Given : `S_((s))+(3)/(2)O_(2(g))rarrSO_(3(g)+2X Kcal`
`SO_(2(s))+(1)/(2)O_(2(g))rarrSO_(3(g)+Y Kcal`
The heat of formation of `SO_(2)` is `:-`

Options

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

Explanation

To find the heat of formation of SO₂, we can use the provided reactions and manipulate them accordingly. Let's break down the steps:

### Step 1: Write down the given reactions
1. \( S_{(s)} + \frac{3}{2} O_{2(g)} \rightarrow SO_{3(g)} + 2X \, \text{Kcal} \) (Equation 1)
2. \( SO_{2(s)} + \frac{1}{2} O_{2(g)} \rightarrow SO_{3(g)} + Y \, \text{Kcal} \) (Equation 2)

### Step 2: Rearrange the second reaction
We can rearrange Equation 2 to express it in terms of the formation of SO₂:
\[ SO_{3(g)} \rightarrow SO_{2(s)} + \frac{1}{2} O_{2(g)} + Y \, \text{Kcal} \]
This means that the reverse of Equation 2 releases \( Y \) Kcal of heat.

### Step 3: Combine the reactions
Now, we can combine the two reactions. We will subtract Equation 2 from Equation 1:
\[ \left( S_{(s)} + \frac{3}{2} O_{2(g)} \rightarrow SO_{3(g)} + 2X \right) - \left( SO_{3(g)} \rightarrow SO_{2(s)} + \frac{1}{2} O_{2(g)} + Y \right) \]

### Step 4: Cancel out common terms
When we combine these reactions, the \( SO_{3(g)} \) on both sides cancels out:
\[ S_{(s)} + \frac{3}{2} O_{2(g)} - \left( SO_{2(s)} + \frac{1}{2} O_{2(g)} \right) \rightarrow 2X - Y \]

### Step 5: Simplify the equation
This simplifies to:
\[ S_{(s)} + O_{2(g)} \rightarrow SO_{2(s)} + (2X - Y) \, \text{Kcal} \]

### Step 6: Identify the heat of formation of SO₂
The heat of formation of SO₂ is the amount of heat released when 1 mole of SO₂ is formed from its elements in their standard states. From our equation, the heat of formation of SO₂ is:
\[ \Delta H_f(SO_2) = 2X - Y \]

### Conclusion
Thus, the heat of formation of SO₂ is \( 2X - Y \) Kcal.

---