Calculating Spin-Only Magnetic Moments

The spin-only magnetic moment ($\mu_{s}$) is calculated using the formula:

$ \mu_{s} = \sqrt{n(n+2)} \text{ Bohr magnetons (BM)} $

where '$n$' is the number of unpaired electrons.

Determining Unpaired Electrons for Each Complex

We need to find the number of unpaired electrons for the central metal ion in each complex, given their atomic numbers (Mn=25, Co=27, Ni=28, Zn=30).

• $[ZnCl_4]^{2–}$:
  • Metal ion: $Zn^{2+}$
  • Electronic configuration: $[Ar] 3d^{10}$
  • Number of unpaired electrons ($n$): 0
  • Magnetic moment ($\mu_{s}$): $\sqrt{0(0+2)} = 0$ BM
• $[NiCl_4]^{2–}$:
  • Metal ion: $Ni^{2+}$
  • Electronic configuration: $[Ar] 3d^8$
  • Number of unpaired electrons ($n$): 2 (In tetrahedral geometry, $3d^8$ usually corresponds to 2 unpaired electrons)
  • Magnetic moment ($\mu_{s}$): $\sqrt{2(2+2)} = \sqrt{8} \approx 2.83$ BM
• $[CoCl_4]^{2–}$:
  • Metal ion: $Co^{2+}$
  • Electronic configuration: $[Ar] 3d^7$
  • Number of unpaired electrons ($n$): 3 (In tetrahedral geometry, $3d^7$ usually corresponds to 3 unpaired electrons)
  • Magnetic moment ($\mu_{s}$): $\sqrt{3(3+2)} = \sqrt{15} \approx 3.87$ BM
• $[MnCl_4]^{2–}$:
  • Metal ion: $Mn^{2+}$
  • Electronic configuration: $[Ar] 3d^5$
  • Number of unpaired electrons ($n$): 5 (In tetrahedral geometry, $3d^5$ corresponds to 5 unpaired electrons)
  • Magnetic moment ($\mu_{s}$): $\sqrt{5(5+2)} = \sqrt{35} \approx 5.92$ BM

Ordering the Magnetic Moments

Comparing the calculated magnetic moments:

• $[MnCl_4]^{2–}$ ($\approx 5.92$ BM)
• $[CoCl_4]^{2–}$ ($\approx 3.87$ BM)
• $[NiCl_4]^{2–}$ ($\approx 2.83$ BM)
• $[ZnCl_4]^{2–}$ (0 BM)

Therefore, the correct order of spin-only magnetic moments is:

$[MnCl_4]^{2–}> [CoCl_4]^{2–}> [NiCl_4]^{2–}> [ZnCl_4]^{2–}$