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The Physical Chemistry behind the Periodic Table

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Overview of the Periodic Table
Hydrogen | Group 1 - Alkali Metals | Group 2 - Alkaline Earth Metals | Group 12

Chemistry is an enormous subject with extensively broad horizons. It shares many areas of knowledge with physics and encompasses most of molecular biology. The subject of chemistry is historically divided into three main disciplines: physical, organic and inorganic.

Physical chemistry, as the name implies, is the study of the 'physics' that explains chemistry and covers such areas as thermodynamics, kinetics (rates of chemical reactions) and much of quantum mechanics. Organic chemistry was originally the study of the molecules of life, but this has been extended to the study and synthesis of all compounds that contain both carbon and hydrogen, as well as other elements, such as oxygen, nitrogen, sulphur or the halogens. Inorganic chemistry covers every element of the periodic table. It has overlaps with both organic and physical chemistry, and involves studying the properties of molecular compounds and the chemistry of solid materials. It encompasses the properties of ionic solids, such as NaCl; simple inorganic molecules, such as HCl; co-ordination compounds; complexes, such as [Cu(H2O)6]2+; and organometallic molecules in which metal-carbon bonds are formed.

This entry gives an introduction to inorganic chemistry. Firstly the structure of atoms and hence the structuring of the periodic table of elements is discussed. From this, key observable periodic trends in the properties of the elements are explained. Other fundamental concepts in inorganic chemistry are then introduced, such as the properties of co-ordination compounds and complexes. Other important areas of inorganic chemistry, such as acids and bases and the nature of ions, have been discussed elsewhere.

The Periodic Table

To begin understanding the chemistry of the elements, a knowledge of how the periodic table of elements is constructed is required. For this we must know a little about the structure of the atoms. The first periodic tables were constructed by the Russian chemist Dimitri Mendeleev in the 19th century but these were based on observations of chemical similarities for groups of elements. Accounts of the periodic table and the structure of atoms are given elsewhere (Electron Shells and Orbitals and The History of the Periodic Table of the Elements), but a brief summary is also given here.

Atoms consist of three basic particles:

  1. Positively charged protons
  2. Negatively charged electrons
  3. Uncharged neutrons

The protons and neutrons form a very small nucleus (approximately 1/10,000 of the atomic radius) surrounded by the electrons. The electrons are grouped into a set of levels that have specific energies relative to the separated electron and nucleus. These are called 'shells', or 'principle energy levels', and are given labels 'K', 'L', 'M', 'N' and 'O' etc or '1', '2', '3', '4' etc. Each principle energy level can only accommodate a specific number of electrons. The lowest energy shell, K, which is the most tightly held to the nucleus can only accommodate two electrons. The next shell up, L, can hold eight. Shell M can hold 18, and shell N 32.

The highest shell in energy in the neutral atom that contains electrons is called the valence shell. Each of these shells consists of sub-shells called orbitals, each of which holds two electrons. Orbitals are three dimensional mathematical shapes, that are described by quantum mechanics, and are essentially standing waves centred on the nucleus. The amplitude of these waves describes the probability of being able to find an electron in that orbital at any given point within the atom. An electron can, thus, be imagined to be 'smeared out' over the atom in a wave-like way, taking the shape of the wave describing the orbital.

There are various different types and shapes of orbital. The simplest is an s orbital, which is spherical. Each principle shell contains one s orbital. As the number of electrons increases, a new type of orbital becomes available. In the second shell, in addition to one s orbital, there are three dumb-bell shaped orbitals: p orbitals. In the third shell there is one s orbital, three p orbitals and now five d orbitals.

The shapes of d orbitals are more complicated than those of p orbitals, while those the f orbitals, which appear in the fourth principle shell, are too complicated to easily describe. In the fourth shell, there is a set of seven f orbitals. In successive shells, more types of orbital are introduced labelled alphabetically from g upwards, though these are purely of theoretical interest since there are no known stable atoms large enough to have enough electrons to fill them.

