---
title: "Inner/outer orbital complexes; VBT of [Fe(CN)₆]³⁻"
subject: "Engineering Chemistry"
chapter: 6
key: "semester_2/engineering_chemistry:inner-outer-vbt-fecn6"
source: https://www.bctengineer.com/q/semester_2/engineering_chemistry/inner-outer-vbt-fecn6
site: BCT Engineering
---

# Inner/outer orbital complexes; VBT of [Fe(CN)₆]³⁻

Engineering Chemistry · Chapter 6: Coordination Complexes

- Asked in: 2071 Bhadra, 2+3 marks
- Video: [Inner and outer-orbital octahedral complexes](https://www.youtube.com/watch?v=hhTWbZL5WmQ) — Chem-Matics (Chemistry+ Mathematics)
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_2/engineering_chemistry/inner-outer-vbt-fecn6
- Whole chapter: https://www.bctengineer.com/md/semester_2/engineering_chemistry/chapter-6

## Question

What are the inner orbital and outer orbital complexes? Explain formation of [Fe(CN)₆]³⁻ on the basis of valence bond theory and predict its magnetic behavior.

## Short answer

Inner orbital complexes use (n-1)d orbitals (e.g., d2sp3), low spin; outer orbital use nd (sp3d2), high spin. [Fe(CN)6]3-: Fe3+ with strong CN- pairs d electrons, one unpaired, d2sp3 hybridization (inner orbital), octahedral, paramagnetic (μ=1.73 BM).

## Answer

#### Inner and outer orbital complexes
- **Inner orbital complex:** the metal uses inner (n−1)d orbitals for hybridisation (d²sp³ or dsp²). Strong-field ligands cause electron pairing, so these are low spin. Example: [Fe(CN)₆]³⁻.
- **Outer orbital complex:** the metal uses outer nd orbitals (sp³d²) and the d electrons stay unpaired with weak-field ligands. These are high spin. Example: [FeF₆]³⁻.

#### [Fe(CN)₆]³⁻
Fe³⁺ is 3d⁵. Strong-field CN⁻ forces the five d electrons to pair in two orbitals (one electron unpaired), freeing two 3d orbitals. These with 4s and three 4p give six **d²sp³** hybrids.
```text
3d: [↑↓][↑↓][↑ ][  ][  ]  4s [ ]  4p [ ][ ][ ]
                  \___ d²sp³ ___/
```
**Geometry:** octahedral, inner orbital. **Magnetism:** one unpaired electron, so paramagnetic, μ = 1.73 BM.

## Check yourself

The answer's key points as multiple-choice questions, with the correct option and why.

1. Which orbitals does an inner orbital complex use for hybridisation?
   A. outer nd
   B. only s
   C. only p
   D. inner (n-1)d orbitals
   Answer: D. The correct option is: inner (n-1)d orbitals. This follows from the answer on inner. (Key point: Inner)

2. An inner orbital complex formed with strong-field ligands is
   A. low spin
   B. high spin
   C. no spin
   D. random
   Answer: A. The correct option is: low spin. This follows from the answer on spin. (Key point: Spin)

3. How many unpaired electrons does [Fe(CN)6]3- have?
   A. 5
   B. 1
   C. 0
   D. 3
   Answer: B. The correct option is: 1. This follows from the answer on unpaired electrons. (Key point: Unpaired electrons)

4. Which is an outer orbital (high spin) complex?
   A. [Fe(CN)6]3-
   B. [Ni(CN)4]2-
   C. [FeF6]3-
   D. [Co(NH3)6]3+
   Answer: C. The correct option is: [FeF6]3-. This follows from the answer on outer. (Key point: Outer)

## Related in Engineering Chemistry

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