Question

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

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

Hint:

For reactions involving gases, the relationship between \( \Delta H \) and \( \Delta U \) depends on the volume change and can include the term \( RT \).

Answer 1

The Correct Option is B

Step 1: Using the first law of thermodynamics.
In a reaction at constant pressure, the change in enthalpy (\( \Delta H \)) is related to the change in internal energy (\( \Delta U \)) by the formula: \[ \Delta H = \Delta U + P \Delta V \] For reactions involving gases, the relationship between \( \Delta H \) and \( \Delta U \) can be modified to include the ideal gas constant (\( R \)) and temperature (\( T \)).

Step 2: Analyzing the options.
(A) \( \Delta H = \Delta U - 2RT \): Incorrect — This is not the correct relationship.
(B) \( \Delta H = \Delta U - RT \): Correct — This is the correct relationship for the given reaction.
(C) \( \Delta H = \Delta U + 2RT \): Incorrect — This is not applicable for this reaction.
(D) \( \Delta H = \Delta U + RT \): Incorrect — This is not the correct relationship.

Step 3: Conclusion.
The correct answer is (B) \( \Delta H = \Delta U - RT \), as it describes the relation between enthalpy and internal energy for the reaction.