The number of unpaired electrons responsible for the paramagnetic nature of the following complex species are respectively :
$ [Fe(CN)_6]^{3-}, [FeF_6]^{3-}, [CoF_6]^{3-}, [Mn(CN)_6]^{3-} $
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To determine the number of unpaired electrons in coordination complexes, first find the oxidation state of the central metal ion and its \( d \) electron configuration. Then, consider the nature of the ligand (strong field or weak field) to determine the electron pairing in the \( d \) orbitals based on the magnitude of crystal field splitting (\( \Delta_o \) compared to the pairing energy \( P \)). Strong field ligands favor pairing in the lower energy \( t_{2g} \) orbitals, leading to low spin complexes, while weak field ligands favor high spin complexes with electrons occupying both \( t_{2g} \) and \( e_g \) orbitals according to Hund's rule.
To determine the number of unpaired electrons responsible for the paramagnetic nature of the given complex species, we need to analyze the electronic configuration of the central metal ion in each complex. The presence of unpaired electrons in the d-orbitals of the central metal ion makes the complex paramagnetic.
Complex: [Fe(CN)_6]^{3-}
The oxidation state of Fe in this complex is +3.
Electronic configuration of Fe: [Ar] 3d^6 4s^0
Fe3+ ion: [Ar] 3d^5
CN- is a strong field ligand and causes pairing of electrons in the 3d orbitals.
Since all five d electrons are paired, there is 1 unpaired electron.
Complex: [FeF_6]^{3-}
Oxidation state of Fe is +3.
Fe3+ ion: [Ar] 3d^5
F- is a weak field ligand and does not cause pairing of electrons.
Hence, all five d electrons remain unpaired, resulting in 5 unpaired electrons.
Complex: [CoF_6]^{3-}
Oxidation state of Co is +3.
Electronic configuration of Co: [Ar] 3d^7 4s^0
Co3+ ion: [Ar] 3d^6
F- is a weak field ligand, so electrons do not pair completely.
This results in 4 unpaired electrons.
Complex: [Mn(CN)_6]^{3-}
Oxidation state of Mn is +3.
Electronic configuration of Mn: [Ar] 3d^5 4s^2
Mn3+ ion: [Ar] 3d^4
CN- is a strong field ligand, so it causes pairing of electrons.
This results in 2 unpaired electrons.
Following the above analysis, the number of unpaired electrons responsible for the paramagnetic nature in each complex species is respectively: 1, 5, 4, 2.
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To determine the number of unpaired electrons responsible for the paramagnetic nature of the given complex species, we need to understand the electronic configuration of the metal ions and the nature of the ligands involved. Let's analyze each complex:
Complex: [Fe(CN)_6]^{3-}
Metal Ion: Fe3+
Configuration of Fe: [Ar]3d^6
Configuration of Fe3+: [Ar]3d^5
CN- is a strong field ligand, causing pairing of electrons.
Thus, all electrons are paired: Number of unpaired electrons = 1.
Complex: [FeF_6]^{3-}
Metal Ion: Fe3+
Configuration of Fe3+: [Ar]3d^5
F- is a weak field ligand, does not cause pairing of electrons.
All five d electrons remain unpaired: Number of unpaired electrons = 5.
Complex: [CoF_6]^{3-}
Metal Ion: Co3+
Configuration of Co: [Ar]3d^7
Configuration of Co3+: [Ar]3d^6
F- is a weak field ligand, causing partial pairing.
Typically, 4 electrons remain unpaired: Number of unpaired electrons = 4.
Complex: [Mn(CN)_6]^{3-}
Metal Ion: Mn3+
Configuration of Mn: [Ar]3d^5
Configuration of Mn3+: [Ar]3d^4
CN- is a strong field ligand, causing full pairing.
Pairing leaves 2 unpaired electrons: Number of unpaired electrons = 2.
Therefore, the number of unpaired electrons in the complexes are 1, 5, 4, and 2, respectively, for [Fe(CN)_6]^{3-}, [FeF_6]^{3-}, [CoF_6]^{3-}, and [Mn(CN)_6]^{3-}.
