In the reactions,
`S+ 3/2 O_2 to SO_3 + 2x kJ and
SO_2 + 1/2 O_2 to SO_3` + y kJ
Heat of formation of `SO_2`is _________.

Options

A. `(y - 2x)`
B. `(2x + y)`
C. `(x + y)`
D. `(2x//y)`

Answer

To find the heat of formation of SO₂, we need to analyze the given reactions and manipulate them appropriately.

### Step-by-Step Solution:

1. **Identify the Given Reactions**:
- Reaction 1: \( S + \frac{3}{2} O_2 \rightarrow SO_3 + 2x \, \text{kJ} \)
- Reaction 2: \( SO_2 + \frac{1}{2} O_2 \rightarrow SO_3 + y \, \text{kJ} \)

2. **Rearranging the Second Reaction**:
- We can rearrange Reaction 2 to express it in terms of the formation of SO₂:
\[ SO_2 + \frac{1}{2} O_2 \rightarrow SO_3 \implies SO_3 \leftarrow SO_2 + \frac{1}{2} O_2 + y \, \text{kJ} \]
This means that the reverse reaction would release \( y \, \text{kJ} \) when forming \( SO_2 \).

3. **Subtracting the Reactions**:
- Now, we can subtract Reaction 2 from Reaction 1:
\[ (S + \frac{3}{2} O_2 \rightarrow SO_3 + 2x) - (SO_2 + \frac{1}{2} O_2 \rightarrow SO_3 + y) \]
- The \( SO_3 \) on both sides cancels out:
\[ S + \frac{3}{2} O_2 - SO_2 - \frac{1}{2} O_2 \rightarrow 2x - y \]
- This simplifies to:
\[ S + O_2 \rightarrow SO_2 + (2x - y) \, \text{kJ} \]

4. **Heat of Formation of SO₂**:
- The heat of formation of \( SO_2 \) from its elements (S and O₂) is given by the energy change in the reaction:
\[ \text{Heat of formation of } SO_2 = 2x - y \, \text{kJ} \]

### Final Answer:
The heat of formation of \( SO_2 \) is \( 2x - y \, \text{kJ} \).

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