The transition metals occur in many interesting and important molecular forms. Species that are assemblies of a central transition-metal ion bonded to a group of surrounding molecules or ions, such as [Ag(NH3)2]+ and [Fe(H2O)6]3+, are called metal complexes, or merely complexes.* If the complex carries a net charge, it is generally called a complex ion (Section 17.5) Compounds that contain complexes are known as coordination compounds.

The molecules or ions that bond to the metal ion in a complex are known as ligands (from the Latin word ligare, “to bind”). There are two NH3 ligands bonded to Ag+ in the complex ion [Ag(NH3)2]+, for instance, and six H2O ligands bonded to Fe3+ in [Fe(H2O)6]3+. Each ligand functions as a Lewis base and so donates a pair of electrons to form the ligand–metal bond.  (Section 16.11) Thus, every ligand has at least one unshared pair of valence electrons. Four of the most frequently encountered ligands

illustrate that most ligands are either polar molecules or anions. In forming a complex, the ligands are said to coordinate to the metal.


Is the interaction between an ammonia ligand and a metal cation a Lewis acid–base interaction? If so, which species acts as the Lewis acid?

TABLE 23.3 • Properties of Some Ammonia Complexes of Cobalt(III)


The Development of Coordination Chemistry: Werner's Theory

Because compounds of the transition metals are beautifully colored, the chemistry of these elements fascinated chemists even before the periodic table was introduced. During the late 1700s through the 1800s, the many coordination compounds that were isolated and studied had properties that were puzzling in light of the bonding theories prevailing at the time. TABLE 23.3, for example, lists a series of CoCl3-NH3 compounds that have strikingly different colors. Note that the third and fourth species have different colors even though the originally assigned formula was the same for both, CoCl3 • 4 NH3.

The modern formulations of the compounds in Table 23.3 are based on various lines of experimental evidence. For example, all four compounds are strong electrolytes  (Section 4.1) but yield different numbers of ions when dissolved in water. Dissolving CoCl3 • 6 NH3 in water yields four ions per formula unit ([Co(NH3)6]3+ plus three Cl ions), whereas CoCl3 • 5 NH3 yields only three ions per formula unit ([Co(NH3)5Cl] and two Cl ions). Furthermore, the reaction of the compounds with excess aqueous silver nitrate leads to the precipitation of different amounts of AgCl(s). When CoCl3 • 6 NH3 is treated with excess AgNO3(aq), 3 mol of AgCl(s) are produced per mole of complex, which means all three Cl ions in the complex can react to form AgCl(s). By contrast, when CoCl3 • 5 NH3 is treated with excess AgNO3(aq), only 2 mol of AgCl(s) precipitate per mole of complex, telling us that one of the Cl ions in the complex does not react. These results are summarized in Table 23.3.

In 1893 the Swiss chemist Alfred Werner (1866-1919) proposed a theory that successfully explained the observations in Table 23.3. In a theory that became the basis for understanding coordination chemistry, Werner proposed that any metal ion exhibits both a primary valence and a secondary valence. The primary valence is the oxidation state of the metal, which is +3 for the complexes in Table 23.3.  (Section 4.4) The secondary valence is the number of atoms bonded to the metal ion, which is also called the coordination number. For these cobalt complexes, Werner deduced a coordination number of 6 with the ligands in an octahedral arrangement around the Co3+ ion.

Werner's theory provided a beautiful explanation for the results in Table 23.3. The NH3 molecules are ligands bonded to the Co3+ ion; if there are fewer than six NH3 molecules, the remaining ligands are Cl ions. The central metal and the ligands bound to it constitute the coordination sphere of the complex.

In writing the chemical formula for a coordination compound, Werner suggested using square brackets to signify the makeup of the coordination sphere in any given compound. He therefore proposed that CoCl3 • 6 NH3 and CoCl3 • 5 NH3 are better written as [Co(NH3)6]Cl3 and [Co(NH3)5Cl]Cl2, respectively. He further proposed that the chloride ions that are part of the coordination sphere are bound so tightly that they do not dissociate when the complex is dissolved in water. Thus, dissolving [Co(NH3)5Cl]Cl2 in water produces a [Co(NH3)5Cl]2+ ion and two Clions.

Werner's ideas also explained why there are two forms of CoCl3 • 4 NH3. Using Werner's postulates, we write the formula as [Co(NH3)4Cl2]Cl. As shown in FIGURE 23.7, there are two ways to arrange the ligands in the [Co(NH3)4Cl2]+ complex, called the cis and trans forms. In thecis form, the two chloride ligands occupy adjacent vertices of the octahedral arrangement. In trans-[Co(NH3)4Cl2]+ the two chlorides are opposite each other. It is this difference in positions of the Cl ligands that leads to two compounds, one violet and one green.

