For the reaction `PCl_(5)(g)toPCl_(3)(g)+Cl_(2)(g)` where ΔH and ΔE represents enthalpy change and internal energy change respectively.

Options

A. `DeltaH=DeltaE`
B. `DeltaH gtDeltaE`
C. `DeltaHltDeltaE`
D. None

Answer

To solve the problem regarding the relationship between the enthalpy change (ΔH) and the internal energy change (ΔE) for the reaction:

\[ \text{PCl}_5(g) \rightarrow \text{PCl}_3(g) + \text{Cl}_2(g) \]

we will follow these steps:

### Step 1: Write the equation relating ΔH and ΔE
The relationship between enthalpy change (ΔH) and internal energy change (ΔE) 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 universal gas constant,
- \( T \) is the temperature in Kelvin.

### Step 2: Calculate ΔNg
Next, we need to calculate \( \Delta N_g \):

- On the reactant side, we have 1 mole of PCl5 (gas).
- On the product side, we have 1 mole of PCl3 (gas) and 1 mole of Cl2 (gas).

Thus, the total number of moles of gas on the product side is:

\[ \text{Total moles of products} = 1 + 1 = 2 \]

Now, we calculate \( \Delta N_g \):

\[ \Delta N_g = \text{(moles of products)} - \text{(moles of reactants)} = 2 - 1 = 1 \]

### Step 3: Substitute ΔNg into the equation
Now we can substitute \( \Delta N_g \) into the equation for ΔH:

\[ \Delta H = \Delta E + (1)RT \]

### Step 4: Analyze the equation
Since \( R \) (the universal gas constant) and \( T \) (temperature in Kelvin) are both positive values, the term \( RT \) is also positive. Therefore, we can conclude:

\[ \Delta H = \Delta E + RT \]

This implies that:

\[ \Delta H > \Delta E \]

### Conclusion
Thus, for the given reaction, the change in enthalpy (ΔH) is greater than the change in internal energy (ΔE).

### Final Answer
The answer is that \( \Delta H > \Delta E \).

---