Metal oxides that are more stable than carbon dioxide will not react with carbon. This means the metal oxide must have a higher Gibbs free energy of formation than carbon dioxide.

Here's a breakdown:

* The reaction: Metal oxides react with carbon to produce the metal and carbon dioxide:

```

MO + C → M + CO₂

```

* Stability: The reaction will only proceed if the products (metal and carbon dioxide) are more stable than the reactants (metal oxide and carbon).

* Gibbs free energy: Gibbs free energy (ΔG) is a thermodynamic property that indicates the spontaneity of a reaction. A negative ΔG indicates a spontaneous reaction, while a positive ΔG indicates a non-spontaneous reaction.

* Stability vs. Gibbs free energy: More stable compounds have a more negative ΔG of formation.

Therefore, metal oxides with a higher ΔG of formation than carbon dioxide will not react with carbon.

Examples of metal oxides that do not react with carbon:

* Aluminum oxide (Al₂O₃)

* Magnesium oxide (MgO)

* Calcium oxide (CaO)

* Titanium oxide (TiO₂)

Note: This is a general rule, and there are exceptions. For example, some metal oxides can react with carbon at very high temperatures. However, under normal conditions, the metal oxides listed above are considered stable and will not react with carbon.