Part 2 · Chapter 19

Coordination Compounds

Metals at the centre of a molecular embrace — how ligands bind, how we name and picture the result, and the two great theories that explain their shape, colour and magnetism

Fundamentals of Chemistry Prof. Mithun Mondal Reading time ≈ 58 min

i What you'll learn

Werner's theory and the difference between primary and secondary valencies.
The vocabulary — central atom, ligands, coordination number, denticity, chelates.
How to name a coordination compound by IUPAC rules.
The kinds of isomerism: structural and stereo (geometrical, optical).
Valence bond theory (inner vs outer orbital) and crystal field theory (d-splitting).
The spectrochemical series, the origin of colour and magnetism, and the chelate effect.

Section 19-1

Werner's Theory

A coordination compound keeps its identity in solution: the metal and its attached groups stay together as a single complex ion. Alfred Werner explained this in 1893 by proposing that a metal exercises two kinds of valency. Unlike a double salt (which dissociates completely into its ions in water), a complex's inner set of bonds survives dissolution.

🔑

Werner's two valencies

Primary (ionizable, = oxidation state) · Secondary (non-ionizable, = coordination number, directional)

The primary valency is satisfied by negative ions and is ionizable. The secondary valency is satisfied by ligands, is fixed for a given metal, and points in fixed directions — so it determines the geometry of the complex.

How Werner proved it. Treating \(\ce{CoCl3.6NH3}\) with \(\ce{AgNO3}\) precipitates all three chlorides, but \(\ce{CoCl3.4NH3}\) precipitates only one — because the other two chlorides are bound inside the coordination sphere. Counting the "free" ions revealed the structure long before X-rays could.

Section 19-2

The Language of Complexes

Inside the square brackets sits the coordination sphere; outside sit the counter ions. A handful of terms describe everything within.

Term	Meaning	Example in \(\ce{[Co(NH3)6]Cl3}\)
Central atom/ion	the Lewis-acid metal	\(\ce{Co^3+}\)
Ligand	Lewis base donating a lone pair	\(\ce{NH3}\)
Coordination number	donor atoms bonded to metal	6
Coordination sphere	metal + ligands in brackets	\(\ce{[Co(NH3)6]^3+}\)
Counter ion	ion outside the brackets	\(3\ \ce{Cl-}\)
Oxidation number	charge on metal if ligands removed	\(+3\)

Section 19-3

Types of Ligands

Ligands are classed by how many donor atoms they offer — their denticity. A ligand that grips the metal at two or more points forms a ring called a chelate, named from the Greek for "claw".

Type	Donor atoms	Examples
Monodentate	one	\(\ce{Cl-},\ \ce{H2O},\ \ce{NH3},\ \ce{CN-}\)
Bidentate	two	ethylenediamine (en), oxalate (ox)
Polydentate	many	EDTA (hexadentate)
Ambidentate	one of two possible	\(\ce{NO2-}/\ce{ONO-},\ \ce{SCN-}/\ce{NCS-}\)

Ambidentate ligands have two faces. The nitrite ion can bind through nitrogen (nitro, \(\ce{-NO2}\)) or through oxygen (nitrito, \(\ce{-ONO}\)). Which atom it uses gives rise to linkage isomerism, met below.

Section 19-4

IUPAC Nomenclature

Naming follows a fixed recipe: name the cation before the anion; within the complex, list ligands alphabetically, then the metal with its oxidation state in Roman numerals. Anionic ligands end in -o; if the whole complex is an anion, the metal name takes the suffix -ate.

Ligand	Name	Ligand	Name
\(\ce{Cl-}\)	chlorido	\(\ce{H2O}\)	aqua
\(\ce{CN-}\)	cyanido	\(\ce{NH3}\)	ammine
\(\ce{OH-}\)	hydroxido	\(\ce{CO}\)	carbonyl

🏷️

Two worked names

\(\ce{[Co(NH3)6]Cl3}\) = hexaamminecobalt(III) chloride · \(\ce{K4[Fe(CN)6]}\) = potassium hexacyanidoferrate(II)

Use multiplying prefixes di, tri, tetra for simple ligands and bis, tris, tetrakis for ligands whose names already contain a number (e.g. bis(ethylenediamine)).

Section 19-5

Structural Isomerism

Coordination compounds offer rich isomerism. Structural isomers differ in which atoms are connected.

