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Step-by-Step Explanation
Step 1: Analyze Statement (a)
Statement (a) says: “Octahedral Co(III) complexes with strong-field ligands have very high magnetic moments.”
• In reality, a strong-field ligand causes greater splitting of the d-orbitals ($\Delta_0$) in an octahedral complex.
• For Co(III) (which has a $d^6$ configuration), with a strong-field ligand, the electrons tend to pair up in the lower-energy $t_{2g}$ orbitals, resulting in a low-spin arrangement.
• Low-spin complexes have fewer unpaired electrons and therefore a lower magnetic moment.
• Hence, saying they have “very high magnetic moments” is incorrect.
Step 2: Analyze Statement (b)
Statement (b) says: “When $ \Delta_0 < P$, the d-electron configuration of Co(III) in an octahedral complex is $t_{2g}^4\, e_g^2$.”
• $P$ refers to the pairing energy (the energy required to pair two electrons in the same orbital).
• If $ \Delta_0$ (octahedral crystal field splitting) is smaller than $P$, the compound tends to have a high-spin configuration.
• For Co(III) ($d^6$) under high-spin conditions, the electrons do not fully pair in the $t_{2g}$ level but occupy higher levels as well to minimize the overall energy cost.
• Hence, high-spin arrangement in an octahedral field for $d^6$ leads to $t_{2g}^4\, e_g^2$, which matches the statement.
Therefore, statement (b) is correct.
Step 3: Analyze Statement (c)
Statement (c) says: “Wavelength of light absorbed by [Co(en)3]3+ is lower than that of [CoF6]3–.”
• The complex [Co(en)3]3+ involves ethylenediamine (en), which is a stronger field ligand than fluoride (F–).
• A stronger field ligand produces larger crystal field splitting ($\Delta_0$).
• A larger splitting ($\Delta_0$) means the absorbed photon’s energy is higher, so its wavelength is lower (since $E = \frac{hc}{\lambda}$).
• Hence, the wavelength absorbed by [Co(en)3]3+ indeed is lower than the wavelength absorbed by [CoF6]3–.
• Therefore, the statement (c) is correct.
Step 4: Analyze Statement (d)
Statement (d) says: “If the $ \Delta_0$ for an octahedral complex of Co(III) is 18,000 cm−1, the $ \Delta_t$ for its tetrahedral complex with the same ligand is 16,000 cm−1.”
• The relationship between the tetrahedral splitting ($ \Delta_t$) and octahedral splitting ($ \Delta_0$) for the same ligand is $ \Delta_t = \frac{4}{9}\,\Delta_0$.
• Substituting $ \Delta_0 = 18{,}000 \text{ cm}^{-1}$ gives:
$ \Delta_t = \frac{4}{9} \times 18{,}000 \text{ cm}^{-1} = 8{,}000 \text{ cm}^{-1}.$
• The statement claims $ \Delta_t = 16{,}000 \text{ cm}^{-1}$, which does not match this relation and is therefore incorrect.
Step 5: Conclusion
• Statement (a) is incorrect because strong-field Co(III) complexes are low spin (low magnetic moment), not high magnetic moment.
• Statement (d) is incorrect because $ \Delta_t$ should be $8{,}000 \text{ cm}^{-1}$, not $16{,}000 \text{ cm}^{-1}$.
• Therefore, the incorrect statements are (a) and (d).
