For the reaction `PCl_(5)(g) rightarrow PCl_(3)(g) + Cl_(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 question regarding the reaction \( PCl_5(g) \rightarrow PCl_3(g) + Cl_2(g) \) and the relationship between \( \Delta H \) (change in enthalpy) and \( \Delta E \) (change in internal energy), we can follow these steps:

### Step 1: Write the reaction and identify the components
The given reaction is:
\[ PCl_5(g) \rightarrow PCl_3(g) + Cl_2(g) \]

### Step 2: Understand the relationship between \( \Delta H \) and \( \Delta E \)
The relationship between the change in enthalpy (\( \Delta H \)) and the change in internal energy (\( \Delta E \)) 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.

### Step 3: Calculate \( \Delta N_g \)
To find \( \Delta N_g \), we need to determine the number of moles of gaseous products and reactants.

- **Products**:
- \( PCl_3(g) \): 1 mole
- \( Cl_2(g) \): 1 mole
- Total moles of products = 1 + 1 = 2 moles

- **Reactants**:
- \( PCl_5(g) \): 1 mole
- Total moles of reactants = 1 mole

Now, we can calculate \( \Delta N_g \):
\[ \Delta N_g = \text{(moles of products)} - \text{(moles of reactants)} = 2 - 1 = 1 \]

### Step 4: Substitute \( \Delta N_g \) into the equation
Now, we can substitute \( \Delta N_g \) into the equation for \( \Delta H \):
\[ \Delta H = \Delta E + (1)RT \]

### Step 5: Analyze the equation
Since \( RT \) is a positive term, we can conclude:
\[ \Delta H = \Delta E + RT \quad \Rightarrow \quad \Delta H > \Delta E \]

### Conclusion
Thus, the correct option is that \( \Delta H \) is greater than \( \Delta E \).

### Final Answer
**The correct option is: \( \Delta H > \Delta E \)**