For the reaction `PCI_(5)(g) rightarrow PCI_(3)(g) + CI_(2)(g)`

Options

A. `Delta H = Delta E`
B. `Delta H gt Delta E`
C. `Delta H lt Delta E`
D. Can't predicted

Answer

To solve the problem regarding the reaction \( \text{PCl}_5(g) \rightleftharpoons \text{PCl}_3(g) + \text{Cl}_2(g) \), we need to find the relationship between the change in enthalpy (\( \Delta H \)) and the change in internal energy (\( \Delta E \)).

### Step-by-Step Solution:

1. **Write the Relation**:
The relationship between the change in enthalpy and the change in internal energy is given by the equation:
\[ \Delta H = \Delta E + \Delta N_{g}RT \]
where \( \Delta N_{g} \) is the change in the number of moles of gas, \( R \) is the gas constant, and \( T \) is the temperature in Kelvin.

2. **Identify the Change in Moles**:
- For the given reaction:
- Reactants: 1 mole of \( \text{PCl}_5 \)
- Products: 1 mole of \( \text{PCl}_3 \) + 1 mole of \( \text{Cl}_2 \)
- Total moles of products = 2 moles
- Total moles of reactants = 1 mole
- Therefore, the change in the number of gaseous moles (\( \Delta N_{g} \)) is:
\[ \Delta N_{g} = \text{Moles of products} - \text{Moles of reactants} = 2 - 1 = 1 \]

3. **Substitute Values into the Equation**:
Substitute \( \Delta N_{g} \) into the equation:
\[ \Delta H = \Delta E + (1)RT \]
This simplifies to:
\[ \Delta H = \Delta E + RT \]

4. **Interpret the Result**:
From the equation \( \Delta H = \Delta E + RT \), it is clear that \( \Delta H \) is greater than \( \Delta E \) because \( RT \) is a positive term. This indicates that the change in enthalpy is more than the change in internal energy.

5. **Choose the Correct Option**:
Based on the interpretation, we look for the option where \( \Delta H \) is greater than \( \Delta E \). According to the video transcript, the answer is in part B.

### Final Answer:
The answer is part B, where \( \Delta H \) is greater than \( \Delta E \).