The chemical reactions involved are:

Iron $Fe$ reacts with chlorine gas $Cl2$ to form Iron $II$ chloride $FeCl2$.

2Fe + Cl2 -> 2FeCl2

Iron $II$ chloride $FeCl2$ can be further reacted with chlorine gas $Cl2$ to form Iron $III$ chloride $FeCl3$.

2FeCl2 + Cl2 -> 2FeCl3

Iron $III$ chloride $FeCl3$ can react with water $H2O$ to form Iron $III$ hydroxide $Fe(OH)3$.

FeCl3 + 3H2O -> Fe$OH$3 + 3HCl

Overall, the reactions can be summarized as:

Fe + Cl2 -> FeCl2
2FeCl2 + Cl2 -> 2FeCl3