Intuition The one core ideaA ligand (defined precisely in §0.5 below — for now, "the electron-lending guest") is a species that lends one of its spare electron pairs to a hungry metal ion, and the whole subject is just careful bookkeeping of how many electron-lending "hands" each ligand offers to one metal at one time. Get that counting right and you can predict the shape, stability, and even the colour of the complex — so before any of that, we must be fluent in every tiny symbol the parent note quietly assumed.
This page assumes nothing . Every arrow, charge, and word below is built from the ground up so that when you return to the parent topic every symbol is already an old friend.
Before symbols, a scene. Imagine a positively charged metal ion sitting alone. It is short of electrons — that is why it is positive. Now a small molecule floats in that happens to have a spare pair of electrons it isn't using for its own bonds. Opposites attract: the spare pair swings toward the metal and a bond forms.
Figure s01 — A positive metal ion Mn +
That single event — one spare pair reaching a metal — is the atom of this whole chapter. Everything else is counting how many such events happen.
A ligand donates a lone pair of electrons to a central metal atom or ion, forming a bond. (The parent note calls this a "Lewis base" — a name we build up properly in §4.)
In figure s01 the ligand is the blue circle L : it is defined by the fact that it has a spare pair and gives it away .
Intuition Why define the ligand firstEverything on this page is a property of a ligand — its donor atom, its denticity, its stability. So the ligand is the noun; the rest are adjectives. We pin it down now so every later idea has something to attach to. The pieces of this definition (lone pair, bond, Lewis base) are each unpacked below.
Definition Electron & lone pairAn electron sharing electrons in pairs.
A lone pair not already being shared in a bond — it is "free" and available to donate.
Intuition Why we care about the lone pairThe metal is electron-hungry (positive). The only thing a ligand can offer it is electrons. But not just any electron — a pair that isn't busy elsewhere. So the lone pair is the currency of the entire subject: no lone pair, no ligand.
Look at water, H 2 O two extra pairs doing nothing — those are its lone pairs. That is why oxygen , not hydrogen, is the part of water that grabs a metal.
Figure s02 — A water molecule. The lines to the two H atoms are shared "busy" pairs (bonds). The yellow dots on top of oxygen are its two lone pairs — the free ones. This picture is why we always say the donor atom of water is oxygen , reinforcing §1's point that only free pairs can be donated.
The little number is how many units of charge; the sign is which way . No number means "just one" (so C l − − 1
Intuition Why charge matters hereMetals become ligand-grabbers because they are positive (+ − + −
Common mistake Charge on the ion ≠ number of bonds it makesWrong idea: "C a 2 + + 2 Fix: Charge and the number of metal–ligand bonds are different ideas. (That bond-count has its own name, the coordination number , which we meet in §5 and study fully in Coordination Number .) In fact C a 2 + six donor atoms at once. We count bonds , not charge .
Definition Ordinary bond vs coordinate (dative) bondIn an ordinary covalent bond , each atom donates one electron to the shared pair.
In a coordinate bond dative bond), one atom donates both electrons of the pair. We often draw it as an arrow → from the donor to the metal.
Figure s03 — Left: an ordinary bond where atoms A and B each contribute one electron (one yellow, one blue dot). Right: a coordinate bond where the ligand L supplies both electrons (two yellow dots) into metal M, drawn as a yellow arrow. This contrast is exactly why metal–ligand bonds are drawn with an arrow, as claimed in §3.
Intuition Why the arrow, not a plain line?The arrow reminds us where the electrons came from . In coordination chemistry all metal–ligand bonds are this one-sided kind: the ligand brings the whole pair, the metal brings only an empty space. That asymmetry is exactly what "donor" means.
The word donor atom now has a picture: it is the specific atom the arrow starts from — the one holding the lone pair that reached the metal.
Definition Lewis base and Lewis acidA Lewis base donates a lone pair.
A Lewis acid accepts a lone pair (it has an empty spot).
In our scene: ligand = Lewis base , metal ion = Lewis acid .
Intuition Why rename things we already pictured?It's the same arrow from §3, just with role-names. Calling the ligand a "Lewis base" lets us borrow all the reasoning of Lewis Acids and Bases : strong donors bind tightly, empty-orbital metals accept eagerly. The vocabulary connects this topic to the wider acid–base world.
Mnemonic Base gives, acid takesB ase = B ig-hearted, gives away its pair. Acid A ccepts.
Now that "one arrow = one donated pair" is solid, we can count arrows per ligand .
Denticity one ligand that send arrows into the same metal, at the same time .
The name comes from dens = tooth : "how many teeth bite the metal."
Definition Coordination numberThe coordination number total number of donor-atom arrows reaching one metal, summed over all its ligands. You get it by adding up (denticity × how many of that ligand). Full treatment: Coordination Number .
