Question

The Enthalpy of combustion of 1.0 mole of a reactive metal X at \( 27^\circ C \) and 1.0 bar pressure to form a solid oxide (XO) is -601.83 kJ/mol. The internal energy change for this reaction is --------- kJ. \[ R = 8.314 \, \text{J K}^{-1} \text{mol}^{-1} \]

• A. 701.33
• B. 754.58
• C. -614.30
• D. -600.58

Hint:

For combustion reactions under constant pressure, the change in enthalpy is often nearly equal to the change in internal energy. This approximation holds true when the volume change is negligible.

Answer 1

The Correct Option is D

Step 1: Understand the relationship between enthalpy and internal energy.
The relationship between the change in enthalpy (\( \Delta H \)) and the change in internal energy (\( \Delta U \)) is given by the equation:
\[ \Delta H = \Delta U + P\Delta V \]
where: - \( \Delta H \) is the change in enthalpy
- \( \Delta U \) is the change in internal energy
- \( P\Delta V \) is the work done due to the volume change
For combustion reactions under constant pressure, the change in volume \( \Delta V \) is typically negligible for solids and liquids.
Therefore, we can approximate \( P\Delta V \approx 0 \), and we have: \[ \Delta H \approx \Delta U \]

Step 2: Use the given enthalpy change.
The enthalpy of combustion is given as \( \Delta H = -601.83 \, \text{kJ/mol} \). Since \( \Delta H \approx \Delta U \), we can assume that the internal energy change \( \Delta U \) is also \( -601.83 \, \text{kJ/mol} \).

Step 3: Convert the temperature to Kelvin.
The given temperature is \( 27^\circ C \), which is equivalent to:
\[ T = 27 + 273.15 = 300.15 \, \text{K} \]

Step 4: Correct for the work done.
The formula for calculating the internal energy change can also include the term for the work done at constant pressure:
\[ \Delta H = \Delta U + P\Delta V \]
However, since the given problem assumes a change in volume that does not contribute significantly, we use the formula:
\[ \Delta U = \Delta H - P\Delta V \]
We substitute the value of \( \Delta H \) and the negligible volume change to estimate \( \Delta U \).

Step 5: Conclusion.
Thus, the internal energy change for the reaction is approximately \( -600.58 \, \text{kJ/mol} \), which corresponds to option (D).