Unpaired Electrons in Complexes — आसान 3-Step Trick! | JEE Chemistry

 

❓ Concept

Goal: Count unpaired electrons in coordination complexes using a universal 3-step shortcut:
1️⃣ Oxidation state → 2️⃣ d-electron count → 3️⃣ Ligand strength → high/low spin → final unpaired electrons.

This removes the need for drawing full MO diagrams every time.

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✍️ Short Solution

To find unpaired electrons in any complex:

$$\text{Oxidation state} \rightarrow \text{d-electrons} \rightarrow \text{High/Low spin}$$

Everything depends on ligand strength (spectrochemical series).

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1️⃣ Step 1 — Find the Oxidation State

Use:

$$\text{Charge on complex} = \text{metal} + \sum(\text{ligand charges})$$

Then:

$$\text{d-electrons} = \text{atomic d-electrons} - \text{oxidation state}$$

Examples:

• Co (Z = 27) → atomic d = 9
  Co³⁺ → d = 9 – 3 = 6

• Fe (Z = 26) → atomic d = 8
  Fe³⁺ → d = 8 – 3 = 5

• Mn (Z = 25) → atomic d = 7
  Mn³⁺ → d = 7 – 3 = 4

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2️⃣ Step 2 — d-Electron Count Understood

This count determines which octahedral filling pattern applies.

Example:

• d⁴ → can be high spin (4 unpaired) or low spin (2 unpaired)

• d⁵ → high spin (5 unpaired) or low spin (1 unpaired)

• d⁶ → high spin (4 unpaired) or low spin (0 unpaired)

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3️⃣ Step 3 — Ligand Strength = Spin State

According to the spectrochemical series:

Strong field ligands → Low spin

They cause large Δ₀ → pair electrons early.
Examples:

• CN⁻

• CO

• NO₂⁻

Weak field ligands → High spin

Small Δ₀ → electrons spread out first.
Examples:

• F⁻

• Cl⁻

• H₂O

Intermediate

NH₃, oxalate (C₂O₄²⁻) — often low spin with Co³⁺.

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4️⃣ Fill into Octahedral d-Orbitals

Quick memory:

d-count	High Spin	Low Spin
d⁴	4 unpaired	2 unpaired
d⁵	5 unpaired	1 unpaired
d⁶	4 unpaired	0 unpaired

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5️⃣ Quick Application to the Given Complexes

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1. [Co(NH₃)₆]³⁺

• Co³⁺ → d⁶

• NH₃ = intermediate/strong for Co³⁺
  → Low spin

$$\boxed{{\displaystyle 0\text{ unpaired}}}$$

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2. [Co(C₂O₄)₃]³⁻

• Co³⁺ → d⁶

• Oxalate (bidentate) = moderate field, low spin for Co³⁺

$$\boxed{{\displaystyle 0\text{ unpaired}}}$$

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3. [MnCl₆]³⁻

• Mn³⁺ → d⁴

• Cl⁻ weak
  → High spin

$$\boxed{{\displaystyle 4\text{ unpaired}}}$$

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4. [Mn(CN)₆]³⁻

• Mn³⁺ → d⁴

• CN⁻ strong
  → Low spin

$$\boxed{{\displaystyle 2\text{ unpaired}}}$$

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5. [CoF₆]³⁻

• Co³⁺ → d⁶

• F⁻ weak
  → High spin

$$\boxed{{\displaystyle 4\text{ unpaired}}}$$

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6. [Fe(CN)₆]³⁻

• Fe³⁺ → d⁵

• CN⁻ strong
  → Low spin

$$\boxed{{\displaystyle 1\text{ unpaired}}}$$

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7. [FeF₆]³⁻

• Fe³⁺ → d⁵

• F⁻ weak
  → High spin

$$\boxed{{\displaystyle 5\text{ unpaired}}}$$

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✅ Final Summary Table

Complex	Unpaired e⁻
[Co(NH₃)₆]³⁺	0
[Co(C₂O₄)₃]³⁻	0
[MnCl₆]³⁻	4
[Mn(CN)₆]³⁻	2
[CoF₆]³⁻	4
[Fe(CN)₆]³⁻	1
[FeF₆]³⁻	5

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