FIGURE 23.7 Isomers of [Co(NH3)4Cl2]+. The cis isomer is violet, and the trans isomer is green.

The insight Werner provided into the bonding in coordination compounds is even more remarkable when we realize that his theory predated Lewis's ideas of covalent bonding by more than 20 years! Because of his tremendous contributions to coordination chemistry, Werner was awarded the 1913 Nobel Prize in Chemistry.

SAMPLE EXERCISE 23.1 Identifying the Coordination Sphere of a Complex

Palladium(II) tends to form complexes with coordination number 4. A compound has the composition PdCl2 • 3 NH3(a) Write the formula for this compound that best shows the coordination structure. (b) When an aqueous solution of the compound is treated with excess AgNO3(aq), how many moles of AgCl(s) are formed per mole of PdCl2 • 3 NH3?


Analyze We are given the coordination number of Pd(II) and a chemical formula indicating that the complex contains NH3 and Cl. We are asked to determine (a) which ligands are attached to Pd(II) in the compound and (b) how the compound behaves toward AgNO3 in aqueous solution.

Plan (a) Because of their charge, the Cl ions can be either in the coordination sphere, where they are bonded directly to the metal, or outside the coordination sphere, where they are bonded ionically to the complex. The electrically neutral NH3 ligands must be in the coordination sphere, if we assume four ligands bonded to the Pd(II) ion. (b) Any chlorides in the coordination sphere do not precipitate as AgCl.


(a) By analogy to the ammonia complexes of cobalt(III) shown in Figure 23.7, we predict that the three NH3 are ligands attached to the Pd(II) ion. The fourth ligand around Pd(II) is one chloride ion. The second chloride ion is not a ligand; it serves only as a counterion (a noncoor-dinating ion that balances charge) in the compound. We conclude that the formula showing the structure best is [Pd(NH3)3Cl]Cl.

(b) Because only the non-ligand Cl can react, we expect to produce 1 mol of AgCl(s) per mole of complex. The balanced equation is

[Pd(NH3)3Cl]Cl(aq) + AgNO3(aq) → [Pd(NH3)3Cl]NO3(aq) + AgCl(s)

This is a metathesis reaction  (Section 4.2) in which one of the cations is the [Pd(NH3)3Cl]+ complex ion.


Predict the number of ions produced per formula unit in an aqueous solution of CoCl2 • 6 H2O.

Answer: three: [Co(H2O)6]2+ and two Cl

The Metal–Ligand Bond

The bond between a ligand and a metal ion is a Lewis acid–base interaction. Because the ligands have available pairs of electrons, they can function as Lewis bases (electron-pair donors). Metal ions (particularly transition-metal ions) have empty valence orbitals, so they can act as Lewis acids (electron-pair acceptors). We can picture the bond between the metal ion and ligand as the result of their sharing a pair of electrons initially on the ligand:

The formation of metal-ligand bonds can markedly alter the properties we observe for the metal ion. A metal complex is a distinct chemical species that has physical and chemical properties different from those of the metal ion and ligands from which it is formed. As one example, FIGURE 23.8 shows the color change that occurs when aqueous solutions of NCS (colorless) and Fe3+ (yellow) are mixed, forming [Fe(H2O)5NCS]2+.

Complex formation can also significantly change other properties of metal ions, such as their ease of oxidation or reduction. Silver ion, for example, is readily reduced in water,

but the [Ag(CN)2] ion is not so easily reduced because complexation by CN ions stabilizes silver in the +1 oxidation state:

Hydrated metal ions are complexes in which the ligand is water. Thus, Fe3+ (aq) consists largely of [Fe(H2O)6]3+ (Section 16.11) It is important to realize that ligands can undergo reaction. For example, we saw in Figure 16.16 that a water molecule in [Fe(H2O)6]3+(aq) can be deprotonated to yield [Fe(H2O)5OH]2+(aq) and H+(aq). The iron ion retains its oxidation state; the coordinated hydroxide ligand, with a 1− charge, reduces the complex charge to 2+. Ligands can also be displaced from the coordination sphere by other ligands, if the incoming ligands bind more strongly to the metal ion than the original ones. For example, ligands such as NH3, NCS, and CN can replace H2O in the coordination sphere of metal ions.

