Question

The relationship between \(\Delta H\) and \(\Delta U\) for the reaction, \(\text{PCl}_{3}(g)+\text{Cl}_{2}(g)\rightarrow \text{PCl}_{5}(g)\) is given as

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

Hint:

Count the change in gaseous moles and use delta H = delta U + delta n RT.

Answer 1

The Correct Option is D

Step 1: Understanding the Concept
For gaseous reactions, \(\Delta H=\Delta U+\Delta n_g RT\).

Step 2: Find the Change in Moles
Reactants: \(\text{PCl}_3\) and \(\text{Cl}_2\), 2 mol of gas. Product: \(\text{PCl}_5\), 1 mol of gas. So \(\Delta n_g=1-2=-1\).

Step 3: Substitute
\(\Delta H=\Delta U+(-1)RT=\Delta U-RT\).

Final Answer:
The relation is \(\Delta H=\Delta U-RT\). \[ \boxed{\text{(D) }\Delta H=\Delta U-RT} \]