Question

Among the following complexes, the total number of diamagnetic species is ______.
[Mn(NH₃)₆]³⁺, [MnCl₆]³⁻, [FeF₆]³⁻, [CoF₆]³⁻, [Fe(NH₃)₆]³⁺, and [Co(en)₃]³⁺
[Given, atomic number: Mn = 25, Fe = 26, Co = 27;
en = H₂NCH₂CH₂NH₂]

Answer 1

Correct Answer: 1

Step 1: Understanding Diamagnetism 

• A species is diamagnetic if all its electrons are paired.
• Transition metal complexes can be classified based on their ligand field strength and electronic configuration.

Step 2: Electronic Configurations of the Metal Ions

• Mn³⁺: [Ar] 3d⁴
• Fe³⁺: [Ar] 3d⁵
• Co³⁺: [Ar] 3d⁶

Step 3: Determining the Magnetic Properties of Each Complex

• [Mn(NH₃)₆]³⁺ (NH₃ is a weak field ligand, high-spin d⁴ configuration) → Paramagnetic
• [MnCl₆]³⁻ (Cl^- is a weak field ligand, high-spin d⁴ configuration) → Paramagnetic
• [FeF₆]³⁻ (F^- is a weak field ligand, high-spin d⁵ configuration) → Paramagnetic
• [CoF₆]³⁻ (F^- is a weak field ligand, high-spin d⁶ configuration) → Paramagnetic
• [Fe(NH₃)₆]³⁺ (NH₃ is a weak field ligand, high-spin d⁵ configuration) → Paramagnetic
• [Co(en)₃]³⁺ (en is a strong field ligand, low-spin d⁶ configuration) → Diamagnetic

Step 4: Conclusion

• Only [Co(en)₃]³⁺ is diamagnetic.
• Total number of diamagnetic species = 1.

Answer 2

To solve the problem, determine the number of diamagnetic species among the given complexes by analyzing their oxidation states, d-electron counts, ligand field strengths, and spin states.

Given complexes:
1. \([Mn(NH_3)_6]^{3+}\)
2. \([MnCl_6]^{3-}\)
3. \([FeF_6]^{3-}\)
4. \([CoF_6]^{3-}\)
5. \([Fe(NH_3)_6]^{3+}\)
6. \([Co(en)_3]^{3+}\)

Step 1: Determine metal oxidation state and d-electron count

Complex	Metal	Oxidation State	d-electrons (dn)	Ligand Field Strength
[Mn(NH3)6]3+	Mn (25)	+3	d4	NH3 (strong field)
[MnCl6]3−	Mn	+3	d4	Cl− (weak field)
[FeF6]3−	Fe (26)	+3	d5	F− (weak field)
[CoF6]3−	Co (27)	+3	d6	F− (weak field)
[Fe(NH3)6]3+	Fe	+3	d5	NH3 (strong field)
[Co(en)3]3+	Co	+3	d6	en (strong field)

Step 2: Determine spin states and diamagnetism
- Diamagnetic means all electrons paired.

• [Mn(NH₃)₆]³⁺: d⁴ strong field → likely low spin → 2 unpaired electrons → paramagnetic
• [MnCl₆]³⁻: d⁴ weak field → high spin → 4 unpaired electrons → paramagnetic
• [FeF₆]³⁻: d⁵ weak field → high spin → 5 unpaired electrons → paramagnetic
• [CoF₆]³⁻: d⁶ weak field → high spin → 4 unpaired electrons → paramagnetic
• [Fe(NH₃)₆]³⁺: d⁵ strong field → low spin → 1 unpaired electron → paramagnetic
• [Co(en)₃]³⁺: d⁶ strong field → low spin → all electrons paired → diamagnetic

Step 3: Count diamagnetic species
Only <\(Co(en)_3]^{3+}\) is diamagnetic.

Final Answer:
\[ \boxed{1} \]