For reaction, `N_(2)(g) + 3H_(2)(g) iff 2NH_(3)(g)` which of the following is valid?

Options

A. `DeltaH = DeltaU`
B. `DeltaH gt DeltaU`
C. `DeltaH lt DeltaU`
D. None of the above

Explanation

To solve the question regarding the reaction \( N_2(g) + 3H_2(g) \iff 2NH_3(g) \) and determine which statement is valid, we need to analyze the relationship between the change in enthalpy (\( \Delta H \)) and the change in internal energy (\( \Delta U \)) for the reaction.

### Step-by-Step Solution:

1. **Identify the Reaction**:
The given reaction is:
\[ N_2(g) + 3H_2(g) \iff 2NH_3(g) \]

2. **Understand the Variables**:
- \( \Delta H \): Change in enthalpy.
- \( \Delta U \): Change in internal energy.
- \( \Delta N_G \): Change in the number of moles of gas, calculated as moles of products minus moles of reactants.
- \( R \): Universal gas constant.
- \( T \): Temperature in Kelvin.

3. **Calculate \( \Delta N_G \)**:
- Count the number of gaseous moles on the product side:
- Products: \( 2 \) moles of \( NH_3 \) (since it is in gaseous state).
- Count the number of gaseous moles on the reactant side:
- Reactants: \( 1 \) mole of \( N_2 \) + \( 3 \) moles of \( H_2 \) = \( 4 \) moles.
- Therefore, \( \Delta N_G \) is calculated as:
\[ \Delta N_G = \text{(Moles of products)} - \text{(Moles of reactants)} = 2 - 4 = -2 \]

4. **Use the Relationship Between \( \Delta H \) and \( \Delta U \)**:
The relationship between \( \Delta H \) and \( \Delta U \) is given by:
\[ \Delta H = \Delta U + \Delta N_G \cdot RT \]
Substituting the value of \( \Delta N_G \):
\[ \Delta H = \Delta U + (-2)RT \]
This can be rewritten as:
\[ \Delta H = \Delta U - 2RT \]

5. **Analyze the Equation**:
From the equation \( \Delta H = \Delta U - 2RT \), we can see that:
\[ \Delta U = \Delta H + 2RT \]
This implies that \( \Delta U \) is greater than \( \Delta H \) because we are adding a positive term \( 2RT \) to \( \Delta H \).

6. **Conclusion**:
Thus, we conclude that:
\[ \Delta U > \Delta H \]
This statement corresponds to option C, which is valid.

### Final Answer:
The valid statement is: \( \Delta U > \Delta H \) (Option C).