Since each orbital can hold only two electrons, we can see why each principle energy level holds different numbers of electrons. Each individual orbital can be given a label based on which principle energy it belongs to and the type of orbital. So a d orbital in the fourth principle shell is labelled 4d.

Table 1: The principle shells and their constituent orbitals in the atom.
Principle shellAvailable orbitalsNumber of electrons
2s, p8
3s, p, d18
4s, p, d, f32
5s, p, d, f, g50

When electrons are added to an atom, they first fill the shell of lowest energy, shell 1 (or K), and then shells of higher energies. For the hydrogen atom, the different types of orbital that are present in the same shell are all at the same energy, but as the atomic number and the nuclear charge increase, the s and p orbitals of a given shell, for example, will no longer be at the same energy. For a given shell, the energy of the different type of orbitals increase in the order s < p < d < f. Now the construction of the periodic table can be examined.

In groups 1 and 2 of the table, a new principle shell is starting to be filled, and so the highest energy electron is in an s orbital. Therefore, this chunk of the periodic table is called the s block. For the elements in group 3 to 12, the highest energy electron is in a d orbital, and so this area is called the d block. Similarly, groups 13 to 18 are called the p block and the lanthanides and actinides underneath the main body of the table are called the f block.

Going from hydrogen to helium, with increasing atomic number, the 1s orbital is first filled. Next is the second shell containing the 2s, then the 2p orbitals. This takes us from lithium, Li, up to neon, Ne. After this the 3s and then the 3p orbitals are filled, taking us from sodium, Na, up to argon, Ar.

We might expect then to fill the 3d, but, because the different types of orbital in different shells vary in energy by different amounts as we increase in atomic number and hence nuclear charge, it turns out that the next highest orbital is actually 4s, so this is next filled. After 4s (K and Ca) the 3d orbitals are filled (Sc to Zn) and this is why the s and p blocks are separated by the d block. The 4p is then filled, taking us to krypton. The electrons are then put into orbitals in the order 5s, 4d, 5p and 6s. No 4f orbitals have yet been encountered. These begin to be filled after lanthanum, La. The f block underneath the main body of the table should, therefore, be put between groups 3 and 4, but is often drawn separated from the other blocks so the table is not too wide for the page.

We then fill 4f (Ce to Lu) and get to hafnium, Hf, and continue, filling the 5d, 6p and 7s orbitals. We put one electron into a 6d at actinum, Ac, and then fill the 5f (Th to Lr) as it becomes lower in energy. So the order in which orbitals are filled is:

  1. 1s - H to He
  2. 2s - Li to Be
  3. 2p - B to Ne
  4. 3s - Na to Mg
  5. 3p - Al to Ar
  6. 4s - K to Ca
  7. 3d - Sc to Zn
  8. 4p - Ga to Kr
  9. 5s - Rb to Sr
  10. 4d - Y to Cd
  11. 5p - In to Xe
  12. 6s - Cs to Ba
  13. 4f - Ce to Lu
  14. 5d - Hf to Hg
  15. 6p - Tl to Rn
  16. 7s - Fr to Ba
  17. 5f - Th to Lr

The periodic table's structure is based on the electronic structure of the atoms of the elements and so can rationalise their chemical properties. Elements within the same column, or 'group', possess similar chemical and physical properties, because the electrons in their valence shells, which define to a large extent these properties, are arranged in a similar manner. Some of the groups of the table have individual names: the group 1 elements are known as the 'alkali metals', group 2 elements as the 'alkaline earth metals', group 16 elements as the 'chalchogens', group 17 elements as the 'halogens' and group 18 elements as the 'noble gases'. Groups 13, 14 and 15 don't have accepted names, although 'triels', 'tetrels' and 'pentels' are sometimes used. The elements of the d block, groups 3 to 12, are known as the 'transition metals'.

