In the reaction `: S + (3)/(2)O_(2)rarr SO_(3) + 2 x kJ ` and `SO_(2)+(1)/(2)O_(2) rarr SO_(3)+y kJ ` heat of formation of `SO_(2)` is

Options

A. `x-y`
B. `2x+y`
C. `x+y`
D. `y-2x`

Explanation

To find the heat of formation of SO₂, we will use Hess's Law, which states that the total enthalpy change for a reaction is the sum of the enthalpy changes for the individual steps of the reaction.

### Step-by-Step Solution:

1. **Identify the Reactions**:
We have two reactions given:
- Reaction 1: \( S + \frac{3}{2} O_2 \rightarrow SO_3 \) with an enthalpy change of \( +2x \) kJ.
- Reaction 2: \( SO_2 + \frac{1}{2} O_2 \rightarrow SO_3 \) with an enthalpy change of \( +y \) kJ.

2. **Write the Target Reaction**:
We want to find the heat of formation of \( SO_2 \) from its elements:
\[ S + O_2 \rightarrow SO_2 \]

3. **Manipulate the Given Reactions**:
To derive the target reaction from the given reactions, we will subtract Reaction 2 from Reaction 1:
- From Reaction 1, we have:
\[ S + \frac{3}{2} O_2 \rightarrow SO_3 \quad (2x) \]
- From Reaction 2, we have:
\[ SO_2 + \frac{1}{2} O_2 \rightarrow SO_3 \quad (y) \]

4. **Subtract Reaction 2 from Reaction 1**:
When we subtract Reaction 2 from Reaction 1, we get:
\[ (S + \frac{3}{2} O_2) - (SO_2 + \frac{1}{2} O_2) \rightarrow SO_3 - SO_3 \]
This simplifies to:
\[ S + O_2 \rightarrow SO_2 \]

5. **Calculate the Enthalpy Change**:
The enthalpy change for the new reaction can be calculated as follows:
\[ \Delta H = (2x) - (y) = 2x - y \]

6. **Conclusion**:
The heat of formation of \( SO_2 \) is given by:
\[ \Delta H_{f} (SO_2) = 2x - y \text{ kJ} \]