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Ligands as Lewis bases, denticity and chelation, and the coordination number as the count of donor atoms bonded to the metal.
Paper packet. Every task here also exists on screen, where it is checked automatically; answers written on paper are not assessed by Nydus. When you are back at a device, enter your answers there.
By the end of this lesson you will be able to find the denticity of a ligand, the coordination number of a metal in any complex, and the number of chelate rings its ligands close.
You know that a Lewis base donates an electron pair and a Lewis acid accepts one, and that a dative (coordinate) bond is a covalent bond whose two electrons both came from one partner. You can find the lone pairs in a molecule from its Lewis structure. From the last lesson you can find a metal's oxidation state in a complex. This lesson counts how many atoms are bonded to that metal and how the ligands arrange themselves to reach it.
| Term | What it means |
|---|---|
| Donor atom | The atom of a ligand whose lone pair forms the bond to the metal. |
| Coordination number | The number of donor atoms bonded to the metal. |
| Denticity | The number of donor atoms one ligand bonds through at the same time. |
| Monodentate | Bonding through one donor atom, like water, ammonia or chloride. |
| Bidentate | Bonding through two donor atoms, like ethylenediamine (en) or oxalate (ox). |
| Chelate | A complex in which a ligand bonds through two or more donor atoms, closing a ring through the metal. |
| Ambidentate ligand | A ligand that can bond through either of two different atoms, like $\mathrm{SCN^-}$ (through S or N). |
Every bond from a ligand to a metal is a Lewis acid–base bond: the ligand's donor atom supplies an electron pair, and the metal, short of electrons, accepts it. In ammonia the donor atom is nitrogen, with its lone pair; in water it is oxygen; in cyanide it is carbon. The number of donor atoms bonded to the metal is its coordination number. In $\mathrm{[Co(NH_3)_6]^{3+}}$ six ammonia molecules each give one nitrogen, so the coordination number is $6$.
Some ligands have more than one donor atom, spaced so that all of them can reach the same metal at once. The number of donor atoms a ligand uses is its denticity, from the Latin for tooth. Ethylenediamine, $\mathrm{H_2NCH_2CH_2NH_2}$, abbreviated en, has a nitrogen at each end of a two-carbon chain and bonds through both: it is bidentate. Oxalate, $\mathrm{C_2O_4^{2-}}$, bonds through two oxygens. Diethylenetriamine, dien, has three nitrogens and is tridentate, and EDTA wraps a metal with two nitrogens and four oxygens: it is hexadentate.
A ligand that bonds through two or more donor atoms closes a ring that runs from the metal through the ligand and back, and the complex is called a chelate, from the Greek for a crab's claw. Each extra donor atom closes one more ring, so a ligand of denticity $k$ closes $k - 1$ rings.
The rule for the coordination number is then simple:
$$\text{coordination number} = \sum (\text{number of each ligand}) \times (\text{its denticity}).$$
In $\mathrm{[Co(en)_3]^{3+}}$ there are three ligands but six donor atoms, so the coordination number is $3 \times 2 = 6$. In $\mathrm{[Ni(en)_2Cl_2]}$ it is $2 \times 2 + 2 \times 1 = 6$. In $\mathrm{[Co(EDTA)]^-}$ a single ligand supplies all six. The coordination number is almost always $2$, $4$ or $6$ for the first-row metals, with $6$ by far the commonest, and it decides the complex's shape, which is the subject of the next unit.
Another way: picture
Picture the metal as a ball with six hooks around it. A monodentate ligand is a hand that grips one hook; a bidentate ligand is a pair of hands joined by a short arm, gripping two neighboring hooks; EDTA is a creature with six hands that takes every hook at once. However many creatures there are, the coordination number is the number of hooks held, six, and each creature with several hands makes a closed loop with the ball.
