Which of the following proces is (are) expected to be spontaneous at higher temperature but non-spontaneous at lower temperature?

Options

A. `N_(2)(g) + 3H_(2)(g) to 2NH_(3)(g)`
B. `H_(2)(g) to 2H(g)`
C. `CO_(2)(g) + C(s) to 2CO(g)` `[DeltaH_(f)^(Theta),m, CO_(2) =-394 kJ//mol, CO = -212 kJ//mol]`
D. `Na(s) to Na^(+)(g) + e^(-)`

Explanation

To determine which processes are expected to be spontaneous at higher temperatures but non-spontaneous at lower temperatures, we can analyze the Gibbs free energy equation:

\[ \Delta G = \Delta H - T \Delta S \]

Where:
- \(\Delta G\) = Gibbs free energy change
- \(\Delta H\) = Enthalpy change
- \(T\) = Temperature (in Kelvin)
- \(\Delta S\) = Entropy change

### Step-by-step Solution:

1. **Understanding Spontaneity**:
- A process is spontaneous when \(\Delta G < 0\).
- A process is non-spontaneous when \(\Delta G > 0\).

2. **Analyzing the Equation**:
- At low temperatures, the term \(T \Delta S\) will be small.
- If \(\Delta H > 0\) and \(\Delta S > 0\), then \(\Delta G\) can be greater than zero, indicating non-spontaneity.
- At high temperatures, the term \(T \Delta S\) becomes significant. If \(T \Delta S\) is larger than \(\Delta H\), then \(\Delta G\) can become negative, indicating spontaneity.

3. **Identifying Conditions**:
- For a process to be non-spontaneous at low temperatures and spontaneous at high temperatures:
- \(\Delta H > 0\) (endothermic process)
- \(\Delta S > 0\) (increase in disorder)

4. **Evaluating Each Option**:
- **Option 1: Formation of Ammonia (Haber's Process)**:
- This process is exothermic (\(\Delta H < 0\)) and has a negative \(\Delta S\). Thus, it is not suitable.

- **Option 2: Atomization of H2**:
- This process requires energy (endothermic), so \(\Delta H > 0\).
- The reaction produces 2 moles of gas from 1 mole of gas, leading to \(\Delta S > 0\).
- Therefore, this process is non-spontaneous at low temperatures and spontaneous at high temperatures.

- **Option 3: Formation of CO2 from CO**:
- This reaction is exothermic (\(\Delta H < 0\)), so it does not fit the criteria.

- **Option 4: Ionization of a Solid**:
- This process also requires energy (endothermic), so \(\Delta H > 0\).
- The process increases the number of gaseous moles, leading to \(\Delta S > 0\).
- Thus, this process is also non-spontaneous at low temperatures and spontaneous at high temperatures.

5. **Conclusion**:
- The processes that are spontaneous at higher temperatures but non-spontaneous at lower temperatures are:
- **Option 2: Atomization of H2**
- **Option 4: Ionization of a Solid**

### Final Answer:
The processes expected to be spontaneous at higher temperatures but non-spontaneous at lower temperatures are **Option 2 and Option 4**.