The reaction in which `DeltaH gt DeltaU` is .

Options

A. `N_(2g) + O_(2g) to 2NO_(g)`
B. `CaCO_(3)(s) to CaO_(s) + CO_(2)`
C. `N_(2)(g) + 3H_(2)(g) to 2NH_(3)(g)`
D. `CH_(4)(g) + 2O_(2)(g) to CO_(2)(g) + 2H_(2)O_(l)`

Explanation

To determine the reaction in which \( \Delta H > \Delta U \), we need to understand the relationship between enthalpy change (\( \Delta H \)) and internal energy change (\( \Delta U \)). The relationship can be expressed as:

\[ \Delta H = \Delta U + \Delta n_g RT \]

Where:
- \( \Delta H \) is the change in enthalpy.
- \( \Delta U \) is the change in internal energy.
- \( \Delta n_g \) is the change in the number of moles of gas during the reaction.
- \( R \) is the universal gas constant.
- \( T \) is the temperature in Kelvin.

### Step-by-Step Solution:

1. **Identify the relationship**: Start with the equation \( \Delta H = \Delta U + \Delta n_g RT \). This equation shows how the change in enthalpy relates to the change in internal energy and the change in the number of moles of gas.

2. **Analyze the term \( \Delta n_g \)**: The term \( \Delta n_g \) is crucial. It represents the change in the number of moles of gaseous products minus the gaseous reactants. If \( \Delta n_g \) is positive, it means there are more moles of gas in the products than in the reactants, which will contribute positively to \( \Delta H \).

3. **Determine conditions for \( \Delta H > \Delta U \)**: For \( \Delta H > \Delta U \), the term \( \Delta n_g RT \) must be positive. This occurs when:
- \( \Delta n_g > 0 \) (more gaseous products than reactants).

4. **Example reactions**:
- Consider a reaction where 1 mole of gas is produced from solid or liquid reactants. For example:
\[ \text{C (s)} + \text{2 H}_2 (g) \rightarrow \text{CH}_4 (g) \]
Here, \( \Delta n_g = 1 - 2 = -1 \) (not suitable since \( \Delta n_g \) is negative).
- Now consider:
\[ \text{N}_2 (g) + 3 \text{H}_2 (g) \rightarrow 2 \text{NH}_3 (g) \]
Here, \( \Delta n_g = 2 - 4 = -2 \) (again not suitable).
- A suitable reaction could be:
\[ \text{A (s)} \rightarrow \text{B (g)} \]
Here, \( \Delta n_g = 1 - 0 = 1 \) (suitable since \( \Delta n_g \) is positive).

5. **Conclusion**: The reaction in which \( \Delta H > \Delta U \) occurs when there is an increase in the number of gaseous moles during the reaction, leading to a positive contribution from the \( \Delta n_g RT \) term.