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 will follow these steps:

### Step 1: Write down the given thermochemical equations
1. \( S(\text{rhombic}) + \frac{3}{2} O_2(g) \rightarrow SO_3(g), \quad \Delta H_1 = -2x \, \text{kJ mol}^{-1} \)
2. \( SO_2(g) + \frac{1}{2} O_2(g) \rightarrow SO_3(g), \quad \Delta H_2 = -y \, \text{kJ mol}^{-1} \)

### Step 2: Identify the target reaction for the formation of SO₂
The heat of formation of SO₂(g) can be represented by the following reaction:
\[ S(\text{rhombic}) + \frac{1}{2} O_2(g) \rightarrow SO_2(g) \]

### Step 3: Manipulate the given equations
To derive the target reaction from the given equations, we will subtract the second equation from the first equation.

1. **First equation**:
\[ S(\text{rhombic}) + \frac{3}{2} O_2(g) \rightarrow SO_3(g) \]
\[ \Delta H_1 = -2x \]

2. **Second equation (reversed)**:
\[ SO_3(g) \rightarrow SO_2(g) + \frac{1}{2} O_2(g) \]
\[ \Delta H_2 = +y \] (since we reversed the reaction, the sign of ΔH changes)

### Step 4: Combine the reactions
Now, we can combine the two reactions:
- From the first equation, we have \( S + \frac{3}{2} O_2 \rightarrow SO_3 \)
- From the reversed second equation, we have \( SO_3 \rightarrow SO_2 + \frac{1}{2} O_2 \)

Combining these gives:
\[ S + \frac{3}{2} O_2 - SO_3 + SO_3 \rightarrow SO_2 + \frac{1}{2} O_2 \]
This simplifies to:
\[ S + 1 O_2 \rightarrow SO_2 \]

### Step 5: Calculate the overall ΔH
The overall change in enthalpy for the formation of SO₂(g) is given by:
\[ \Delta H = \Delta H_1 - \Delta H_2 \]
Substituting the values:
\[ \Delta H = (-2x) - (-y) \]
\[ \Delta H = -2x + y \]

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