It is true that under certain condition, Mg can reduce `Al_2O_3` and Al can reduce `MgO`? What are those conditions?

Explanation

To determine the conditions under which magnesium (Mg) can reduce aluminum oxide (Al₂O₃) and aluminum (Al) can reduce magnesium oxide (MgO), we can refer to the Ellingham diagram, which provides insights into the thermodynamic feasibility of these reactions based on temperature.

### Step-by-Step Solution:

1. **Understanding the Reduction Process**:
- Reduction is a chemical reaction where a metal oxide is converted to its elemental form by removing oxygen. For example, Mg can reduce Al₂O₃ to produce Al, and Al can reduce MgO to produce Mg.

2. **Ellingham Diagram**:
- The Ellingham diagram is a graphical representation that shows the stability of metal oxides and the temperature dependence of their reduction. It plots the Gibbs free energy change (ΔG) for the formation of oxides against temperature.

3. **Conditions for Mg to Reduce Al₂O₃**:
- According to the Ellingham diagram, magnesium can reduce aluminum oxide (Al₂O₃) at temperatures below **1350°C**. This means that at lower temperatures, the Gibbs free energy change for the reduction of Al₂O₃ by Mg becomes favorable.

4. **Conditions for Al to Reduce MgO**:
- Conversely, aluminum can reduce magnesium oxide (MgO) at temperatures above **1350°C**. At these higher temperatures, the Gibbs free energy change for the reduction of MgO by Al becomes favorable.

5. **Summary of Conditions**:
- **Mg can reduce Al₂O₃**: Below **1350°C**
- **Al can reduce MgO**: Above **1350°C**

### Final Answer:
- Yes, under certain conditions:
- Magnesium can reduce aluminum oxide (Al₂O₃) at temperatures below **1350°C**.
- Aluminum can reduce magnesium oxide (MgO) at temperatures above **1350°C**.