Periodic Trends of the Elements

The construction of the periodic table is based on the electronic structures of the atoms. Because of patterns in electronic structure, periodic trends in the physical properties of the elements can easily be seen. Interesting and imaginative computer generated landscapes that depict these trends can be found on the website of the Royal Society of Chemistry.

Ionisation Energies

Trends can also be observed in the first ionisation energies of the elements. This is the minimum energy that is required to completely remove the highest energy electron from the neutral atom. Going through the elements in order of increasing atomic number, there can be seen a series of minima, corresponding to the alkali metals of group 1 where elements are easy to ionise, meaning relatively little energy is required, and a series of maxima, corresponding to the noble gases of group 18 where the elements are hard to ionise, meaning that relatively large amounts of energy are required.

The valence shells of the noble gases have a full complement of electrons and form a 'closed shell'. This is a particularly stable configuration and so large amounts of energy are required to remove an electron from the atom. For the alkali metals there is only one electron in the valence shell, beneath which there is a noble gas-like closed shell. This results in a low ionisation energy for this lone electron.

A second trend that can be observed is a fall in ionisation energy on descending a given group. This is because the valence electrons are in successively higher shells that are larger and less tightly held by the nucleus. Another trend can be observed within single horizontal rows of the periodic table. The negatively charged electron in the shells below the valence shell somewhat shield the valence electrons from the positive charge of nucleus. This shielding isn't perfect, however, and the outer electrons feel what is called an effective nuclear charge.

The idea of effective nuclear charge was put forward by JC Slater, and is the resultant charge felt by an electron in a given orbital after shielding by inner electrons. The effective nuclear charge, Z* is can be calculated by the following equation:

Z = Z* - σ

Z is the element's atomic number (the number of positively charged protons in its nucleus) and σ is a screening factor dependent on the other electrons present in the atom. If the electron we are calculating Z* for is in an s or p orbital:

  • Electrons in higher principle shells contribute 0 to the value of σ

  • Each electron in the same principle shell contribute 0.35 to σ

  • Each electron in the next principle shell down contribute 0.85 to σ

  • Each electron in shells deeper than this all contribute 1.0 to σ

If the electron we are calculating Z* is in a d or f orbital:

  • Electrons in higher principle shell contribute 0 to the value of σ

  • Each electron in the same principle shell contribute 0.35 to σ

  • All inner electrons contribute 1.0 to σ

As the atomic number increases from left to right across the row, or 'period', the effective nuclear charge felt by the valence electrons also increases and so they are more tightly held, resulting in an increase in the first ionisation energy (figure 1). This is not entirely linear, with a few peaks and troughs. As can also be seen in figure 1, the ionisation energy increases from Li to Be but then falls as B, rises again until N, drops at O then increases to the end of the row at Ne. This is because different types of orbital contain the highest energy electrons for different elements. For Li and Be, this is the 2s orbital, while for the other elements it is the 2p.

s orbitals are said to be more penetrating than p orbitals, with most of the amplitude of its wave function actually inside the nucleus. p, orbitals which are dumbbell shaped, have most of the amplitude, and therefore electron density, to either side of the nucleus. Electrons in s orbitals, therefore, feel a greater effective nuclear charge than p electrons. So, despite an increase in the overall nuclear charge, the p electron in a boron atom is more easily removed than the s electron of a beryllium atom.

Nitrogen has three p electrons, one in each of the 2p orbitals. Oxygen has an extra electron in one of these singly occupied orbitals. This results in an electrostatic electron-electron repulsion that makes ionisation much more easy than might have been expected. The ionisation energy then increases to a maximum for the row when we reach neon.

Figure 1: Diagram of the trend in first ionisation energies for the elements lithium to neon.
Energy ↑       º
    º º 
   º º  

Atomic and Ionic Radii

There are three measurements that give an indication of the sizes of atoms:

  1. Single-bond covalent radius (rcov)
  2. Van der Waal's radius (rvdw)
  3. Ionic radius (rion)

Values of the single-bond covalent radii are estimated from the known length of single bond in compounds containing the element. Hence the covalent radius of carbon, for example, can be estimated as being half the length of the C-C single bond in diamond.