Another way: steps
| Ligand | Abbreviation | Donor atoms | Denticity | Charge |
|---|---|---|---|---|
| water | — | O | $1$ | $0$ |
| ammonia | — | N | $1$ | $0$ |
| chloride | — | Cl | $1$ | $-1$ |
| cyanide | — | C | $1$ | $-1$ |
| carbon monoxide | — | C | $1$ | $0$ |
| ethylenediamine | en | N, N | $2$ | $0$ |
| oxalate | ox | O, O | $2$ | $-2$ |
| 2,2'-bipyridine | bipy | N, N | $2$ | $0$ |
| acetylacetonate | acac | O, O | $2$ | $-1$ |
| diethylenetriamine | dien | N, N, N | $3$ | $0$ |
| ethylenediaminetetraacetate | EDTA | N, N, O, O, O, O | $6$ | $-4$ |
Two things decide whether a molecule can act as a chelating ligand. It needs two or more atoms with lone pairs, and they must be spaced so that both can reach the metal without straining the ring. The most stable chelate rings have five members: in en the ring is metal, nitrogen, carbon, carbon, nitrogen, and in oxalate it is metal, oxygen, carbon, carbon, oxygen. Hydrazine, $\mathrm{H_2N{-}NH_2}$, has two nitrogens but they are too close together to chelate; it bonds through one, or bridges two metals.
A few monodentate ligands have two different atoms that could donate, and bond through one or the other. Thiocyanate, $\mathrm{SCN^-}$, bonds to soft metals such as mercury through sulfur and to harder metals such as iron(III) through nitrogen; nitrite, $\mathrm{NO_2^-}$, bonds through nitrogen (nitrito-N) or through an oxygen (nitrito-O). Such ligands are ambidentate, and the two ways of bonding give the linkage isomers of lesson 7. An ambidentate ligand still counts one toward the coordination number, because only one of its atoms bonds at a time.
Some ligands bond to two metals at once and hold them together; they are bridging ligands, marked $\mu$ in a formula. Hydroxide and chloride often bridge, and so does oxide. A bridging chloride counts toward the coordination number of each metal it touches. This course's complexes all have a single metal, but bridges are how many minerals and enzymes link metal centers together.
The coordination number is a balance. A metal ion attracts as many ligands as it can fit, because every bond releases energy, but the ligands crowd one another and repel each other's electron pairs. For a first-row ion with a charge of $+2$ or $+3$ and a radius near $70$ pm, six ligands the size of water or ammonia fit comfortably at the corners of an octahedron, and six is the usual answer.
Smaller or softer ions, or bulky ligands, give lower numbers. Copper(I) and silver(I) are often two-coordinate, as in $\mathrm{[Ag(NH_3)_2]^+}$; zinc(II), nickel(II) and platinum(II) are often four-coordinate. Large ions give higher numbers: gadolinium(III), with a radius near $100$ pm, is nine-coordinate in the MRI contrast agents. Because the coordination number sets the geometry, and the geometry sets the d-orbital splitting, this count is the first thing to find about any complex.
The coordination number counts donor atoms, not ligands, so the first check is to go round the metal atom by atom. A chelating ligand such as ethylenediamine contributes two, oxalate two and EDTA six; an ambidentate ligand such as thiocyanate contributes one, because only one of its atoms binds at a time.
The second check is the size of the answer. Most complexes of the first-row metals have coordination number four or six, silver(I) and gold(I) often have two, and counts of seven, eight or nine belong mostly to large ions such as the lanthanides. A count of five or seven for an ordinary cobalt(III) complex is a sign that a donor atom was dropped or counted twice.
The third check looks ahead to lesson 6: the number should agree with the shape. Six donor atoms mean an octahedron, four a tetrahedron or a square plane, two a straight line.
EDTA grips a metal ion through six atoms at once, closing five chelate rings, and that grip is strong enough to hold almost any metal ion out of reach. Food manufacturers add calcium disodium EDTA to mayonnaise, salad dressing and canned beans, at up to about $75$ parts per million in dressings, to lock up the traces of iron and copper that would otherwise catalyze the oxidation of fats and turn the product rancid. Shampoos and detergents carry it to bind calcium and magnesium from hard water, which would otherwise precipitate with the soap.