The two small words in the denticity definition are the whole game:
"same metal" — a ligand bridging two metals is a different scenario."same time" — a ligand that could use either of two atoms but only uses one at once is still denticity 1.
Figure s04 — One ligand (a backbone linking two N donor atoms in blue) sending two yellow arrows into the same metal M at the same time. Two arrows ⇒ denticity 2 ⇒ "bidentate," exactly matching the two-word test in §5.
Intuition Why denticity is the master numberOnce you know each ligand's denticity, you get the Coordination Number for free by the multiply-and-add rule above. Denticity also drives the stability (the chelate effect) and connects to Linkage Isomerism for ambidentate cases. It is the single number the whole chapter revolves around.
These are just spoken forms of a number. When you read "hexadentate EDTA," translate instantly: six arrows from one ligand.
Definition EDTA — the standard exampleEDTA ethylenediaminetetraacetate (the 4 − EDTA 4 − 6 donor atoms : 2 nitrogen atoms plus 4 oxygen atoms (one from each of its four − C O O − hexadentate (denticity 6) — it folds around the metal like a cage. This is why [ Ca(EDTA) ] 2 − C a 2 + + 2 EDTA Titrations .
The parent note uses Δ G Δ H Δ S K R T ln ∘
Definition The standard-state symbol∘ Δ G ∘ "measured at standard conditions" — a fixed agreed reference (usually 1 mol L− 1 same rules so the numbers are comparable. Read "Δ G ∘
Definition The thermodynamics alphabet
Δ "change in" — the value after minus before .Δ H ∘ standard enthalpy change : roughly the heat released or absorbed. Negative Δ H ∘ Δ S ∘ standard entropy change : how much more spread-out / disordered things become. More loose particles = larger positive Δ S ∘ T Δ G ∘ standard Gibbs free-energy change : the overall referee. Negative Δ G ∘ They tie together as Δ G ∘ = Δ H ∘ − T Δ S ∘
K stability constant : a big number means "complex strongly formed."R gas constant , a fixed number equal to 8.314 J mol − 1 K − 1 R T ln Δ G ∘ = − R T ln K
ln ratio of amounts (products over reactants, which multiply) into a sum of energies (which add). The logarithm is exactly the tool that "turns multiplying into adding." That is the one job ln Δ G ∘ = − R T ln K Stability Constants of Complexes — here we only need to recognise the symbols.
Intuition How to read the diagram belowThis is a dependency map . Each box is one idea you built above. An arrow A → B — follow the arrows and you are walking in the order this page taught them. Everything funnels into the parent topic at the bottom.
charge signs plus and minus
Lewis base gives Lewis acid takes
denticity count of arrows
number prefixes mono bi poly
classification of ligands
Parent topic Ligands and denticity
Each box is a symbol or idea you just built; the arrows show which understanding feeds which. Notice everything funnels into denticity , and denticity feeds the three payoffs — classification, Coordination Number , and stability .
Cover the right side and answer aloud; reveal to check.
Ligand An ion or molecule that donates a lone pair to a central metal, forming a bond (a Lewis base).
Lone pair A pair of electrons on an atom not used in any bond — the "spare" pair a ligand donates.
Donor atom The specific atom of a ligand that holds the lone pair and forms the bond (e.g. O in water).
Coordinate (dative) bond A bond where one atom supplies both shared electrons; drawn as an arrow from donor to metal.
The arrow → Shows electrons flowing from the ligand (donor) into the metal.
C l − Chloride ion carrying one negative charge (one extra electron).
C a 2 + Calcium ion missing two electrons, net charge + 2
Lewis base A lone-pair donor — this is what a ligand is.
Lewis acid A lone-pair acceptor with an empty spot — this is what the metal ion is.
Denticity Number of donor atoms of one ligand bonding the same metal at the same time .
Coordination number Total number of donor-atom bonds reaching one metal, summed over all ligands.
"bi-" in bidentate The number-prefix meaning 2 → two donor atoms bonding one metal.
EDTA Ethylenediaminetetraacetate; a hexadentate ligand with 2 N + 4 O donor atoms.
Δ "Change in" — the after-value minus the before-value.
The superscript ∘ "Standard conditions" — a fixed agreed reference so numbers are comparable.
Δ G ∘ Standard Gibbs free-energy change; negative means the reaction proceeds.
Δ S ∘ Standard entropy change; positive means more disorder / more free particles.
R 8.314 J mol − 1 K − 1
Why ln Δ G ∘ = − R T ln K The logarithm converts multiplied concentration ratios into added energies.
Denticity → coordination number Multiply denticity by number of that ligand, then sum over all ligands.
