Question

Relation between \( \Delta H \) and \( \Delta U \) for the reaction \[ \text{2SO}_3 (g) \rightarrow \text{2SO}_2 (g) + \text{O}_2 (g) \] is

• A. \( \Delta H - \Delta U = 2RT \)
• B. \( \Delta H - \Delta U = RT \)
• C. \( \Delta H + \Delta U = -RT \)
• D. \( \Delta H + \Delta U = RT \)

Hint:

For reactions where the number of moles of gas changes, the relation between \( \Delta H \) and \( \Delta U \) depends on the temperature and the change in moles of gas.

Answer 1

The Correct Option is B

Step 1: Understanding the reaction and relationship between \( \Delta H \) and \( \Delta U \).
For the given reaction, the change in enthalpy \( \Delta H \) and the change in internal energy \( \Delta U \) are related by the equation: \[ \Delta H - \Delta U = nRT \] Where \( n \) is the number of moles of gas formed, \( R \) is the universal gas constant, and \( T \) is the temperature. For this reaction, the net change in the number of moles of gas is 1 (from 2 moles of \( \text{SO}_3 \) to 3 moles of gas), so: \[ \Delta H - \Delta U = RT \] Step 2: Conclusion.
The correct answer is (B) \( \Delta H - \Delta U = RT \).