Type	What differs	Example
Ionization	ion inside vs outside sphere	\(\ce{[Co(NH3)5Br]SO4}\) / \(\ce{[Co(NH3)5SO4]Br}\)
Hydrate (solvate)	water inside vs outside	\(\ce{[Cr(H2O)6]Cl3}\) / \(\ce{[Cr(H2O)5Cl]Cl2.H2O}\)
Linkage	which atom of an ambidentate ligand binds	\(\ce{-NO2}\) vs \(\ce{-ONO}\)
Coordination	ligand swap between cation & anion	\(\ce{[Co(NH3)6][Cr(CN)6]}\)

Section 19-6

Stereoisomerism

Stereoisomers have the same connectivity but different spatial arrangements. Geometrical (cis–trans) isomerism appears in square-planar \(\ce{MA2B2}\) and octahedral \(\ce{MA4B2}\) complexes; optical isomerism appears when a complex and its mirror image cannot be superimposed.

Geometrical isomerism in a square-planar MA₂B₂ complex

Optical isomerism in action. The tris-chelate \(\ce{[Co(en)3]^3+}\) has no plane of symmetry, so its mirror image is a distinct, non-superimposable molecule. The two forms rotate plane-polarised light in opposite directions — they are enantiomers.

Section 19-7

Valence Bond Theory

Valence bond theory (VBT) pictures the metal offering empty hybrid orbitals that accept the ligands' lone pairs (coordinate bonds). The hybridisation fixes the geometry, and the count of unpaired electrons predicts the magnetic moment.

Coord. number	Hybridisation	Geometry
4	\(sp^3\)	tetrahedral
4	\(dsp^2\)	square planar
6	\(d^2sp^3\) (inner)	octahedral, low-spin
6	\(sp^3d^2\) (outer)	octahedral, high-spin

Inner vs outer. A strong-field ligand forces pairing and uses inner \((n{-}1)d\) orbitals — an inner-orbital (low-spin) complex like \(\ce{[Co(NH3)6]^3+}\). A weak-field ligand leaves electrons unpaired and uses outer \(nd\) orbitals — an outer-orbital (high-spin) complex like \(\ce{[CoF6]^3-}\). VBT explains shape and magnetism but not colour or the spectrochemical series — that needs crystal field theory.

Section 19-8

Crystal Field Theory

Crystal field theory (CFT) treats ligands as point charges that repel the metal's \(d\)-electrons. In an octahedral field the five \(d\)-orbitals split into a lower set (\(t_{2g}\)) and a higher set (\(e_g\)), separated by the crystal field splitting energy \(\Delta_o\).

Octahedral splitting — three lower t₂g, two higher e_g, gap Δₒ

🌈

Spectrochemical series & spin state

\(\ce{I- < Br- < Cl- < F- < OH- < H2O < NH3 < en < CN- < CO}\)

Weak-field ligands (left) give small \(\Delta_o\): electrons stay unpaired (high-spin). Strong-field ligands (right) give large \(\Delta_o > P\): electrons pair up (low-spin). The size of \(\Delta_o\) also sets which colour is absorbed — hence the complex's colour. In tetrahedral fields the split inverts and shrinks: \(\Delta_t=\tfrac49\Delta_o\), so tetrahedral complexes are almost always high-spin.

Section 19-9

Stability & the Chelate Effect

The stability of a complex is measured by its formation constant \(K_f\) — the larger it is, the more stable the complex. A striking pattern is the chelate effect: a complex with polydentate (ring-forming) ligands is far more stable than an otherwise identical one with separate monodentate ligands.

🔗

Why chelates are extra-stable

\(\ce{[Ni(en)3]^2+}\) is far more stable than \(\ce{[Ni(NH3)6]^2+}\)

Replacing six \(\ce{NH3}\) by three en molecules releases more particles into solution, raising entropy. This entropy gain is the heart of the chelate effect — the basis of EDTA's grip on metal ions.

Section 19-10

Applications

Coordination chemistry is everywhere — in biology, industry and the analytical lab. The same chelate effect that stabilises a complex makes these uses possible.

Field	Example
Biology	haemoglobin (\(\ce{Fe}\)), chlorophyll (\(\ce{Mg}\)), vitamin \(\ce{B12}\) (\(\ce{Co}\))
Analysis	EDTA titration of water hardness
Extraction	silver & gold via cyanide complexes
Catalysis	Wilkinson's catalyst for hydrogenation
Electroplating	complexed metal baths give smooth coats

Worked Examples

Putting It to Work

1 Oxidation state & coordination number

Problem. Find the oxidation state of iron and the coordination number in \(\ce{K4[Fe(CN)6]}\).

