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Step-by-Step Solution
Step 1: Identify the Metal Centers and Their Oxidation States
• (A) Ni(CO)4: The metal is Ni in the 0 oxidation state because CO is a neutral ligand. Thus, Ni has an electronic configuration of 3d84s2 in the free state.
• (B) [Ni(H2O)6]Cl2: Nickel ion is Ni2+. The electronic configuration of Ni2+ is 3d8.
• (C) Na2[Ni(CN)4]: Nickel is again in the +2 oxidation state with an electronic configuration of 3d8.
• (D) PdCl2(PPh3)2: Palladium is Pd2+. Palladium (Z=46) in +2 oxidation state has an electronic configuration of 4d8.
Step 2: Determine the Nature of the Ligands (Weak Field vs. Strong Field)
• CO and CN− are strong field ligands that cause pairing of electrons in the d-orbitals.
• H2O is a weaker field ligand, so pairing is less likely to occur, leaving unpaired electrons.
• In PdCl2(PPh3)2, the ligand environment around Pd2+ leads to a square planar dsp2 complex, which is usually associated with complete electron pairing for d8 metal ions.
Step 3: Count the Number of Unpaired Electrons in Each Complex
1. (A) Ni(CO)4:
• Strong field CO ligands pair all electrons.
• Number of unpaired electrons = 0.
2. (B) [Ni(H2O)6]Cl2:
• Ni2+ (3d8) with a weak field ligand (H2O).
• Typically, 2 unpaired electrons remain (t2g6 eg2 arrangement in octahedral crystal field).
• Number of unpaired electrons = 2.
3. (C) Na2[Ni(CN)4]:
• Ni2+ (3d8) with a strong field ligand (CN−).
• All electrons are paired.
• Number of unpaired electrons = 0.
4. (D) PdCl2(PPh3)2:
• Pd2+ (4d8) in a square planar dsp2 arrangement.
• Square planar d8 complexes usually have all electrons paired.
• Number of unpaired electrons = 0.
Step 4: Calculate the Spin-Only Magnetic Moments
The spin-only magnetic moment (in Bohr Magnetons, B.M.) is given by the formula:
$\mu_\text{spin} = \sqrt{n(n+2)}$,
where $n$ = number of unpaired electrons.
• For 0 unpaired electrons (as in A, C, D):
$ \mu_\text{spin} = 0 $ B.M.
• For 2 unpaired electrons (as in B):
$ \mu_\text{spin} = \sqrt{2(2+2)} = \sqrt{8} \approx 2.83 $ B.M.
Step 5: Arrange According to the Magnetic Moment Values
Since (B) has 2 unpaired electrons and thus a nonzero magnetic moment, and the others (A), (C), and (D) all have zero unpaired electrons, the order of increasing magnetic moment is:
(A) $\approx$ (C) $\approx$ (D) < (B).
Final Answer
The correct order of the calculated spin-only magnetic moments is:
(A) $\approx$ (C) $\approx$ (D) < (B)
