1. The Chemical Process: When iron ($Fe$) is exposed to air and water, it undergoes a series of redox reactions. Initially, $Fe$ is oxidized to $Fe^{2+}$ ions, which are then further oxidized by oxygen to $Fe^{3+}$ ions.
2. Formation of Rust: These $Fe^{3+}$ ions react with water to form a reddish-brown flaky solid known as rust. Chemically, it is identified as a hydrated form of Iron (III) oxide.
3. Chemical Formula: The general formula for rust is represented as:
$$Fe_2O_3 \cdot xH_2O$$
In systematic nomenclature, this is called
Hydrated Ferric Oxide.