Consider the reactions
`(i)" " S("rhombic") + 3//2O_(2)(g) rarr SO_(3)(g),DeltaH_(1)`
`(ii) " "S("monoclinic") + 3//2O_(2)(g) rarr SO_(3)(g),DeltaH_(2)`
`(iii) " "S("rhombic") + O_(3)(g) rarr SO_(3)(g),DeltaH_(3)`
`(iv) " "S("monoclinic") + O_(3)(g) rarr SO_(3)(g),DeltaH_(4)`

Options

A. `DeltaH_(1) lt DeltaH_(2) lt DeltaH_(4)` (magnitude only)
B. `DeltaH_(1) lt DeltaH_(3) lt DeltaH_(4)` (magnitude only)
C. `DeltaH_(1) lt DeltaH_(2) = DeltaH_(3) lt DeltaH_(4)` (magnitude only )
D. `DeltaH_(1) + DeltaH_(4) = DeltaH_(2) + DeltaH_(3)`

Answer

To solve the problem, we need to analyze the four reactions given and their corresponding enthalpy changes (ΔH). The key points to consider are the stability of the reactants and the products formed in each reaction.

### Step-by-Step Solution:

1. **Identify the Stability of Sulfur Forms**:
- Rhombic sulfur is thermodynamically more stable than monoclinic sulfur. This means that rhombic sulfur has lower energy compared to monoclinic sulfur.

2. **Analyze Reactions (i) and (ii)**:
- Reaction (i): Rhombic sulfur + \( \frac{3}{2} O_2(g) \) → \( SO_3(g) \) with ΔH₁
- Reaction (ii): Monoclinic sulfur + \( \frac{3}{2} O_2(g) \) → \( SO_3(g) \) with ΔH₂
- Since rhombic sulfur is more stable, it will have a lower enthalpy (ΔH₁) compared to monoclinic sulfur (ΔH₂). Thus, we can conclude:
\[ ΔH₂ > ΔH₁ \]

3. **Analyze Reactions (iii) and (iv)**:
- Reaction (iii): Rhombic sulfur + \( O_3(g) \) → \( SO_3(g) \) with ΔH₃
- Reaction (iv): Monoclinic sulfur + \( O_3(g) \) → \( SO_3(g) \) with ΔH₄
- Ozone (O₃) is less stable than dioxygen (O₂). Therefore, the reaction involving monoclinic sulfur will have a higher enthalpy change due to the less stable reactant. Thus, we can conclude:
\[ ΔH₄ > ΔH₃ \]

4. **Comparing the Magnitudes of ΔH**:
- From the previous steps, we have established:
- \( ΔH₂ > ΔH₁ \)
- \( ΔH₄ > ΔH₃ \)
- Since both reactions (i) and (ii) produce the same product (SO₃) and both reactions (iii) and (iv) produce the same product (SO₃), we can compare the magnitudes of the enthalpy changes:
- The enthalpy changes for reactions (i) and (ii) are related, and the same goes for reactions (iii) and (iv).

5. **Final Conclusion**:
- The correct relationships based on stability and enthalpy changes are:
\[ ΔH₂ > ΔH₁ \quad \text{and} \quad ΔH₄ > ΔH₃ \]
- Therefore, the correct option is that ΔH₂ is greater than ΔH₁ and ΔH₄ is greater than ΔH₃.