The van der Waal's radius is the closest possible distance that the nucleus of a neutral atom can get to the edge of another atom without the two bonding, and so will be the limit on the distance that two atoms in a solid can come together.

The ionic radius is the radius of the charged atom in the lattice of an ionic solid. It is assumed that the distance between the nuclei of a neighbouring anion and cation will be the sum of their ionic radii. This distance is found by a technique called 'X-ray crystallography', but a starting assumption must be made as to where the boundaries of the ions are - where one ion stops and the other begins. After one assumption is chosen and applied, the ionic radii determined using this assumption will be self-consistent. For example, with an estimation of the ionic radii in an ionic compound, such as sodium fluoride, the radii of other ions can be found by measuring the internuclear distances in the sodium and fluoride salts of other elements.

Table 2: Selected covalent, van der Waal's and ionic radii (numbers in brackets refer to the charge on the ion).
ElementSingle bond covalent
radius, rcov (pm 1)
Van der Waal's
radius, rvdw (pm)
Ionic radius,
rion (pm)
Li14018090 (1+)
Be120-59 (2+)
O70140126 (2-)
F54135119 (1-)
Cl97180167 (1-)
Br114190187 (1-)
I133200206 (1-)

Periodic trends in radii can be observed. On descending through a group of the periodic table, the radii increase due to the use of successively higher principle shell to accommodate valence electrons (note the radii of the halogens, F, Cl, Br and I, quoted in table 2). If we go across a row where the different elements house their valence electrons in the same principle shell, a decrease in covalent and van der Waal's radii with increasing atomic number can be seen. For example, the covalent radii of Li to F in table 2.

This is due to the increasing effective nuclear charge holding the valence electrons closer to the nucleus. The ionic radii of cations are always observed to be smaller than the covalent radius for the parent atom. This is because removal of an electron causes a reduction in the repulsions between the remaining electrons, and so they are held closer by the positive charge of the nucleus.

In the cases where cation formation results in the loss of all valence electrons, as is the case for the alkali metals, only the radius due to the inner closed shell is measured, which is smaller than that of the valence shell. For anions, the ionic radius is larger than the covalent radius. This is because there is a greater repulsion when extra electrons are added, giving a larger size.


The electronegativity, χ, of an atom in a molecule is its ability to attract the electrons in its bonds to itself. There have been several ways developed to determine values for an element's electronegativity.

The method developed by Mulliken uses the average of the ionisation energy and the negative of the electron attachment enthaply to give a value for χ. The electron attachment enthalpy, ΔHEA, is the energy that is given out when a neutral atom in the gas phase combines with a free electron. Elements where this value is positive, that is energy is required to attach the electron, resist anion formation. This is typical of the alkaline earth metals, which favour formation of cationic 2+ ions.

Hence, electronegativy can be seen as a balance between an atom's ability to gain and to lose electrons. This can't give a full set of elecronegativity values for the whole periodic table, however, as the electron attachment enthalpies of many elements can't be measured.

Alternative methods have been put forward by Linus Pauling and jointly by Allred and Rochow. All three methods give similar values for the electronegativities of the elements and show similar trends. On moving across a row of the periodic table, in order of increasing atomic number, the value of χ increases, mainly due to the increasing effective nuclear charge.

Electronegativities fall when descending a given group because the atoms become larger and more polarisable. This means that they become less able to pull the electrons in bonds toward them, meaning, by definition, that their electronegativities are reduced. Therefore, fluorine, in the top right hand side of the periodic table, is found to have the highest electronegativity, with a value of about 4.0, depending on the method used, while the lowest values are found for the heavier alkali metals of group 1, where values of approximately 0.8 - 0.9 are found. The difference in electronegativities is the cause of polarities in bonds, where the atoms hold partial charges, and forms the basis of intermolecular forces of attraction, such as hydrogen-bonding and dipole-dipole forces.

