using the formula:

\[ \Delta H_R = \Delta H_f(\text{products}) - \Delta H_f(\text{reactants}) \]

### Step 3: Identify the products and reactants
In our reaction:
- Products: SO₃
- Reactants: SO₂ and \(\frac{1}{2}\) O₂

### Step 4: Write the equation for ΔH_R
Using the heat of formation values, we can express ΔH_R as follows:

\[ \Delta H_R = \Delta H_f(\text{SO}_3) - \left[ \Delta H_f(\text{SO}_2) + \Delta H_f\left(\frac{1}{2} \text{O}_2\right) \right] \]

### Step 5: Substitute the values
Since the heat of formation of elemental oxygen (O₂) in its standard state is 0, we can simplify:

\[ \Delta H_R = \Delta H_f(\text{SO}_3) - \Delta H_f(\text{SO}_2) \]

Substituting the values:

\[ \Delta H_R = (-98.2 \text{ kJ/mol}) - (-298.2 \text{ kJ/mol}) \]

### Step 6: Calculate ΔH_R
Now, perform the calculation:

\[ \Delta H_R = -98.2 + 298.2 \]
\[ \Delta H_R = 200 \text{ kJ/mol} \]

### Conclusion
The heat of reaction for the given reaction is:

\[ \Delta H_R = +200 \text{ kJ/mol} \]