Using the following thermochemical equations :
`S("rhombic") + 3/2 O_(2)(g) rarr SO_(3)(g), " "Delta H = - 2x kJ mol^(-1)`
II. `SO_(2)(g) + 1/2 O_(2)(g) rarr SO_(3)(g), " "Delta H = -Y kJ mol^(-1)`
Find out the heat of formation of `SO_(2)(g)` in `kJ mol^(-1)`.

Options

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

Explanation

To find the heat of formation of SO₂(g) using the given thermochemical equations, we can follow these steps:

### Step 1: Write the formation reaction for SO₂(g)
The heat of formation of SO₂(g) can be represented by the following reaction:
\[ \text{S (rhombic)} + \text{O}_2(g) \rightarrow \text{SO}_2(g) \]
This reaction represents the formation of one mole of SO₂ from its elements in their standard states.

### Step 2: Analyze the given thermochemical equations
We have two thermochemical equations:
1. \( \text{S (rhombic)} + \frac{3}{2} \text{O}_2(g) \rightarrow \text{SO}_3(g), \quad \Delta H = -2x \, \text{kJ mol}^{-1} \)
2. \( \text{SO}_2(g) + \frac{1}{2} \text{O}_2(g) \rightarrow \text{SO}_3(g), \quad \Delta H = -y \, \text{kJ mol}^{-1} \)

### Step 3: Rearranging the second equation
To find the heat of formation of SO₂, we need to manipulate the second equation. We can reverse it to express SO₂ in terms of SO₃:
\[ \text{SO}_3(g) \rightarrow \text{SO}_2(g) + \frac{1}{2} \text{O}_2(g) \]
When we reverse a reaction, the sign of ΔH changes:
\[ \Delta H = +y \, \text{kJ mol}^{-1} \]

### Step 4: Combine the equations
Now we will combine the first equation with the reversed second equation:
1. \( \text{S (rhombic)} + \frac{3}{2} \text{O}_2(g) \rightarrow \text{SO}_3(g), \quad \Delta H = -2x \)
2. \( \text{SO}_3(g) \rightarrow \text{SO}_2(g) + \frac{1}{2} \text{O}_2(g), \quad \Delta H = +y \)

Adding these two reactions:
\[ \text{S (rhombic)} + \frac{3}{2} \text{O}_2(g) + \text{SO}_3(g) \rightarrow \text{SO}_3(g) + \text{SO}_2(g) + \frac{1}{2} \text{O}_2(g) \]
The SO₃(g) cancels out, giving:
\[ \text{S (rhombic)} + \text{O}_2(g) \rightarrow \text{SO}_2(g) \]

### Step 5: Calculate the overall ΔH
The overall change in enthalpy (ΔH) for the formation of SO₂(g) is:
\[ \Delta H = -2x + y \]

### Conclusion
Thus, the heat of formation of SO₂(g) is:
\[ \Delta H = y - 2x \, \text{kJ mol}^{-1} \]