If `DeltaH` is the enthalpy change and `DeltaU` the change in internal energy accompanying a gaseous reaction, then

Options

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

Explanation

To solve the question regarding the relationship between the enthalpy change (ΔH) and the change in internal energy (ΔU) for a gaseous reaction, we can follow these steps:

### Step 1: Understand the relationship between ΔH and ΔU
The relationship between the change in enthalpy (ΔH) and the change in internal energy (ΔU) for a gaseous reaction is given by the equation:
\[ \Delta H = \Delta U + \Delta n_g RT \]
where:
- Δn_g = change in the number of moles of gas (moles of gaseous products - moles of gaseous reactants)
- R = universal gas constant
- T = temperature in Kelvin

### Step 2: Analyze the significance of Δn_g
The term Δn_g indicates whether the number of gaseous products is greater than, less than, or equal to the number of gaseous reactants:
- If Δn_g > 0: There are more moles of gas in the products than in the reactants.
- If Δn_g < 0: There are fewer moles of gas in the products than in the reactants.
- If Δn_g = 0: The number of gaseous moles remains the same.

### Step 3: Determine the implications of Δn_g
1. **If Δn_g > 0**:
- The equation becomes:
\[ \Delta H = \Delta U + \text{(positive term)} \]
- This implies that ΔH > ΔU.

2. **If Δn_g < 0**:
- The equation becomes:
\[ \Delta H = \Delta U + \text{(negative term)} \]
- This implies that ΔH < ΔU.

### Step 4: Conclusion based on the analysis
From the analysis:
- ΔH can be greater than or less than ΔU depending on the value of Δn_g.
- Thus, we cannot say that ΔH is always greater than or always less than ΔU; it depends on the reaction.

### Step 5: Identify the correct statement
Based on the above analysis, the correct statement is:
- If Δn_g > 0, then ΔH > ΔU.
- If Δn_g < 0, then ΔH < ΔU.

Thus, the correct answer is **Option B**: ΔH is less than ΔU when the number of gaseous products is greater than the number of gaseous reactants.