$$\ce{Fe2O3 + 6HI -> 2FeI2 + I2 + 3H2O}$$
Why don't we get $\ce{FeI3}$? After all, iron's oxidation state is $+3$ in the reagent.
Should one just memorize that up to bromine, it's $\ce{FeX3}$, and below it's $\ce{FeX2}$?
Chemistry Stack Exchange is a question and answer site for scientists, academics, teachers, and students in the field of chemistry. It only takes a minute to sign up.
Sign up to join this community$$\ce{Fe2O3 + 6HI -> 2FeI2 + I2 + 3H2O}$$
Why don't we get $\ce{FeI3}$? After all, iron's oxidation state is $+3$ in the reagent.
Should one just memorize that up to bromine, it's $\ce{FeX3}$, and below it's $\ce{FeX2}$?
The standard reduction potentials for the following half reactions can be found here.
$$ \begin{align} \ce{Fe^3+(aq) + e- &-> Fe^2+(aq)} &\quad E^\circ &= \pu{+0.77 V} \\ \ce{I2(s) + 2 e- &-> 2 I-(aq)} &\quad E^\circ &= \pu{+0.54V} \\ \ce{Br2(l) + 2 e- &-> 2 Br-(aq)} &\quad E^\circ &= \pu{+1.07V} \\ \ce{Cl2(g) + 2 e- &-> 2 Cl-(aq)} &\quad E^\circ &= \pu{+1.36V} \end{align} $$
You can see from this that only iodide is a strong enough reducing agent to reduce $\ce{Fe^3+}$ to $\ce{Fe^2+}$ at standard conditions. Even with non-standard concentrations it will be very difficult to get bromide to do the reduction because the difference in electrode potential is large.
The trend in electrode potentials for the halogens can be explained in terms of the increasing electronegativity going from iodine to chlorine which increases the first electron affinity. It just so happens that the crossover point with the iron reduction is between iodine and bromine.
As it is pointed out in other answers and in literature, it is indeed thermodynamically unstable and its reaction synthesis has unfavorable pathways. But, is it "non-existent"? Not quite. There was a possibility of its existence indicated by the fact that hydrated ferric oxide dissolves in hydriodic acid, yielding a brown solution. Its thermodynamic limitation was known in aqueous medium, so its synthesis was thought to be carried in non-aqueous medium. It was the year 1989 that the synthesis was somehow achieved. Diiodotetracarbonyl(II) iron was photochemically reacted with iodine in n-hexane medium to yield the product:
$$\ce{2(OC)4FeI2 + I2 ->[h\nu][C6H14] 2FeI3 + 8CO }$$
However, there were some limitation to this reaction:
$$\ce{2FeI3 ->[h\nu] 2FeI2 + I2}$$
$$\ce{FeI3 + I- -> FeI4-}$$
Ref.: Ferric iodide as a nonexistent compound, K. B. Yoon and J. K. Kochi Inorganic Chemistry 1990 29 (4), 869-874, DOI: 10.1021/ic00329a058
Iron(III) iodide as a binary salt is highly unstable/transitory, but stable complexes are known with appropriate ligands.
Pohl et al. [1] first synthesized such a complex, $\ce{FeI3(SC(N(CH3)2)2)}$, actually oxidizing iron(II) iodide with elemental iodine in the presence of a carefully controlled amount of $\ce{((CH3)2N)2CS}$. The iron(III) iodide, despite the high oxidation state of iron, acts as a soft acid, coordinating to sulfur instead of nitrogen (picture from Ref. [1]):
Barnes et al. [2] report that reaction of iron metal with trimethylarsine diiodide affords the complex $\ce{FeI3(As(CH3)3)2}$, a trigonal bipyramidal complex with a structure similar to that of lighter halide complexes (picture from Ref. [2]).
These reactions, together with the oxidation of the iron(II) iodide-carbonyl complex reported in Nilay Ghosh's answer, share some common characteristics:
The iodine comes from nonionic sources, even where the reactant has it in the -1 oxidation state as in Ref. [2].
The environment avoids water and other hard bases, which would presumably bind to the iron (III) and displace iodide ions. The iron(III) iodide, which has significant covalent character and would be a softer acid than ionic $\ce{Fe^{3+}}$, is instead bound to soft bases.
These features suggest that $\ce{FeI3}$, as such, is not all that unstable; rather it is the combination of $\ce{Fe^{3+}}$ and $\ce{I^-}$ ions that doesn't hold up. If the iron(III) iodide were to be formed in a process that avoids the use or generation of the separate ions, it would more likely be sustained.
Compare these results with cerium(IV) chloride.
References
1. Siegfried Pohl, Ulrich Bierbach, Wolfgang Saak; "FeI3SC(NMe2)2, a Neutral Thiourea Complex of Iron(III) Iodide", Angewandte Chemie International Edition in English (1989) 28 (6), 776-777. https://doi.org/10.1002/anie.198907761
2. Nicholas A. Barnes, Stephen M.Godfrey, Nicholas Ho, Charles A.McAuliffe, Robin G.Pritchard; "Facile synthesis of a rare example of an iron(III) iodide complex, [FeI3(AsMe3)2], from the reaction of Me3AsI2 with unactivated iron powder", Polyhedron (2013) 55, 67-72. https://doi.org/10.1016/j.poly.2013.02.066