Sidgwick EAN Rule: Effective Atomic Number Calculations
In Class 12 board examinations and entrance tests like JEE Main, NEET UG, and CUET UG, coordination chemistry is a central scoring chapter. While crystal field theory explains spectra, coordination stability was first systematised by Nevil Sidgwick using the Effective Atomic Number (EAN) rule. Calculating the EAN provides a reliable method to verify electron counts, evaluate stability, deduce magnetic character, and explain metal carbonyl bonding.
Concept and Principles of Sidgwick's EAN Rule
Nevil Sidgwick extended the octet rule to transition metal complexes, postulating that the central metal atom or ion accepts electron pairs from ligands until total electrons around the metal match the next noble gas.
The target noble gas configurations are:
• 3d series (Sc to Zn): Krypton (Kr, Z = 36)
• 4d series (Y to Cd): Xenon (Xe, Z = 54)
• 5d series (La to Hg): Radon (Rn, Z = 86)
When a complex reaches the atomic number of the next noble gas, its valence orbitals are completely filled, providing high stability. Complexes not reaching the noble gas count may still exist stably, but they are often reactive, easily oxidised or reduced, or paramagnetic.
The EAN Formula and Electron Counting Methods
To determine the Effective Atomic Number of a transition metal in a coordination entity, use the standard formula:
EAN = Z − OS + Le + Mb
For complexes with monodentate 2-electron ligands:
EAN = Z − OS + (2 × CN)
Variables and Units:
• Z = Atomic number of central metal
• OS = Oxidation state of central metal (subtracted algebraically)
• Le = Total electrons donated by ligands (2 electrons per coordinate bond)
• CN = Coordination number (number of donor atom bonds)
• Mb = Electrons from metal-metal bonds (1 electron per single bond)
Exam details
- Source: practice problem written for this article (not a past-paper question)
- Relevant exams: CBSE Class 12, ISC Class 12, State Boards, JEE Main, NEET UG, CUET UG
- Topic: Coordination Chemistry - Sidgwick Effective Atomic Number (EAN) Rule
- Difficulty: School / Foundation
Worked Numerical Examples
Question: Calculate the Effective Atomic Number (EAN) of iron in [Fe(CN)6]4− and state whether it follows Sidgwick's EAN rule. The atomic number of iron is Z = 26.
Step 1: Find the oxidation state of iron.
Let x be the oxidation state of Fe.
Cyanide has charge −1: x + 6(−1) = −4 ⇒ x = +2 (Fe2+).
Step 2: Determine electrons on the metal ion.
Electrons on Fe2+ = Z − OS = 26 − 2 = 24 electrons.
Step 3: Count ligand electrons donated.
Six monodentate CN− ligands donate: 6 × 2 = 12 electrons.
Step 4: Compute EAN.
EAN = 24 + 12 = 36.
This matches Krypton (Z = 36), so the complex obeys Sidgwick's EAN rule.
Second Route Verification:
Apply the 18-electron valence rule: Fe(II) has 6 valence electrons (d6).
Six CN− ligands donate 12 electrons. Valence count = 6 + 12 = 18 electrons.
EAN = 18 (core) + 18 (valence) = 36. Both methods give 36.
Answer: EAN = 36 (obeys Sidgwick EAN rule, matching Krypton)
Question: Calculate the Effective Atomic Number (EAN) of copper in [Cu(NH3)4]2+. The atomic number of copper is Z = 29. State whether it obeys the EAN rule and deduce its magnetic character.
Step 1: Find the oxidation state of copper.
Ammonia (NH3) is neutral (charge 0). Oxidation state of copper = +2 (Cu2+).
Step 2: Determine electrons on the metal ion.
Electrons on Cu2+ = Z − OS = 29 − 2 = 27 electrons.
Step 3: Count ligand electrons donated.
Four monodentate ammine ligands donate: 4 × 2 = 8 electrons.
Step 4: Compute EAN.
EAN = 27 + 8 = 35.
Because Kr has Z = 36, the complex falls short by 1 electron and does not follow the EAN rule.
Second Route Verification:
Valence count: Cu(II) has 9 valence electrons (d9).
Four NH3 ligands donate 8 electrons. Valence count = 9 + 8 = 17 electrons.
EAN = 18 (core) + 17 = 35 electrons.
An odd electron count indicates one unpaired electron, making the complex paramagnetic. Both routes confirm 35.
Answer: EAN = 35 (does not obey Sidgwick EAN rule, paramagnetic)
Question: Calculate the Effective Atomic Number (EAN) per manganese atom in dimanganese decacarbonyl, Mn2(CO)10, which contains a metal-metal bond. The atomic number of manganese is Z = 25.
Step 1: Determine oxidation state and ligand donation.
CO is a neutral ligand, so manganese is in the 0 oxidation state (Mn0).
Each Mn atom bonds to 5 terminal CO ligands: 5 × 2 = 10 electrons.
Step 2: Account for the metal-metal bond.
The single Mn−Mn covalent bond donates 1 electron to each manganese atom (Mb = 1).
Step 3: Compute EAN per manganese atom.
EAN = Z − OS + Le + Mb = 25 − 0 + 10 + 1 = 36.
This matches Krypton (Z = 36).
Second Route Verification:
Valence count per Mn: Mn(0) is Group 7 (7 electrons).
Five CO ligands give 10 electrons. The Mn−Mn bond gives 1 electron.
Valence count = 7 + 10 + 1 = 18 electrons.
EAN = 18 (core) + 18 (valence) = 36 per Mn atom. Both methods match.
Answer: EAN = 36 per manganese atom (obeys Sidgwick EAN rule, matching Krypton)
Specific Mistakes Students Make
- Adding instead of subtracting oxidation state: For positive metal ions, subtract the charge. A Fe2+ ion loses 2 electrons, so use 26 − 2 = 24, not 26 + 2.
- Misidentifying ligand denticity: Bidentate ligands like oxalate or ethylenediamine donate 4 electrons each (2 pairs), not 2 electrons.
- Forgetting metal-metal bond electrons: In dinuclear carbonyls like Mn2(CO)10, each single M−M bond contributes 1 electron per metal atom.
- Assuming non-EAN complexes are unstable: Many square planar complexes of Pt(II) and Ni(II) have 16 valence electrons and are stable without obeying EAN.
- Using wrong noble gas target: For 3d metals the target is Kr (36); for 4d metals it is Xe (54); for 5d metals it is Rn (86).
Exam Relevance and Question Patterns
| Examination | How the Topic Is Tested | Key Concepts Emphasised |
|---|---|---|
| CBSE Class 12 & State Boards | Short answer questions determining EAN and checking noble gas configuration. | Applying EAN formula, oxidation states, and ligand electron donation. |
| JEE Main | Numerical questions finding EAN or identifying complexes obeying the EAN rule. | Counting electrons in mixed-ligand complexes and bridging carbonyls. |
| NEET UG | Multiple-choice questions linking EAN to magnetic character and stability. | Recognising Kr (36), Xe (54), and Rn (86) targets, and spotting odd electron species. |
| CUET UG | Assertion-reason questions comparing EAN rule with crystal field theory. | Understanding successes and limitations of Sidgwick model. |
Turn this concept into marks: solve previous-year CSIR-NET questions and take a timed quiz.
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