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Stability of Metal Complexes

Ligands like chloride, water, and ammonia are said to be monodentate (one-toothed, from the Greek mono, meaning “one,” and the Latin dent-, meaning “tooth”): they are attached to the metal via only a single atom. Ligands can, however, be bidentate (two-toothed, from the Greek di, meaning “two”), tridentate (three-toothed, from the Greek tri, meaning “three”), or, in general, polydentate (many-toothed, from the Greek poly, meaning “many”), indicating that they are attached to the metal at two, three, or several sites, respectively. Ethylenediamine (H2NCH2CH2NH2, often abbreviated as en) and diethylenetriamine (H2NCH2CH2NHCH2CH2NH2, often abbreviated as dien) are examples of a bidentate and a tridentate ligand, respectively, because each nitrogen atom has a lone pair that can be shared with a metal ion. When a bidentate ligand such as ethylenediamine binds to a metal such as Ni2+, a five-membered ring is formed. A metal-containing ring like that shown is called a chelate ring (from the Greek chele, meaning “claw”). Correspondingly, a polydentate ligand is a chelating agent, and complexes that contain polydentate ligands are called chelate complexes.

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Experimentally, it is observed that metal complexes of polydentate ligands are significantly more stable than the corresponding complexes of chemically similar monodentate ligands; this increase in stability is called the chelate effect. For example, the complex of Ni2+ with three ethylenediamine ligands, [Ni(en)3]2+, should be chemically similar to the Ni2+ complex with six ammonia ligands, [Ni(NH3)6]2+. In fact, the equilibrium constant for the formation of [Ni(en)3]2+ is almost 10 orders of magnitude larger than the equilibrium constant for the formation of [Ni(NH3)6]2+ (Table E4):

\(\begin{align} & [\mathrm{Ni(H_2O)_6]^{2+}+6NH_3} & \rightleftharpoons \mathrm{[Ni(NH_3)_6]^{2+}+6H_2O(l)} \hspace{3mm} & K_\mathrm f=\mathrm{4\times10^8} \\
& \mathrm{[Ni(H_2O)_6]^{2+}+3en} & \rightleftharpoons \mathrm{[Ni(en)_3]^{2+}+6H_2O(l)} \hspace{3mm} & K_\mathrm f=\mathrm{2\times10^{18}}\end{align} \tag{23.10}\)
 
The formation constants are formulated as ligand exchange reactions with aqua ligands being displaced by new ligands (\(NH_3\)  or \(en\)) in the examples above.

Note

Chelate complexes are more stable than the analogous complexes with monodentate ligands.

The stability of a chelate complex depends on the size of the chelate rings. For ligands with a flexible organic backbone like ethylenediamine, complexes that contain five-membered chelate rings, which have almost no strain, are significantly more stable than complexes with six-membered chelate rings, which are in turn much more stable than complexes with four- or seven-membered rings. For example, the complex of nickel (II) with three ethylenediamine ligands is about 363,000 times more stable than the corresponding nickel (II) complex with trimethylenediamine (H2NCH2CH2CH2NH2, abbreviated as tn):

\(\begin{align} & \mathrm{[Ni(H_2O)_6]^{2+}+3en} & & \rightleftharpoons \mathrm{[Ni(en)_3]^{2+}+6H_2O(l)} & K_\mathrm f=6.76*10^{17} \\  & \mathrm{[Ni(H_2O)_6]^{2+}+3tn} & & \rightleftharpoons \mathrm{[Ni(tn)_3]^{2+}+6H_2O(l)} & K_\mathrm f=1.86*10^{12}\end{align} \tag{23.11}\)

*The above measurements were done in a solution of ionic strength 0.15 at 25º C.

Example 5

Arrange [Cr(en)3]3+, [CrCl6]3−, [CrF6]3−, and [Cr(NH3)6]3+ in order of increasing stability.

Given: four Cr(III) complexes

Asked for: relative stabilities

Strategy:

A Determine the relative basicity of the ligands to identify the most stable complexes.

B Decide whether any complexes are further stabilized by a chelate effect and arrange the complexes in order of increasing stability.

SOLUTION

A The metal ion is the same in each case: Cr3+. Consequently, we must focus on the properties of the ligands to determine the stabilities of the complexes. Because the stability of a metal complex increases as the basicity of the ligands increases, we need to determine the relative basicity of the four ligands. Our earlier discussion of acid–base properties suggests that ammonia and ethylenediamine, with nitrogen donor atoms, are the most basic ligands. The fluoride ion is a stronger base (it has a higher charge-to-radius ratio) than chloride, so the order of stability expected due to ligand basicity is [CrCl6]3− < [CrF6]3− < [Cr(NH3)6]3+ ≈ [Cr(en)3]3+.

B Because of the chelate effect, we expect ethylenediamine to form a stronger complex with Cr3+ than ammonia. Consequently, the likely order of increasing stability is [CrCl6]3− < [CrF6]3− < [Cr(NH3)6]3+ < [Cr(en)3]3+.

Exercise

Arrange [Co(NH3)6]3+, [CoF6]3−, and [Co(en)3]3+ in order of decreasing stability.

Answer: [Co(en)3]3+ > [Co(NH3)6]3+ > [CoF6]3−