The reddish-brown color of rust is due to the formation of iron oxide, specifically iron(III) oxide (Fe2O3), when iron metal reacts with oxygen in the presence of moisture. Here's an explanation of the process:

1. Oxidation: Iron undergoes oxidation, losing electrons to oxygen atoms. This process converts elemental iron (Fe) into iron ions (Fe2+).

2. Hydration: Water molecules surround the iron ions, forming hydrated ions called aquated iron(II) ions (Fe(H2O)6^2+).

3. Further Oxidation: In the presence of oxygen and moisture, the aquated iron(II) ions undergo further oxidation, losing more electrons to become iron(III) ions (Fe3+).

4. Hydrolysis: The iron(III) ions react with water molecules, undergoing hydrolysis to form iron(III) hydroxide (Fe(OH)3).

5. Dehydration and Formation of Iron Oxide: Iron(III) hydroxide is initially a gelatinous, greenish-brown precipitate. Over time, this precipitate loses water molecules through dehydration, transforming into iron(III) oxide (Fe2O3), which is the primary component of rust.

The reddish-brown color of rust is characteristic of Fe2O3. It is important to note that the exact color and composition of rust can vary depending on factors such as the type of metal, the environment, and the stage of the oxidation process.