Under which of the following condition `Delta H = Delta E ?`

Options

A. When a process is carried out in a closed vessel
B. When reaction involves only solids and liquids
C. When `Delta n_(g) = 0`
D. All of these

Answer

To determine under which conditions \(\Delta H = \Delta E\), we can analyze the relationship between enthalpy change (\(\Delta H\)) and internal energy change (\(\Delta E\)). The relationship is given by the equation:

\[ \Delta H = \Delta E + P \Delta V \]

Where:
- \(\Delta H\) is the change in enthalpy.
- \(\Delta E\) is the change in internal energy.
- \(P\) is the pressure.
- \(\Delta V\) is the change in volume.

### Step-by-Step Solution:

1. **Understanding the Equation**:
- From the equation \(\Delta H = \Delta E + P \Delta V\), we can see that \(\Delta H\) will equal \(\Delta E\) when the term \(P \Delta V\) is zero.

2. **Condition for \(P \Delta V = 0\)**:
- The term \(P \Delta V\) is zero under two conditions:
- When the process occurs in a closed vessel (no volume change).
- When there are no gaseous reactants or products involved, meaning the reaction involves only solids and liquids.

3. **Analyzing the Given Conditions**:
- **Condition 1**: When a process is carried out in a closed vessel.
- In a closed vessel, there is no change in volume (\(\Delta V = 0\)), thus \(\Delta H = \Delta E\).
- **Condition 2**: When the reaction involves only solids and liquids.
- For solids and liquids, there is no change in the number of moles of gases (\(\Delta N_G = 0\)), hence \(P \Delta V\) is also zero, leading to \(\Delta H = \Delta E\).
- **Condition 3**: When \(\Delta N_G = 0\).
- If the difference in the number of moles of gaseous reactants and products is zero, then \(P \Delta V = 0\) and thus \(\Delta H = \Delta E\).

4. **Conclusion**:
- All three conditions lead to the conclusion that \(\Delta H = \Delta E\). Therefore, the correct answer is that all the given conditions are correct.

### Final Answer:
All of the above conditions lead to \(\Delta H = \Delta E\).