Question

For the reaction,
\[ C_2H_5OH(l) + 3O_2(g) \rightarrow 2CO_2(g) + 3H_2O(l) \] Which among the following is true?

• 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:

Only gaseous species are counted while calculating $\Delta n_{gas}$ in thermodynamic equations.

Answer 1

The Correct Option is C

Step 1: Write the relation between $\Delta H$ and $\Delta U$.
For reactions involving gases, the relation is:
\[ \Delta H = \Delta U + \Delta n_{gas}RT \]
Step 2: Calculate change in number of moles of gaseous species.
Moles of gaseous reactants $= 3$ (only $O_2$)
Moles of gaseous products $= 2$ (only $CO_2$)
\[ \Delta n_{gas} = 2 - 3 = -1 \]
Step 3: Substitute the value of $\Delta n_{gas$. \[ \Delta H = \Delta U + (-1)RT \]
\[ \Delta H = \Delta U - RT \]
Step 4: Conclusion.
The correct thermodynamic relation for the given reaction is $\Delta H = \Delta U - RT$.