Final answer:
In [Fe(NO2)6]³⁻, all six d-electrons will be paired while in [FeF6]³⁻ four of the six d-electrons will remain unpaired.
Step-by-step explanation:
In terms of crystal field theory, the number of unpaired electrons in a coordination compound can be determined based on the ligand's strength in splitting the d-orbitals of the central metal ion. In the case of [Fe(NO2)6]³⁻, nitrite is a strong-field ligand, resulting in a low spin complex.
Therefore, all six d-electrons will be paired, leading to 0 unpaired electrons. On the other hand, [FeF6]³⁻ involves weak-field ligand fluoride, leading to a high spin complex. In this case, four of the six d-electrons will remain unpaired, resulting in 4 unpaired electrons.