Under which of the following condition `Delat H = Delat 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 start with the relationship between enthalpy change (\( \Delta H \)) and internal energy change (\( \Delta E \)).

### Step-by-Step Solution:

1. **Understand the Relationship**:
The relationship between enthalpy change and internal energy change is given by the equation:
\[ \Delta H = \Delta E + P \Delta V \]
where \( P \) is the pressure and \( \Delta V \) is the change in volume.

2. **Identify Conditions for \( \Delta H = \Delta E \)**:
For \( \Delta H \) to equal \( \Delta E \), the term \( P \Delta V \) must be zero:
\[ P \Delta V = 0 \]
This can happen under two conditions:
- When the process occurs in a closed vessel (where the volume does not change).
- When there is no change in the number of moles of gas (\( \Delta n_g = 0 \)).

3. **Evaluate Each Condition**:
- **Closed Vessel**: In a closed vessel, the volume remains constant, hence \( \Delta V = 0 \). Therefore, \( P \Delta V = 0 \) and \( \Delta H = \Delta E \).
- **Only Solids and Liquids**: If the reaction involves only solids and liquids, there are no gaseous products or reactants, which means \( \Delta n_g = 0 \). Thus, \( P \Delta V = 0 \) and \( \Delta H = \Delta E \).
- **\( \Delta n_g = 0 \)**: If there is no change in the number of moles of gas during the reaction, \( \Delta n_g = 0 \) implies that \( P \Delta V = 0 \). Therefore, \( \Delta H = \Delta E \).

4. **Conclusion**:
All three conditions lead to the conclusion that \( \Delta H = \Delta E \). Therefore, the correct answer is:
\[ \text{All of the above} \]