The balanced equation for the synthesis of magnesium oxide from magnesium metal and oxygen gas is:

2 Mg (s) + O₂ (g) → 2 MgO (s)

Here's a breakdown:

* 2 Mg (s): This represents two moles of solid magnesium.

* O₂ (g): This represents one mole of oxygen gas.

* 2 MgO (s): This represents two moles of solid magnesium oxide.

This equation is balanced because there are the same number of atoms of each element on both sides of the equation:

* Magnesium (Mg): 2 on each side

* Oxygen (O): 2 on each side