Question

Arrange the following in the increasing order of their magnetic moments
I. \( [\text{Mn(CN)}_6]^{3-} \)
II. \( [\text{MnCl}_6]^{3-} \)
III. \( [\text{Fe(CN)}_6]^{3-} \)
IV. \( [\text{FeF}_6]^{3-} \)

• A. \(III<I<IV<II\)
• B. \(III<IV<II<I\)
• C. \(IV<II<I<III\)
• D. \(III<I<II<IV\)

Hint:

Strong field ligands cause pairing of electrons, while weak field ligands do not.

Answer 1

The Correct Option is D

I. \( [\text{Mn(CN)}_6]^{3-} \) 

Mn is in +3 oxidation state. Mn\(^{3+}\) has \( d^4 \) configuration. CN\(^-\) is a strong field ligand, so it causes pairing. The electron configuration for \( d^4 \) with pairing is:

\( t_{2g}^4 e_g^0 \). The number of unpaired electrons is 2. Magnetic moment \( \mu = \sqrt{n(n+1)} \) BM, where \( n \) is the number of unpaired electrons. \( \mu = \sqrt{2(2+1)} = \sqrt{8} \) BM.

II. \( [\text{MnCl}_6]^{3-} \)

Mn is in +3 oxidation state. Mn\(^{3+}\) has \( d^4 \) configuration. Cl\(^-\) is a weak field ligand, so pairing does not occur. The electron configuration for \( d^4 \) without pairing is:

\( t_{2g}^3 e_g^1 \). The number of unpaired electrons is 4. Magnetic moment \( \mu = \sqrt{n(n+1)} \) BM. \( \mu = \sqrt{4(4+1)} = \sqrt{20} \) BM.

III. \( [\text{Fe(CN)}_6]^{3-} \)

Fe is in +3 oxidation state. Fe\(^{3+}\) has \( d^5 \) configuration. CN\(^-\) is a strong field ligand, so it causes pairing. The electron configuration for \( d^5 \) with pairing is:

\( t_{2g}^5 e_g^0 \). The number of unpaired electrons is 1. Magnetic moment \( \mu = \sqrt{n(n+1)} \) BM. \( \mu = \sqrt{1(1+2)} = \sqrt{3} \) BM.

IV. \( [\text{FeF}_6]^{3-} \)

Fe is in +3 oxidation state. Fe\(^{3+}\) has \( d^5 \) configuration. F\(^-\) is a weak field ligand, so pairing does not occur. The electron configuration for \( d^5 \) without pairing is:

\( t_{2g}^3 e_g^2 \). The number of unpaired electrons is 5. Magnetic moment \( \mu = \sqrt{n(n+1)} \) BM. \( \mu = \sqrt{5(5+1)} = \sqrt{30} \) BM.

Arranging in increasing order of magnetic moments:

III \( < \) I \( < \) II \( < \) IV.