Covalent and Ionic Inorganic Compounds.

There are many examples of covalently-bonded compounds throughout inorganic chemistry, where their structure is dependent on the formation of chemical bonds between atoms that share electrons. These include discrete molecules, such as water, and polymeric inorganic solids, such the halides of beryllium. Many co-ordination compounds of the transition metals and organometallic compounds can also be described as being covalent in nature, as can many compounds of the lighter alkali and alkaline earth elements - lithium, beryllium and some compounds of magnesium. Much of the chemistry of the elements of the p block (groups 13-17) is also covalent. The principles of chemical bonding can be found in Valence Bond Theory and the Molecular Orbital Theory of Chemical Bonding.

Much of inorganic chemistry deals with the chemistry of ionic compounds. These consist of positively-charged cations and negatively charged anions. The simplest ionic compounds are those in which there are monatomic cations, such as Na+ or Ca2+, and monatomic anions, such as the chalcogenides, O2-, S2-, halides such as F- and Cl-. For example, rock salt (NaCl).

There are also compounds with more complicated cations and anions. For example, we can form molecular cations from group 15 elements, such as ammonium and phosphonium ions (eg, NH4+, and P(CH3)4+), which are covalently bonded but have an overall charge. The chemistry of molecular cations containing metal ions, and also molecular anions that contain metal cations depending on the ligands, is generally considered to be the realm of co-ordination chemistry.

There are also many examples of molecular anions. These include oxo anions, such as nitrate, NO3-; sulphate, SO42-; carbonate, CO32-; and phosphate, PO43-. There are also carboxylates, which are the salts of various carboxylic acids. Other important anions are hydroxide, OH-; and alkoxides, RO-, which are deprotonated alcohols.

Co-ordination Chemistry

Co-ordination chemistry deals with the chemistry and behaviour of compounds containing metal atoms or ions surrounded by other ions or molecules. These groups which surround and bind to the metal are called ligands and can generally be divided into two broad types:

  1. Those which bind to the metal through carbon atoms
  2. Those that bond through atoms of other elements

Associations of metals and ligands are called 'complexes'. Complexes containing ligands that bind to the metal through carbon atom are called 'organometallic complexes' and tend to be treated separately from mainstream co-ordination chemistry due to some of their unique features.

Co-ordination compounds dominate the chemistry of the transition metals elements. However, co-ordination chemistry is not limited to the transition metals: complex formation also occurs for the alkali and alkaline earth metals, metallic elements of the p block and the lanthanides and actinides. The interactions between the metal and ligand can vary between being highly covalent and being mainly electrostatic, that is ionic, in nature.

It is convenient to classify these types of substances as co-ordination compounds as they can be described in terms of a positively charged metal ion, Mn+, with a virtually limitless range of ligands, L, that can be arranged about it. Complexes can be positively or negatively charged or neutral; the overall charge being the sum of the charges of the metal ion and the ligands. For example, chloride ligands have a 1- charge by convention, and so in the Pt2+ complex [Pt(NH3)2Cl2], there is no overall charge, but there is a 2- chrage for the complex [PtCl4]2-.

Only the basic concepts which apply to all complexes are described here.

Co-ordination Number and Complex Geometry.

The number of groups that surround the metal is called the 'co-ordination number'. This has a direct impact on the geometry of the ligands about the metal in complexes. Complexes with a co-ordination number of two are quite rare, and are usually relegated to complexes of Cu+, Ag+ and Au+ ions - for example [Ag(NH3)2]+ - and also some complexes of Hg2+. Other complexes can be found with a co-ordination number of two if the ligands are very bulky and are too large to allow the incorporation of further ligands around the metal.

