If one mole of ammonia and one mole of hydrogen chloride are mixed in a closed container to form ammonium chloride vapor, then

Options

A. `Delta H gt Delta U`
B. `Delta H = Delta U`
C. `Delta H lt Delta U`
D. No relationship

Answer

To solve the problem, we need to analyze the reaction between ammonia (NH3) and hydrogen chloride (HCl) to form ammonium chloride (NH4Cl) and determine the relationship between the change in enthalpy (ΔH) and the change in internal energy (ΔU).

### Step-by-Step Solution:

1. **Identify the Reaction**:
The reaction can be written as:
\[ \text{NH}_3(g) + \text{HCl}(g) \rightarrow \text{NH}_4\text{Cl}(g) \]
Here, one mole of ammonia reacts with one mole of hydrogen chloride to produce one mole of ammonium chloride vapor.

2. **Determine the Number of Moles**:
- Reactants: 1 mole of NH3 + 1 mole of HCl = 2 moles of reactants.
- Products: 1 mole of NH4Cl = 1 mole of products.

3. **Calculate ΔN (Change in Moles)**:
\[ \Delta N_g = \text{Number of moles of products} - \text{Number of moles of reactants} = 1 - 2 = -1 \]

4. **Relate ΔH and ΔU**:
The relationship between the change in enthalpy (ΔH) and the change in internal energy (ΔU) is given by:
\[ \Delta H = \Delta U + \Delta N_g \cdot R \cdot T \]
where \( R \) is the gas constant and \( T \) is the temperature.

5. **Substitute ΔN_g**:
Substitute ΔN_g into the equation:
\[ \Delta H = \Delta U + (-1) \cdot R \cdot T \]
This simplifies to:
\[ \Delta H = \Delta U - R \cdot T \]

6. **Analyze the Relationship**:
From the equation \( \Delta H = \Delta U - R \cdot T \):
- If \( \Delta U \) is a positive value, then \( \Delta H \) will be less than \( \Delta U \) because we are subtracting a positive quantity \( R \cdot T \) from \( \Delta U \).

7. **Conclusion**:
Thus, we conclude that:
\[ \Delta H < \Delta U \]
Therefore, the correct option is that ΔH is less than ΔU.