3.4.6 · D5Coordination Chemistry
Question bank — Effective Atomic Number (EAN) rule
True or false — justify
Each ligand contributes 2 electrons to the EAN count regardless of the ligand's own charge.
True for the counting — the Coordinate (dative) bond is one shared lone pair = 2 electrons, so the "" is fixed; the ligand's charge affects the oxidation state term, not the donated-electron term.
A complex whose EAN equals a noble-gas atomic number is guaranteed to exist and be stable.
False — EAN matching a Noble gas configuration is a stability heuristic, not a guarantee; existence depends on synthesis, sterics and thermodynamics, and many EAN-obeyers are still reactive.
If a complex violates the EAN rule it cannot be stable.
False — has EAN yet is perfectly stable; the rule is a guide that works best for Metal carbonyls and low-oxidation-state species.
EAN and the 18-electron rule can disagree about whether a given carbonyl is stable.
False — they are the same count read two ways; EAN counts all electrons aiming at a noble-gas , the 18-e rule counts only valence electrons, and both flip together.
Doubling the coordination number always increases EAN by twice the coordination number.
False as stated — adding donors raises the donated term by per new donor, but changing coordination often changes the oxidation state too, so the net EAN change is not simply "twice CN".
Two complexes with the same central metal always have the same EAN.
False — EAN depends on oxidation state and coordination number, not just the metal; e.g. Ni in gives 36 but Ni in gives 38.
The in the EAN formula is the atomic number of the metal ion, not the neutral atom.
False — is the neutral metal's atomic number; the ion's electron loss is handled separately by the "" term, so using ion double-counts the loss.
Nevil Sidgwick's rule targets the nearest noble gas, which for most transition-metal complexes is the next heavier one.
True in practice — the target is whichever noble-gas the EAN lands on, and for the common -block carbonyls that number is (Kr), the nearest heavier noble gas that closes the valence shell.
Spot the error
"In the oxidation state of Fe is because that's the bracket charge."
Error: bracket charge ≠ metal charge. Let be Fe's oxidation state; with six each , ; the Oxidation state of central metal is , not .
"Each of the 6 ligands makes one bond, so 6 ligands donate 6 electrons to EAN."
Error: one dative bond carries a lone pair = 2 electrons, not one; the donated total is , so multiply Coordination number by 2.
"For : EAN , so Ni's oxidation state must be ... wait, I subtracted nothing, error?"
No error — CO is neutral and the complex is neutral, so oxidation state is ; subtracting is legitimate, and EAN .
" — you add the charge because the ion is positive."
Error: you subtract the oxidation state. A positive charge means electrons were lost, so the count goes down: .
": Co is so it lost 3 electrons, leaving ."
Error: losing electrons decreases the count; electrons remain, then donated gives EAN .
"CO donates 2 electrons but donates 3 because it carries an extra charge."
Error: both are 2-electron σ-donors through one Coordinate (dative) bond; the extra charge on changes the oxidation-state arithmetic, never the donated-pair count.
"EAN for means the calculation is wrong somewhere."
Error: the arithmetic is correct (); the rule simply isn't obeyed here, which is allowed — EAN is a heuristic, not a conservation law.
Why questions
Why do we multiply the coordination number by exactly 2 rather than by the ligand's charge?
Because every ligand bonds by giving a lone pair through a dative bond, and a pair is always 2 electrons — the count is about donated electrons, independent of whatever formal charge the ligand carries.
Why do metal carbonyls obey EAN so reliably compared with ammine complexes?
In carbonyls the metal is in a low or zero oxidation state and CO is a strong σ-donor/π-acceptor, so the electron count naturally lands on 18 valence (noble-gas ); higher-oxidation ammines start electron-poorer and often overshoot or undershoot.
Why is "EAN " equivalent to "18 valence electrons"?
Kr has , of which an core holds 18 and the valence shell () holds the other 18; subtracting the fixed core from EAN leaves exactly the 18-electron valence count.
Why does the EAN formula start from the neutral metal's instead of the ion's electron count?
So the formula makes the electron loss explicit and traceable via the "" term; you always know the neutral from the periodic table, whereas ion counts must themselves be derived.
Why is the EAN rule called a rule and not a law?
A law admits no exceptions; EAN has many stable violators (e.g. , ), so it is a predictive guideline — strong for carbonyls, weaker elsewhere.
Why might a complex with EAN below the noble-gas number be reactive toward adding more ligands?
An electron-deficient (sub-noble-gas) metal has empty low-lying orbitals, so it "wants" more donated pairs to reach the closed-shell Noble gas configuration — driving further coordination.
Edge cases
For the metal oxidation state is : does the "" term simply vanish?
Yes — subtracting leaves the full metal electrons, then donated gives EAN ; a zero oxidation state is a valid, not a missing, case.
Do transition-metal complexes ever aim at the lighter noble gas Ar () instead of Kr?
Almost never in practice — a filled shell needs the count, so the EAN target for common -block complexes is the next heavier noble gas (usually ), not Ar; the "magic number" is fixed by which valence shell is being closed.
If a ligand is bidentate (two donor atoms on one molecule), how many electrons does it contribute?
4 electrons — coordination number counts donor atoms, so a bidentate ligand raises CN by 2 and donates via two dative bonds.
How do multi-electron donors like (3-electron) or cyclopentadienyl Cp (5–6 electron) break the simple "2 per ligand" rule?
They don't donate a single σ-pair only — as a linear donor gives 3 electrons and Cp as an ring gives 5–6 electrons, so for these you count their actual donated electrons, not a blanket .
Can a neutral complex still have a non-zero metal oxidation state?
Yes — if the ligands carry charges that sum to non-zero, the metal must balance them; e.g. neutral overall with two ligands forces the metal to , so "neutral bracket" does not imply "oxidation state ".
What happens to EAN if you (mistakenly) count a spectator counter-ion outside the brackets as a ligand?
You'd inflate both CN and the electron count wrongly — only atoms directly dative-bonded to the metal (inside the coordination sphere per Werner's theory) enter the EAN sum.
Recall One-line summary of the traps
EAN (Effective Atomic Number) : ordinary ligands give 2 electrons each (but gives 3 and Cp gives 5–6); oxidation state is bracket charge minus ligand charges; is the neutral metal's; and EAN matching a noble gas is a guide, so stable violators exist.
Connections
- EAN rule (parent) — the formula and worked examples these traps probe.
- Coordinate (dative) bond — source of the fixed "".
- Oxidation state of central metal — the trickiest term to get right.
- Coordination number — counts donor atoms, key to bidentate edge cases.
- 18-electron rule — the valence-only twin of EAN.
- Metal carbonyls — where the rule works best.
- Noble gas configuration — the stability target.