Three co-ordinate complexes tend to be trigonal planar, where the metal atom and the co-ordinating atoms of the ligands, in a triangular arrangement, are all in the same plane. If the metal has a lone pair of electrons then this geometry is distorted, forming a trigonal pyramid with the ligands bent down away from the lone pair, for example as in SnCl3-.

Some co-ordination compounds that might seem to be three co-ordinate may form bridging complexes, where metal atoms actually bind to four ligands. An example of this is AlCl3, which exists as Al2Cl6, where two of the chlorides bridge the two Al ions.

In four co-ordinate complexes of non-transition metals, the most common geometry is tetrahedral, such as BH4- and AlCl4-. Some four co-ordinate complexes of transition metals are also tetrahedral, although complexes of the +1 ions of group 9 and the +2 ions of group 10 are square planar.

Complexes with a co-ordination number of five are trigonal bipyramidal or square pyramidal. Trigonal bipyramidal complexes have an equatorial plane of three ligands, resembling a trigonal planar three co-ordinate complex, but has an extra two ligands in axial positions above and below this equatorial plane. Square pyramidal complexes are like square planar complexes, but with an extra ligand in one of the axial positions. Five co-ordinate complexes often exist as a mixture of these two geometries in equilibrium when in solution.

Complexes with a co-ordination number of six are almost exclusively octahedral in geometry. Here, the six ligands are at right angles to each other. The 3D shape formed by the ligand has eight sides, and so is called an octahedron. Another possible structure is a trigonal prismatic complex, which resembles a short Toblerone box-like shape with the metal in the centre.

Table 3: Common Structures of co-ordination compounds.
Structures of co-ordination compounds
2L-M-L linear
3 L L L L | \ / \ /  M M M M / \ /|\ / \ / \  L L L L L L L L Trigonal Trigonal Bridged planar pyramidal
4 L | L-M-L Square planar or tetrahedral | L
5 L L L L |/ |/  L-M L-M-L |\ /  L L L Trigonal Square bipyramidal pyramidal
6 L L |/  L-M-L /| L L Octahedral

Types of Ligand

Ligands are anions or neutral molecules that can be thought of as donating pairs of electrons to the metal. Ligands such as the halogens, F-, Cl-, Br- and I-; other anions such as cyanide, CN- and hydroxide, OH-; neutral molecules like ammonia, NH3, water, H2O and alcohols, ROH, all bind to the metal through one atom and donate one pair of electrons to a metal atom in a complex. They are therefore called monodentate ligands, which literally means 'one-toothed' ligands.

Ligands may also contain more than one atom which is able to donate an electron pair. Such ligands, which bind through more than one atom, are called 'multidentate ligands'. Such ligands when co-ordinated form a ring containing the metal and can also be called chelating (pronounced kee-lating, from the Greek word for claw) ligands. The most commonly-used multidentate ligands are bidentate, and co-ordinate to the metal through two atoms. Examples include diamines, such as ethylenediamine (abbreviated to en, figure 2), and diphosphines, such as bis(dimethylphosphino)ethane (dmpe). Both of these examples bind to the metal to form a five membered ring.

Carboxylates, the anions of carboxylic acids, can co-ordinate through one of the oxygen atoms, but can also bind to metals through both oxygen atoms, forming a four membered ring. Carboxylates are also capable of binding to two metal ions by bridging them and co-ordinating one oxygen to each metal. The ring formed by the co-ordination of a bidentate ligand is called a 'chelate ring'.

Figure 2: Example of the of the bidentate ligands ethylenediamine (en), bis(dimethylphosphino)ethane (dmpe) and carboxylates bound to a metal. [M] is some metal ion with all other ligands omitted for clarity. [M] [M] / \ / \  H2N NH2 (CH3)2P P(CH3)2 \ / \ /  H2C-CH2 H2C-CH2 en dmpe O / \  R-C [M] \ /  O carboxylate

There are many examples of tridentate ligands which bind through three atoms such as the triamine H2N-CH2CH2-NH-CH2CH2-NH2, an analogue of the bidentate diamine. There are also many tetradentate ligands, like the tetraamine H2N-CH2CH2-NH-CH2CH2-NH-CH2CH2-NH2, and molecules called 'porphyrins'. These are large ring molecules which contain four nitrogen atoms that point into the centre.

