Lesson 1 · 25 min

Complexes and ligands

Why can silver ions precipitate only two of the chlorides in CoCl₃·5NH₃? Werner’s answer founded coordination chemistry: central ion, ligands, coordination number and a naming system.

In this lesson

Use Werner’s coordination theory to separate inner and outer sphere, and read the number of outer ions from precipitation tests
Distinguish monodentate, bidentate and polydentate ligands, and recognise chelates
Find the oxidation state, coordination number and d-electron count from a formula
Name simple complexes by the Chinese and IUPAC rules

Add ammonia to pale-blue copper sulfate and a pale-blue precipitate appears; add more and it dissolves into a deep, jewel-like blue. Nineteenth-century chemists knew a whole class of puzzling “molecular compounds”: $\ce{CoCl3}$ binds 6, 5 or 4 molecules of $\ce{NH3}$ , giving yellow, purple-red and green (or violet) solids. Stranger still, silver nitrate precipitates 3, 2 and 1 equivalents of AgCl from them at once. Ammonia is already a “saturated” molecule — how can it bind anything more? And why can some chlorides be precipitated but not others?

Predict first

Green $\ce{CoCl3.4NH3}$ is dissolved and excess $\ce{AgNO3}$ added. How many AgCl precipitate at once per formula unit?

Pick an answer and lock it in before you look. A wrong guess teaches more than no guess.

0 1 2 3

Werner’s coordination theory

In 1893 the 26-year-old Werner proposed that a metal ion has, besides its ordinary valence (today’s oxidation state), a second “secondary valence”: the number of ligands it binds directly — the coordination number. The central ion and the ligands attached to it form the inner sphere, written in square brackets; ions present only to balance charge sit in the outer sphere. In water the inner sphere stays intact and only the outer ions separate. So $\ce{[Co(NH3)6]Cl3}$ gives 4 ions in solution, $\ce{[CoCl(NH3)5]Cl2}$ gives 3 and $\ce{[CoCl2(NH3)4]Cl}$ gives 2 — exactly what conductivity measurements showed.

Today a coordinate bond is seen as a Lewis acid–base interaction: the ligand (Lewis base) supplies a lone pair and the metal ion (Lewis acid) accepts it. The atom that donates the pair is the donor atom.

q_\text{complex} = x_\text{M} + \sum_i n_i q_i,\qquad d^{\,n}:\ n = \text{group} - x_\text{M}

The charge of a complex is the metal’s oxidation state plus all the ligand charges; a transition-metal ion has group number minus oxidation state d electrons.

$x_\text{M}$: oxidation state of the metal
$n_i,\ q_i$: number and charge of ligand i (NH₃ 0, Cl⁻ −1)
$d^{\,n}$: d-electron count, e.g. Co³⁺ (group 9) is d⁶

Ligands: one hand or several

Monodentate ligands bind through one atom: $\ce{H2O}$ , $\ce{NH3}$ , $\ce{Cl-}$ , $\ce{CN-}$ (through C), $\ce{CO}$ .
Bidentate ligands grip the metal with two atoms at once: the two N of ethylenediamine (en, $\ce{H2NCH2CH2NH2}$ ), the two O of oxalate.
Polydentate ligands: EDTA⁴⁻ wraps a metal ion with 2 N and 4 O — a hexadentate ligand.

A polydentate ligand closes rings through the metal, like a crab’s claw; such complexes are chelates. Some ligands can bind through different atoms (ambidentate): $\ce{NO2-}$ through N (nitro) or O (nitrito), $\ce{SCN-}$ through S or N.

The commonest coordination number is 6, then 4 and 2. Note that the coordination number counts donor atoms, not ligands.

Metal + ligands → charge, coordination number, d count and name

Complex builder and namer

Classic complexes Central metal Oxidation state

Ligands (tap + / −)

NH₃ 0 · denticity 1 0

H₂O 0 · denticity 1 0

Cl 1− · denticity 1 0

Br 1− · denticity 1 0

F 1− · denticity 1 0

OH 1− · denticity 1 0

CN 1− · denticity 1 0

CO 0 · denticity 1 0

NO₂ 1− · denticity 1 0

SCN 1− · denticity 1 0

en 0 · denticity 2 3

ox 2− · denticity 2 0

EDTA 4− · denticity 6 0

The builder stops at coordination number 6.

Counter-ion

Formula

\ce{[Co(en)3]Cl3}

Name tris(ethane-1,2-diamine)cobalt(III) chloride Other language: 三氯化三(乙二胺)合钴(III)

Charge of the complex: 3+
Coordination number: 6
d electrons: d6
Chelate rings: 3
Usual geometry: octahedral

Werner’s tests

Dissolved, each formula unit gives 4 ions

Excess AgNO₃ at once precipitates 3 AgCl per formula unit

Add and remove ligands with + / −: the charge, coordination number, d count and both names update at once. Swap the en of [Co(en)₃]³⁺ for six NH₃, then for three oxalates (the charge becomes 3− and the name takes -ate); choose Fe(II) with six CN⁻ for yellow prussiate.

Naming rules

English (IUPAC 2005): cation first, anion second; ligands in alphabetical order of their names (multiplying prefixes such as di- and tri- are ignored), anionic ligands ending -ido/-ato (chlorido, cyanido, oxalato), neutral ones aqua, ammine, carbonyl; an anionic complex takes the -ate form of the metal (ferrate, cuprate, argentate). Hence $\ce{[CoCl(NH3)5]Cl2}$ is pentaamminechloridocobalt(III) chloride and $\ce{K4[Fe(CN)6]}$ is potassium hexacyanidoferrate(II).

Chinese names (rules of the Chinese Chemical Society) are built the same way round: ligands before the metal, anionic ligands before neutral ones and inorganic before organic, with the oxidation state in Roman numerals, while an anionic complex is named like the salt of an acid. The Chinese version of this lesson spells out the examples.

Worked example

Potassium trioxalatoferrate(III)

Emerald-green $\ce{K3[Fe(C2O4)3]}$ decomposes in light and was once used for blueprints. Find iron’s oxidation state, coordination number and d count, and name it.

Concept check

What are the oxidation state and coordination number of cobalt in $\ce{[CoCl2(en)2]+}$ ?

+1, 4 +3, 4 +3, 6 +1, 6

Try the calculation

0.0100 mol of $\ce{[CoCl(NH3)5]Cl2}$ is dissolved and excess $\ce{AgNO3}$ added. How many moles of AgCl form at once?

Key takeaways

A complex joins a central metal ion (Lewis acid) with ligands (Lewis bases); the inner sphere is written in brackets, and outer ions separate in water.
The coordination number counts donor atoms: en and oxalate are bidentate, EDTA hexadentate, and polydentate ligands form chelate rings.
Complex charge = metal oxidation state + ligand charges; d count = group number − oxidation state.
In names the ligands come before the metal, with the oxidation state in Roman numerals; an anionic complex takes the -ate ending (in Chinese it is named like the salt of an acid).

Progress is stored only in this browser and never uploaded.

Data and references

IUPAC, Nomenclature of Inorganic Chemistry — IUPAC Recommendations 2005 (the “Red Book”), ch. IR-9 (coordination compounds).
中国化学会，《无机化学命名原则》（1980），科学出版社（1982）.
A. Werner, “On the constitution and configuration of higher-order compounds”, Nobel Lecture, 11 December 1913.
C. E. Housecroft, A. G. Sharpe, Inorganic Chemistry, 5th ed., Pearson (2018), ch. 7 (coordination complexes) and ch. 19.