Question

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-} $

• A. 1, 5, 4, 2
• B. 1, 5, 5, 2
• C. 1, 1, 4, 2
• D. 1, 4, 4, 2

Hint:

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.

Answer 1

The Correct Option is A

Step 1: Determine the oxidation state of the central metal ion in each complex.
\( [Fe(CN)_6]^{3-} \): Let the oxidation state of Fe be \( x \). The charge of \( CN^- \) is -1. \( x + 6(-1) = -3 \) \( x - 6 = -3 \) \( x = +3 \) Electronic configuration of \( Fe^{3+} \) (\( d^5 \)): \( [Ar] 3d^5 \) \( [FeF_6]^{3-} \): Let the oxidation state of Fe be \( x \). The charge of \( F^- \) is -1. \( x + 6(-1) = -3 \) \( x - 6 = -3 \) \( x = +3 \) Electronic configuration of \( Fe^{3+} \) (\( d^5 \)): \( [Ar] 3d^5 \) \( [CoF_6]^{3-} \): Let the oxidation state of Co be \( x \). The charge of \( F^- \) is -1. \( x + 6(-1) = -3 \) \( x - 6 = -3 \) \( x = +3 \) Electronic configuration of \( Co^{3+} \) (\( d^6 \)): \( [Ar] 3d^6 \) \( [Mn(CN)_6]^{3-} \): Let the oxidation state of Mn be \( x \). The charge of \( CN^- \) is -1. \( x + 6(-1) = -3 \) \( x - 6 = -3 \) \( x = +3 \) Electronic configuration of \( Mn^{3+} \) (\( d^4 \)): \( [Ar] 3d^4 \)
Step 2: Determine the number of unpaired electrons using Crystal Field Theory.
\( [Fe(CN)_6]^{3-} \): \( CN^- \) is a strong field ligand, causing large crystal field splitting (\( \Delta_o>P \)). The \( d^5 \) electrons will pair up in the lower \( t_{2g} \) orbitals. \( t_{2g}^5 e_g^0 \) (Unpaired electrons = 1) \( [FeF_6]^{3-} \): \( F^- \) is a weak field ligand, causing small crystal field splitting (\( \Delta_o<P \)). The \( d^5 \) electrons will follow Hund's rule and occupy the orbitals singly before pairing. \( t_{2g}^3 e_g^2 \) (Unpaired electrons = 5) \( [CoF_6]^{3-} \): \( F^- \) is a weak field ligand. The \( d^6 \) electrons will be arranged as: \( t_{2g}^4 e_g^2 \) (Unpaired electrons = 4) \( [Mn(CN)_6]^{3-} \): \( CN^- \) is a strong field ligand. The \( d^4 \) electrons will pair up in the lower \( t_{2g} \) orbitals. \( t_{2g}^4 e_g^0 \) (Unpaired electrons = 2)
Step 3: List the number of unpaired electrons for each complex.
\( [Fe(CN)_6]^{3-} \): 1 unpaired electron \( [FeF_6]^{3-} \): 5 unpaired electrons \( [CoF_6]^{3-} \): 4 unpaired electrons \( [Mn(CN)_6]^{3-} \): 2 unpaired electrons
Step 4: Match the number of unpaired electrons with the given options.
The number of unpaired electrons are 1, 5, 4, 2 respectively, which matches option (1).