The number of paramagnetic metal complex species among $ [Co(NH_3)_6]^{3+}, [Co(C_2O_4)_3]^{3-}, [MnCl_6]^{3-}, [Mn(CN)_6]^{3-}, [CoF_6]^{3-}, [Fe(CN)_6]^{3-} $ and $ [FeF_6]^{3-} $ with same number of unpaired electrons is _____.
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Correct Answer: 3
Approach Solution - 1
- $[Co(NH_3)_6]^{3+}$: Co3+ is a low-spin d6, having 0 unpaired electrons.
- $[Co(C_2O_4)_3]^{3-}$: Co3+ is again low-spin d6, 0 unpaired electrons due to oxalate's strong field.
- $[MnCl_6]^{3-}$: Mn3+ is a high-spin d4, having 4 unpaired electrons.
- $[Mn(CN)_6]^{3-}$: Mn3+ is a low-spin d4, having 2 unpaired electrons due to cyanide's strong field.
- $[CoF_6]^{3-}$: Co3+ is a high-spin d6, having 4 unpaired electrons.
- $[Fe(CN)_6]^{3-}$: Fe3+ is low-spin d5, having 1 unpaired electron.
- $[FeF_6]^{3-}$: Fe3+ is high-spin d5, having 5 unpaired electrons.
The final number is 2.
Approach Solution -2
Step 1: Determine the number of unpaired electrons for each complex using Crystal Field Theory.
\( [Co(NH_3)_6]^{3+} \) (\( d^6 \), strong field): 0 unpaired electrons (diamagnetic)
\( [Co(C_2O_4)_3]^{3-} \) (\( d^6 \), weak field): 4 unpaired electrons (paramagnetic)
\( [MnCl_6]^{3-} \) (\( d^4 \), weak field): 4 unpaired electrons (paramagnetic)
\( [Mn(CN)_6]^{3-} \) (\( d^4 \), strong field): 2 unpaired electrons (paramagnetic)
\( [CoF_6]^{3-} \) (\( d^6 \), weak field): 4 unpaired electrons (paramagnetic)
\( [Fe(CN)_6]^{3-} \) (\( d^5 \), strong field): 1 unpaired electron (paramagnetic)
\( [FeF_6]^{3-} \) (\( d^5 \), weak field): 5 unpaired electrons (paramagnetic)
Step 2: Identify the number of unpaired electrons for each paramagnetic species.
The paramagnetic species have 4, 4, 2, 4, 1, and 5 unpaired electrons respectively.
Step 3: Count the number of paramagnetic species that share the same number of unpaired electrons.
One unpaired electron: \( [Fe(CN)_6]^{3-} \) (1 species)
Two unpaired electrons: \( [Mn(CN)_6]^{3-} \) (1 species)
Four unpaired electrons: \( [Co(C_2O_4)_3]^{3-} \), \( [MnCl_6]^{3-} \), \( [CoF_6]^{3-} \) (3 species)
Five unpaired electrons: \( [FeF_6]^{3-} \) (1 species)
The maximum number of paramagnetic species with the same number of unpaired electrons is 3 (all having 4 unpaired electrons).
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