Inorganic Chemistry
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Inorganic Chemistry

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most important complexes are those 
formed between a metal cation and ligands, which may be ions (e.g. halides, cyanide, oxalate) or 
neutral molecules (e.g. ammonia, pyridine). The ligand acts as a donor and replaces one or more 
water molecules from the primary solvation sphere, and thus a complex is distinct from an ion pair, 
which forms through purely electrostatic interactions in solvents of low polarity (see Topic E1). 
Although complex formation is especially characteristic of transition metal ions it is by no means 
confined to them. 
Several steps of complex formation may be possible, and the successive equilibrium constants for 
the reactions 
and so on are known as the stepwise formation constants K1, K2\u2026. The overall equilibrium 
constant for the reaction 
is given by 
Key Notes 
Complexes are formed in aqueous solution when a ligand molecule or ion replaces solvating 
water molecules. Successive ligands may be attached, giving a series of step wise formation 
(equilibrium) constants. 
Hard and soft 
Class a (hard) cations complex more strongly with small electronegative ligands whereas 
class b (soft) cations have more affinity for less electronegative and more polarizable 
ligands. The difference involves entropic and enthalpic solvation terms. 
Chealates and 
Polydentate or chelating ligands have more than one atom available for coordination to the 
metal, and form stronger complexes than monodentate ligands. The effect is enhanced in 
macrocyclic ligands, which have more rigid structures. 
Effect of pH Basic ligands become protonated at low pH and complex formation is suppressed. 
Related topics Lewis acids and bases (C9) 
Group 12: zinc, cadmium and mercury (G4) 
3d series: aqueous ions (H3) 
Complexes: structure and isomerism (H6) 
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Successive stepwise formation constants often decrease regularly K1>K2>\u2026of the maximum value 
being determined by the number of ligands that can be accommodated: this is often six except for 
chelating ligands (see below). The decrease can be understood on entropic (statistical) grounds, as 
each successive ligand has one less place available to attach. Exceptional effects may result from the 
charge and size of ligands, and a reversal of the normal sequence can sometimes be attributed to 
specific electronic or structural effects. It is important to remember that each ligand replaces one or 
more solvating water molecules. For example, in the Cd2+/Br\u2212 system K4>K3 as the octahedral 
species [Cd(H2O)3Br3]
\u2212 is converted to tetrahedral [CdBr4]
2\u2212 with an entropy gain resulting from 
the increased freedom of three water molecules. 
Hard and soft behavior 
For cations formed from metals in early groups in the periodic table the complexing strength with 
halide ions follows the sequence 
whereas with some later transition metals and many post-transition metals the reverse sequence is 
found (e.g. Pt2+, Hg2+, Pb2+; see Topics G4, G6 and H5). The former behavior is known as class a 
and the latter as class b behavior, and the difference is an example of hard and soft properties, 
respectively (see Topic C9). Class b ions form strong complexes with ligands such as ammonia, 
which are softer than water, whereas class a ions do not complex with such ligands appreciably in 
Solvation plays an essential part in understanding the factors behind class a and b behavior. 
Trends in bond strengths show that almost every ion would follow the class a sequence in the gas 
phase, and the behavior in water is a partly a consequence of the weaker solvation of larger anions. 
With a class b ion such as Hg2+ the bond strengths decrease more slowly in the sequence Hg-F>Hg-
Cl>\u2026 than do the solvation energies of the halide ions. With a class a ion such as Al3+, on the other 
hand, the change in bond strengths is more marked than that in the solvation energies. 
In solution the difference between the two classes is often manifested in different thermodynamic 
behavior. Class b complex formation is enthalpy dominated (i.e. driven by a negative \u394H) whereas 
class a formation is often entropy dominated (driven by positive \u394S). The strongest class a ions are 
small and highly charged (e.g. Be2+, Al3+) and have very negative entropies of solvation (see Topic 
E1). Complexing with small highly charged ions such as F\u2212 reduces the overall charge and hence 
frees up water molecules, which are otherwise ordered by solvation. Hard cations with low 
charge/size ratio, such as alkali ions, form very weak complexes with all ligands except macrocycles 
(see below). 
Some polyatomic ions such as and have very low complexing power to either 
class a or b metals. They are useful as counterions for studying the thermodynamic properties of 
metal ions (e.g. electrode potentials; see Topic E5) unaffected by complex formation. 
Chelates and macrocycles 
Chelating ligands are ones with two or more donor atoms capable of attaching simultaneously to a 
cation: they are described as bidentate, tridentate,\u2026according to the number of atoms capable of 
binding. Chelating ligands include bidentate ethylenediamine (1) and ethylenediamine tetraacetate 
(EDTA, 2), which is hexadentate, having two nitrogen donors and four oxygens (one from each 
carboxylate). Chelating ligands generally form stronger complexes than unidentate 
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ones with similar donor properties. They are useful for analysis of metal ions by complexometric 
titration and for removing toxic metals in cases of poisoning (see Topic J3). 
The origin of the chelate effect is entropic. Each ligand molecule can replace more than one 
solvating water molecule, thus giving a favorable entropy increase. Structural requirements 
occasionally subvert the effect: for example, Ag+ does not show the expected increase of K1 with 
ethylenediamine compared with ammonia, because it has a strong bonding preference for two ligand 
atoms in a linear configuration, which is structurally impossible with the bidentate ligand. 
The length of the chain formed between ligand atoms is important in chelate formation, the most 
stable complexes generally being formed with four atoms (including the donors) so that with the 
metal ion a five-membered ring is formed. Smaller ring sizes are less favorable because of the bond 
angles involved, larger ones because of the increased configurational entropy of the molecule 
(coming from free rotation about bonds), which is lost in forming the complex. Limiting the 
possibility of bond rotation increases the complexing power even with optimum ring sizes, so that 
phenanthroline (3) forms stronger complexes than bipyridyl (4). 
Reducing the configurational entropy is important in macrocyclic ligands, where several donor 
atoms are already \u2018tied\u2019 by a molecular framework into the optimal positions for complex formation. 
Examples are the cyclic crown ethers (e.g. 18-crown-6, 5) and bicyclic cryptands (e.g. [2.2.1]-
crypt, 6). As expected, complexing strength is enhanced, and the resulting macrocyclic effect allows 
complexes to be formed with ions such as those of group 1, which otherwise have very low 
complexing power (see Topic G2). Another feature of macrocyclic ligands is the size selectivity 
corresponding to different cavity sizes. Thus with ligand 6 complex stability follows the order 
Li+<Na+>K+>Rb+ and the selectivity can be altered by varying the ring size. 
Chelating and macrocyclic effects are important in biological chemistry (see Topic J3). Metal 
binding sites in metalloproteins contain several ligand atoms,