Medicine uses the same grip. In lead poisoning, calcium disodium EDTA given intravenously trades its calcium for lead: lead(II) binds EDTA about $10^{7}$ times more strongly than calcium does, so the lead is pulled from the tissues and carried out in the urine as a soluble complex. The calcium form is used rather than plain sodium EDTA so that the drug does not strip calcium from the blood, a mistake that has caused deaths when the two were confused. Lesson 17 puts numbers on why six donor atoms in one molecule hold so much more tightly than six separate ones.
Each of the four heme groups in a hemoglobin molecule holds one iron(II) ion inside a porphyrin, a flat ring with four nitrogen donor atoms pointing inward. The porphyrin supplies four of the iron's six positions. A fifth is a nitrogen from a histidine side chain of the protein, below the ring, and the sixth, above the ring, is where an oxygen molecule binds in the lungs and is released in the tissues. The coordination number is $4 + 2 = 6$ when oxygen is bound and $5$ when it is not.
Carbon monoxide poisons by taking that sixth position: it binds heme iron about $200$ times more strongly than oxygen does, so air with only $0.1\%$ carbon monoxide can occupy half the hemoglobin in a few hours. Treatment is breathing pure oxygen, which shortens carbon monoxide's half-life in the blood from about five hours to about one hour by competing for the same site. Counting the donor atoms is what shows that there is only one free site to fight over.
The formula shows ligands, and it is natural to count what the formula shows. For $\mathrm{[Co(NH_3)_6]^{3+}}$ that gives the right answer, six, because each ammonia bonds once. For $\mathrm{[Co(en)_3]^{3+}}$ it gives three, when the cobalt is bonded to six nitrogen atoms and has the same octahedral shape as the ammine complex. The coordination number is about the metal: how many atoms touch it. A chelating ligand touches it more than once.
The opposite slip is to count a large ligand's atoms rather than its donor atoms. EDTA contains ten carbons, two nitrogens and eight oxygens, but only six of those atoms, the two nitrogens and one oxygen of each carboxylate, bond to the metal. Denticity counts the atoms that bond, and a ligand's table entry is the place to look it up, not its molecular formula.
List the ligands.
$6 \times \mathrm{NH_3}$
Six ammonia molecules sit inside the brackets.
Give each its denticity.
$\mathrm{NH_3}: k = 1$
Ammonia bonds through its one nitrogen lone pair.
Multiply and add.
$6 \times 1 = 6$
One donor atom from each of six ligands.
Count the chelate rings.
$6 \times (1 - 1) = 0$
Monodentate ligands close no rings.
Check the result.
$\text{CN} = 6 = \text{number of ligands}$
With only monodentate ligands, the two counts agree.
List the ligands.
$3 \times \mathrm{en}$
Three ethylenediamine molecules.
Give en its denticity.
$\mathrm{en}: k = 2$
It bonds through the nitrogen at each end of its carbon chain.
Multiply and add.
$3 \times 2 = 6$
Three ligands supply six donor atoms.
Count the chelate rings.
$3 \times (2 - 1) = 3$
Each en closes one five-membered ring through the cobalt.
Check with the shortcut.
$\text{rings} = 6 - 3 = 3$
Donor atoms minus ligands gives the rings.
Compare with the wrong count.
$\text{ligands} = 3 \ne \text{CN} = 6$
Counting ligands would suggest a three-coordinate cobalt, which is not what is there.
List the ligands in $\mathrm{[Ni(en)_2Cl_2]}$.
$2 \times \mathrm{en}, \quad 2 \times \mathrm{Cl^-}$
Two kinds of ligand, two of each.
Give each its denticity.
$\mathrm{en}: 2, \quad \mathrm{Cl^-}: 1$
En chelates; chloride bonds through one atom.
Multiply and add.
$2 \times 2 + 2 \times 1 = 6$
Four nitrogens and two chlorines.
