Question

What is the value of ΔH – ΔU for the following reaction? 2C(s) + 3H₂(g) → C₂H₆(g)

• A. 4RT
• B. -5RT
• C. RT
• D. -2RT

Hint:

Key Exam Tip:
The equation $\Delta H = \Delta U + RT \Delta n$ is essential for relating enthalpy and internal energy changes in reactions involving gases, where $\Delta n$ is the change in moles of gas.

Answer 1

The Correct Option is D

The relationship between enthalpy change ($\Delta H$) and internal energy change ($\Delta U$) at constant pressure and temperature is given by:
$\Delta H = \Delta U + P\Delta V$
For reactions involving gases, assuming ideal gas behavior, $P\Delta V = \Delta(PV) = \Delta(nRT)$. If the temperature ($T$) is constant, this simplifies to $RT\Delta n$, where $\Delta n$ is the change in the number of moles of gas.
So, $\Delta H = \Delta U + RT \Delta n$.
The given reaction is:
$2\text{C(s)} + 3\text{H}_2\text{(g)} \rightarrow \text{C}_2\text{H}_6\text{(g)}$
We need to find $\Delta n$, the change in the number of moles of gas.
Moles of gaseous products = 1 (for $\text{C}_2\text{H}_6$)
Moles of gaseous reactants = 3 (for $\text{H}_2$)
(Solid carbon does not contribute to the change in moles of gas).
$\Delta n = n_{products(gas)} - n_{reactants(gas)} = 1 - 3 = -2$.
Substituting this value into the equation:
$\Delta H = \Delta U + RT(-2)$
$\Delta H = \Delta U - 2RT$
We are asked to find the value of $\Delta H - \Delta U$. Rearranging the equation:
$\Delta H - \Delta U = -2RT$.
Final Answer: \(\boxed{D}\)