If `DeltaH` is the change in enthalpy and `DeltaE` the change in internal energy for a gaseous reaction then

Options

A. `DeltaH ` is always greater than `DeltaE`
B. `DeltaH lt DeltaE` only if the number of moles of the products is greater than the number of the reactants
C. `DeltaH ` is always less than `DeltaE`
D. `DeltaH lt DeltaE` only if the number of moles of the products is less than the number of moles of the reactants

Answer

To solve the question regarding the relationship between the change in enthalpy (ΔH) and the change in internal energy (ΔE) for a gaseous reaction, we will use the thermodynamic relationship that connects these two quantities.

### Step-by-Step Solution:

1. **Understand the Relationship**:
The relationship between ΔH and ΔE is given by the equation:
\[ \Delta H = \Delta E + \Delta N_g RT \]
where ΔN_g is the change in the number of moles of gas (moles of products - moles of reactants), R is the gas constant, and T is the temperature.

2. **Analyze ΔN_g**:
- If ΔN_g = 0: This means the number of moles of gaseous products equals the number of moles of gaseous reactants. In this case, ΔH = ΔE.
- If ΔN_g > 0: This occurs when the number of moles of gaseous products is greater than the number of moles of gaseous reactants. Here, ΔH will be greater than ΔE because you are adding a positive value (ΔN_g RT) to ΔE.
- If ΔN_g < 0: This occurs when the number of moles of gaseous products is less than the number of moles of gaseous reactants. In this case, ΔH will be less than ΔE because you are subtracting a positive value from ΔE.

3. **Evaluate the Options**:
- **Option A**: ΔH is always greater than ΔE. (Incorrect)
- **Option B**: ΔH is less than ΔE only if the number of moles of products is greater than the number of moles of reactants. (Incorrect)
- **Option C**: ΔH is always less than ΔE. (Incorrect)
- **Option D**: ΔH is less than ΔE only if the number of moles of products is less than the number of moles of reactants. (Correct)

4. **Conclusion**:
Based on the analysis, the correct answer is **Option D**. ΔH is less than ΔE only if the number of moles of products is less than the number of moles of reactants.