* Organic molecules are defined as molecules that contain carbon (C) and hydrogen (H) atoms, and often other elements like oxygen (O), nitrogen (N), phosphorus (P), and sulfur (S).

Let's break down the options:

* Iron oxide (Fe₂O₃) is an inorganic compound containing iron and oxygen.

* Water (H₂O) is an inorganic compound containing hydrogen and oxygen.

* Oxygen gas (O₂) is an inorganic molecule containing only oxygen.

* Sucrose (C₁₂H₂₂O₁₁) is a carbohydrate containing carbon, hydrogen, and oxygen, making it an organic molecule.

Therefore, sucrose is the only organic molecule among the given choices.