Which of the following is the most stable complex ion?

The stability of a complex ion depends primarily on the strength of the metal-ligand bonds.

The complex \([Fe(CO)_5]\) is a neutral coordination entity, not a complex ion.

For the ions \([Fe(CN)_6]^{3-}\), \([Fe(C_2O_4)_3]^{3-}\), and \([Fe(H_2O)_6]^{3+}\), the central metal ion is \(Fe^{3+}\) in all cases. The stability is thus determined by the nature of the ligands.

According to the spectrochemical series, the field strength of the ligands follows the order \(H_2O < C_2O_4^{2-} < CN^-\).

The cyanide ligand (\(CN^-\)) is a very strong field ligand. It acts as an excellent \(\sigma\)-donor and \(\pi\)-acceptor. The resulting synergic bonding creates an exceptionally strong bond between the iron ion and the cyanide ligands.

While the oxalate ion (\(C_2O_4^{2-}\)) is a bidentate chelating ligand and provides stability via the chelate effect, the thermodynamic stability constant for the cyanide complex is significantly higher than that for the oxalate complex due to the overwhelming strength of the \(Fe-CN\) bonds.

Therefore, \([Fe(CN)_6]^{3-}\) is the most stable complex ion among the given options.