Consider the two complex ions \([CoF_6]^{3-}\) and \([Co(C_2O_4)_3]^{3-}\), which of the following statement (s) is/are false :

(A) Both are octahedral.

(B) \([Co(C_2O_4)_3]^{3-}\) is diamagnetic, while \([CoF_6]^{3-}\) is paramagnetic.

(C) Both are outer orbital complexes.

(D) In both the complexes the central metal is in the same oxidation state.

Choose the correct answer from the options given below:

(C) Only

The correct answer is option 3. (C) Only.

Let us delve into each statement and its validity:

(A) Both are octahedral. This statement is true. Both \([CoF_6]^{3-}\) and \([Co(C_2O_4)_3]^{3-}\) have a coordination number of 6, meaning they each have six ligands surrounding the central cobalt ion. The geometry associated with a coordination number of 6 is octahedral, where the ligands are arranged symmetrically around the central metal ion.

(B) \([Co(C_2O_4)_3]^{3-}\) is diamagnetic, while \([CoF_6]^{3-}\) is paramagnetic. This statement is true. Diamagnetism occurs when all the electrons in a substance are paired, resulting in a net magnetic moment of zero. In \([Co(C_2O_4)_3]^{3-}\), cobalt is in the +3 oxidation state and has no unpaired electrons, leading to diamagnetism. Paramagnetism, on the other hand, arises from the presence of unpaired electrons, as is the case with \([CoF_6]^{3-}\), where cobalt is also in the +3 oxidation state but has unpaired electrons due to the weak field ligand fluoride.

(C) Both are outer orbital complexes. This statement is false. In coordination chemistry, complexes are classified as inner or outer orbital complexes based on the electronic configuration of the metal ion. Outer orbital complexes occur when the ligands are strong field ligands, leading to the pairing of electrons in the lower-energy orbitals (\(t_{2g}\) level). \([CoF_6]^{3-}\) falls under this category because fluoride is a strong field ligand. However, \([Co(C_2O_4)_3]^{3-}\) is an inner orbital complex as oxalate is a weak field ligand, and the electrons remain unpaired in the \(t_{2g}\) level.

(D) In both the complexes the central metal is in the same oxidation state. This statement is true. Both \([CoF_6]^{3-}\) and \([Co(C_2O_4)_3]^{3-}\) have cobalt in the +3 oxidation state.

So, the false statement is (C) Both are outer orbital complexes.

Therefore, the correct answer is option (3) (C) Only.