Solution. Let Fe \(=x\); six \(\ce{CN-}\) and four \(\ce{K+}\) balance the charge:

Working

\[ x + 6(-1) = -4 \Rightarrow x = +2;\quad \text{C.N.} = 6 \]

2 Name the complex

Problem. Give the IUPAC name of \(\ce{[Cr(H2O)4Cl2]Cl}\).

Solution. Ligands alphabetically (aqua, chlorido), Cr is \(+3\):

Working

\[ \text{tetraaquadichloridochromium(III) chloride} \]

3 Which isomerism?

Problem. \(\ce{[Co(NH3)5(NO2)]^2+}\) and \(\ce{[Co(NH3)5(ONO)]^2+}\) differ how?

Solution. The ambidentate nitrite binds through N or O:

Working

\[ \Rightarrow\ \textbf{linkage isomerism} \]

4 VBT hybridisation

Problem. Predict the hybridisation and magnetism of \(\ce{[Fe(CN)6]^4-}\) (\(\ce{Fe^2+},\ 3d^6\)).

Solution. \(\ce{CN-}\) is a strong-field ligand → pairing → inner-orbital:

Working

\[ d^2sp^3,\ \text{octahedral, all paired} \Rightarrow \textbf{diamagnetic} \]

5 High-spin or low-spin?

Problem. Will \(\ce{[CoF6]^3-}\) be high- or low-spin? Explain using the spectrochemical series.

Solution. \(\ce{F-}\) is a weak-field ligand → small \(\Delta_o < P\):

Working

\[ \text{small }\Delta_o \Rightarrow \textbf{high-spin (outer-orbital }sp^3d^2) \]

6 Optical activity

Problem. Is \(\ce{[Co(en)3]^3+}\) optically active? Why?

Solution. A tris-chelate octahedron lacks a plane of symmetry:

Working

\[ \text{non-superimposable mirror images} \Rightarrow \textbf{optically active} \]

Review

Chapter Summary

✓ Werner

Primary (ionizable) & secondary (directional) valencies; secondary fixes geometry.

✓ Vocabulary

Central atom, ligands, coordination number, denticity, chelates, ambidentate.

✓ Naming

Cation before anion; ligands alphabetical; metal + oxidation state; anion → -ate.

✓ Isomerism

Structural (ionization, hydrate, linkage, coordination) and stereo (cis–trans, optical).

✓ Two theories

VBT (inner/outer orbital, shape, magnetism); CFT (d-splitting, colour, spin state).

✓ Stability

\(K_f\) measures stability; the chelate effect (entropy) makes ring ligands win.

Practice

Problems

For each item, first decide which idea it tests — Werner's theory, naming, isomerism, or a bonding theory — then apply the relevant rule. Difficulty rises down the list.

State Werner's theory and distinguish primary from secondary valency.
Differentiate a double salt from a coordination compound, with one example of each.
Define ligand, coordination number and denticity. Give one bidentate ligand.
Name \(\ce{[Co(NH3)6]Cl3}\) and \(\ce{K3[Fe(CN)6]}\) by IUPAC rules.
Find the oxidation state and coordination number of the metal in \(\ce{[Pt(NH3)2Cl2]}\).
What is linkage isomerism? Illustrate with an ambidentate ligand.
Draw the cis and trans forms of \(\ce{[Pt(NH3)2Cl2]}\).
Explain why \(\ce{[Co(en)3]^3+}\) is optically active.
Using VBT, predict the hybridisation and magnetism of \(\ce{[Ni(CN)4]^2-}\).
Using CFT, sketch the octahedral splitting and define \(\Delta_o\).
Arrange \(\ce{F-},\ \ce{H2O},\ \ce{NH3},\ \ce{CN-}\) in the spectrochemical series.
What is the chelate effect, and why does \(\ce{[Ni(en)3]^2+}\) exceed \(\ce{[Ni(NH3)6]^2+}\) in stability?

Tip: work a complex in a fixed order — find the metal's oxidation state and coordination number first, then the geometry, then (if asked) feed the field strength of the ligands into VBT or CFT for magnetism and colour. Get the bookkeeping right at the start and the theory questions fall into place.