FIGURE 23.8 Reaction of Fe3+(aq) and NCS(aq).


Write a balanced chemical equation for the reaction that causes the color change in Figure 23.8.

Charges, Coordination Numbers, and Geometries

The charge of a complex is the sum of the charges on the metal and on the ligands. In [Cu(NH3)4]SO4 we can deduce the charge on the complex ion because we know that the charge of the sulfate ion is 2–. Because the compound is electrically neutral, the complex ion must have a 2+ charge, [Cu(NH3)4]2+. We can then use the charge of the complex ion to deduce the oxidation number of copper. Because the NH3 ligands are uncharged molecules, the oxidation number of copper must be +2:

SAMPLE EXERCISE 23.2 Determining the Oxidation Number of a Metal in a Complex

What is the oxidation number of the metal in [Rh(NH3)5Cl](NO3)2?


Analyze We are given the chemical formula of a coordination compound and asked to determine the oxidation number of its metal atom.

Plan To determine the oxidation number of Rh, we need to figure out what charges are contributed by the other groups. The overall charge is zero, so the oxidation number of the metal must balance the charge due to the rest of the compound.

Solve The NO3 group is the nitrate anion, which has a 1– charge. The NH3 ligands carry zero charge, and the Cl is a coordinated chloride ion, which has a 1– charge. The sum of all the charges must be zero:

The oxidation number of rhodium, x, must therefore be +3.


What is the charge of the complex formed by a platinum(II) metal ion surrounded by two ammonia molecules and two bromide ions?

Answer: zero

SAMPLE EXERCISE 23.3 Determining the Formula of a Complex Ion

A complex ion contains a chromium(III) bound to four water molecules and to two chloride ions. What is the formula and charge of this ion?


Analyze We are given a metal, its oxidation number, and the number of ligands of each kind in a complex ion containing the metal, and we are asked to write the chemical formula and charge of the ion.

Plan We write the metal first, then the ligands. We can use the charges of the metal ion and ligands to determine the charge of the complex ion. The oxidation state of the metal is +3, water has no charge, and chloride has a 1– charge.


The charge on the ion is 1+, [Cr(H2O)4Cl2]+.


Write the formula for the complex described in the Practice Exercise accompanying Sample Exercise 23.2.

Answer: [Pt(NH3)2Br2]

Recall that the number of atoms directly bonded to the metal atom in a complex is the coordination number of the complex. Thus, the silver ion in [Ag(NH3)2]+ has a coordination number of 2, and the cobalt ion has a coordination number of 6 in all four complexes in Table 23.3.

Some metal ions have only one observed coordination number. The coordination number of chromium(III) and cobalt(III) is invariably 6, for example, and that of platinum(II) is always 4. For most metals, however, the coordination number is different for different ligands. In these complexes, the most common coordination numbers are 4 and 6.

The coordination number of a metal ion is often influenced by the relative sizes of the metal ion and the ligands. As the ligand gets larger, fewer of them can coordinate to the metal ion. Thus, iron(III) is able to coordinate to six fluorides in [FeF6]3– but to only four chlorides in [FeCl4].

Ligands that transfer substantial negative charge to the metal also produce reduced coordination numbers. For example, six ammonia molecules can coordinate to nickel(II), forming [Ni(NH3)6]2+, but only four cyanide ions can coordinate to this ion, forming [Ni(CN)4]2–.

Complexes in which the coordination number is 4 have two common geometries—tetrahedral and square planar (FIGURE 23.9). The tetrahedral geometry is the more common of the two and is especially common among nontransition metals. The square-planar geometry is characteristic of transition-metal ions with eight d electrons in the valence shell, such as platinum(II) and gold(III).


What is the size of the NH3-Zn-NH3 bond angle? Of the NH3-Pt-NH3 bond angle?

FIGURE 23.9 In complexes having coordination number 4, the molecular geometry can be tetrahedral or square planar.

The vast majority of complexes in which the coordination number is 6 have an octahedral geometry. The octahedron, which has eight faces and six vertices, is often represented as a square with ligands above and below the plane, as in FIGURE 23.10. Recall, however, that all six vertices on an octahedron are geometrically equivalent.  (Section 9.2) The octahedron can also be thought of as two square pyramids that share the same square base.

FIGURE 23.10 In complexes having coordination number 6, the molecular geometry is almost always octahedral. Two ways to draw octahedral geometry are shown.


What are the geometries most commonly associated with

a. coordination number 4,

b. coordination number 6?