© All Rights reserved @ LearnWithDash
Step-by-Step Solution
Step 1: Determine the Electron Configuration of Fe³⁺
Iron (Fe) has an atomic number of 26, so its ground-state electron configuration is
[{\rm Ar}]\,3d^6\,4s^2 . Therefore, Fe³⁺ (which has lost three electrons) has the electron configuration
[{\rm Ar}]\,3d^5 .
Step 2: Identify the Nature of the Ligands
Two ligands are mentioned:
\mathrm{SCN^-} (thiocyanato-S): generally considered a weak ligand with respect to crystal field splitting.
\mathrm{CN^-} (cyanide): a strong ligand that produces a much larger splitting in the d -orbitals.
Step 3: Determine the Number of Unpaired Electrons in Each Complex
For an octahedral complex of Fe³⁺ with the weak ligand ( \mathrm{SCN^-} ), the crystal field splitting \Delta_{\text{o}} is not large enough to pair the electrons. Thus, all five d electrons remain unpaired:
Weak field: t_{2g}^3\, e_g^2 \rightarrow n = 5\text{ unpaired electrons.}
For an octahedral complex of Fe³⁺ with the strong ligand ( \mathrm{CN^-} ), the splitting is large and forces pairing in the lower t_{2g} orbitals, leaving fewer unpaired electrons:
Strong field: t_{2g}^5\, e_g^0 \rightarrow n = 1\text{ unpaired electron.}
Step 4: Use the Spin-Only Magnetic Moment Formula
The spin-only magnetic moment \mu_\mathrm{so} in Bohr magnetons (BM) is given by:
\mu_\mathrm{so} = \sqrt{n(n+2)}
where n is the number of unpaired electrons.
Step 5: Calculate the Magnetic Moments for Each Complex
With weak ligand ( \mathrm{SCN^-} ): n = 5
\mu_\mathrm{so} = \sqrt{5 \times (5+2)} = \sqrt{35} \approx 5.92\ \mathrm{BM}.
With strong ligand ( \mathrm{CN^-} ): n = 1
\mu_\mathrm{so} = \sqrt{1 \times (1+2)} = \sqrt{3} \approx 1.73\ \mathrm{BM}.
Step 6: Find the Difference in the Spin-Only Magnetic Moments
\Delta \mu = \mu_{\text{(weak ligand)}} - \mu_{\text{(strong ligand)}}
\approx 5.92\ \mathrm{BM} - 1.73\ \mathrm{BM}
= 4.19\ \mathrm{BM}.
Rounding to the nearest integer gives approximately 4 Bohr magnetons.
Final Answer
The difference between the spin-only magnetic moments in these two complexes is about 4 Bohr magnetons.