Count the chelate rings.
$2 \times 1 + 2 \times 0 = 2$
Only the en ligands close rings.
Check with the shortcut.
$6 - 4 = 2$
Six donor atoms, four ligands, two rings.
Find the charge of the complex.
$(+2) + 2 \times 0 + 2 \times (-1) = 0$
Nickel(II), two neutral en and two chlorides: a neutral complex, which is why it has no brackets' charge.
Give oxalate its denticity.
$\mathrm{C_2O_4^{2-}}: k = 2$
It bonds through one oxygen on each carbon.
Multiply and add.
$3 \times 2 = 6$
Three oxalates supply six donor atoms.
Count the rings.
Match each ligand to the number of donor atoms it binds through.
| monodentate (1 donor atom) | bidentate (2 donor atoms) | tridentate (3 donor atoms) | hexadentate (6 donor atoms) | |
|---|---|---|---|---|
| water | ||||
| ethylenediamine (en) | ||||
| diethylenetriamine (dien) | ||||
| EDTA |
Complete the worked solution for the magnesium in chlorophyll. It is bound by a chlorin ring, which supplies $4$ donor atoms, and by $1$ other donor atoms. What is its coordination number?
Say what the coordination number counts here.
$\text{CN} = (\text{large ligand's donor atoms}) + (\text{other donor atoms})$
Every atom bonded to the metal counts once, whichever ligand it belongs to.
Add the other donor atoms to those of the large ligand.
$\text{CN} = (\text{large ligand's donor atoms}) + (\text{other donor atoms}) =$ c
The coordination number counts every donor atom bonded to the metal.
Check the size of the count.
$\text{CN} > \text{large ligand's donor atoms}$
The other donor atoms can only add to the count; a total no larger means one was dropped.
What is the coordination number of the metal in $\mathrm{[Cr(acac)_3]}$?
Fill in the table for $\mathrm{[Co(NH_3)_6]^{3+}}$, $\mathrm{[Ni(en)_2Cl_2]}$ and $\mathrm{[Ni(en)_3]^{2+}}$, in that order.
| ligands | coordination number | chelate rings | |
|---|---|---|---|
| the first complex | |||
| the second complex | |||
| the third complex |
The complex $\mathrm{[Co(NH_3)_4(C_2O_4)]^{+}}$ has $5$ ligands. What is the coordination number of its metal?
Answer: donor atoms bonded to the metal
How many chelate rings does the complex $\mathrm{[Co(EDTA)]^{-}}$ contain? Its coordination number is $6$.
Answer: chelate rings around the metal
Three metal centers: the cobalt in vitamin B12, held by a corrin ring and $2$ other donor atoms; the gadolinium in the MRI contrast agent gadoterate, held by the ligand DOTA and $1$ others; and the calcium in calcium disodium EDTA, a food preservative, held by EDTA and $0$ others. For each, in that order, fill in the donor atoms the large ligand supplies and the coordination number. A porphyrin, corrin or chlorin ring supplies $4$; DOTA supplies $8$; EDTA supplies $6$.
| donor atoms from the large ligand | coordination number | |
|---|---|---|
| the first center | ||
| the second center | ||
| the third center |
Lesson test: one question per skill, one attempt each, no hints. Your answers are checked when you submit.
Fill in the table for $\mathrm{[Fe(CO)_5]}$, $\mathrm{[Ni(en)_2Cl_2]}$ and $\mathrm{[Ni(en)_3]^{2+}}$, in that order.
| ligands | coordination number | chelate rings | |
|---|---|---|---|
| the first complex | |||
| the second complex | |||
| the third complex |
You can count donor atoms and chelate rings. Explain to someone why $\mathrm{[Co(en)_3]^{3+}}$ is six-coordinate although it has only three ligands.
15. Your turn: what is the coordination number of the metal in $\mathrm{[Fe(C_2O_4)_3]^{3-}}$?, step 3
$6 - 3 = 3$
One ring per oxalate.