Question

The correct order of spin-only magnetic moments among the following is: [Given: Atomic numbers: Mn = 25, Fe = 26, Co = 27]

• A. \( [\text{Fe(CN)}_6]^{4+} \) $>$ \( [\text{MnCl}_4]^{2-} \) $>$ \( [\text{CoCl}_4]^{2-} \)
• B. \( [\text{MnCl}_4]^{2-} \) $>$ \( [\text{CoCl}_4]^{2-} \) $>$ \( [\text{Fe(CN)}_6]^{4-} \)
  $$
• C. \( [\text{Fe(CN)}_6]^{4+} \) $>$ \( [\text{CoCl}_4]^{2-} \) $>$ \( [\text{MnCl}_4]^{2-} \)
• D. \( [\text{MnCl}_4]^{2-} \) $>$ \( [\text{Fe(CN)}_6]^{4+} \) $>$ \( [\text{CoCl}_4]^{2-} \)

Hint:

The magnetic moment is directly related to the number of unpaired electrons in the complex. A higher number of unpaired electrons results in a higher magnetic moment.

Answer 1

The Correct Option is B

Step 1: Understand the concept of spin-only magnetic moments.
The magnetic moment for a complex ion can be calculated using the formula for spin-only moments:
\[ \mu_s = \sqrt{n(n + 2)} \] where \( n \) is the number of unpaired electrons.

Step 2: Consider the electron configuration and number of unpaired electrons.
- For \( \text{Mn}^{2+} \) (in \( [\text{MnCl}_4]^{2-} \)), \( 3d^5 \) configuration leads to 5 unpaired electrons.
- For \( \text{Co}^{2+} \) (in \( [\text{CoCl}_4]^{2-} \)), \( 3d^7 \) configuration leads to 3 unpaired electrons.
- For \( \text{Fe}^{2+} \) (in \( [\text{Fe(CN)}_6]^{4-} \)), \( 3d^6 \) configuration leads to 4 unpaired electrons, as the cyanide ligand stabilizes low-spin complexes, and thus fewer unpaired electrons.

Step 3: Apply the magnetic moment formula.
- For \( \text{MnCl}_4^{2-} \), with 5 unpaired electrons:
\[ \mu_s = \sqrt{5(5 + 2)} = \sqrt{35} \approx 5.92 \, \mu_B \]
- For \( \text{CoCl}_4^{2-} \), with 3 unpaired electrons:
\[ \mu_s = \sqrt{3(3 + 2)} = \sqrt{15} \approx 3.87 \, \mu_B \]
- For \( \text{Fe(CN)}_6^{4-} \), with 4 unpaired electrons:
\[ \mu_s = \sqrt{4(4 + 2)} = \sqrt{24} \approx 4.90 \, \mu_B \]

Step 4: Conclusion.
Thus, the order of magnetic moments is:
\[ \text{MnCl}_4^{2-} > \text{CoCl}_4^{2-} > \text{Fe(CN)}_6^{4-} \]
This matches option (B).