These types of ligands are important in nature and are the molecules incorporated into proteins such as heamoglobin, where it acts act as the ligand for the Fe2+ ion. Higher denticities are also possible, and another important ligand is ethylenediaminetetracetate, or EDTA4- (figure 3). This can co-ordinate to a metal ion through two nitrogen atoms and through one oxygen atom in each of its four carboxylate groups. Here the individual carboxylate are monodentate rather than bidentate, and so the ligand is hexadentate overall.

Figure 3: Structure of the hexadentate ligand EDTA4-. O- O- | | O=C-CH2 H2C-C=O \ /  :N-CH2-CH2-N: / \  O=C-CH2 H2C-C=O | | O- O-

Stability of Complexes

The stability of complexes in solution depends on the extent to which the metal ion associates with its ligands. This is all down to the thermodynamic equilibria associated with the reactions that form complexes. If a metal ion, M, is put it into solution with a ligand, L, then an equilibrium will be formed:

M + L ↔ ML

An equilibrium constant, K, describing the extent to which the complex ML forms can be described by the equation:


[ML], [M] and [L] are the concentrations of each of these species. If there is more than one ligand in the complex this gives us the equilibrium and equation:

M + n L ↔ MLn

β is the overall constant of formation for the complex. Since there will be separate equilibria for the sequential addition of each ligand, β is the product of all the equilibrium constants. The larger the value of β, the more stable the complex will be. If a complex ML*n with different ligands, L*, has a greater value of β than that for MLn, addition of the ligand L* to a solution of MLn will result in ligand displacement:

MLn + n L* → ML*n + n Ln

An important factor in the stability of complexes is the 'chelate effect'. A complex that contains bidentate ligands, and, therefore, chelate rings, will be more stable than a similar complex that has the same donating atoms but where the chelate rings are absent. For example, the bidentate ligand ethylenedaimine, or 'en', (H2N-CH2CH2-NH2) can be imagined to co-ordinate to a metal in a similar way to two monodentate ammonia molecules, NH3.

Complexes containing an en ligand will therefore be more stable than a complex containing two ammonia ligands. If ethylenediamine is added to a solution of the complex [Ni(NH3)6]2+ then ligand substitution will take place.

[Ni(NH3)6]2+ + 3 en → [Ni(en)3]2+ + 6 NH3

Why does the chelate effect work? One way to look at this is that the complexes are present in equilibrium, with small amounts of metal ion and dissociated ligand. For the bidentate ligand, if one nitrogen comes off the metal, the other is still attached, and so can't go far away, resuling in rapid reco-ordination.

We can also look at it thermodynamically. The overall energy change during the formation of the complexes [Ni(NH3)6]2+ and [Ni(en)3]2+ by addition of the ligands to solutions of the aqua ion [Ni(H2O)6]2+ will have two components:

  1. The enthalpy change, ΔH - the difference in energy due to the breaking and forming of bonds
  2. The entropy change, ΔS - the energy component due to the change in randomness of the system

It is found by studying many different complexes which contain different types of ligands and metal ions that the enthalpy change for the formation of a chelated complex is sometimes more favourable (more negative in value) or less favourable (more positive in value) than the value for non-chelated complexes. This difference between the enthalpies for a chelating and a non-chelating complex is often very small, however, and so doesn't have a great effect.

On the other hand, the entropy change for the formation of a chelated complex is always much more favourable than that of the non-chelated complex.

In forming [Ni(NH3)6]2+ from [Ni(H2O)6]2+, there are six ammonia molecules replacing and freeing six water molecules, forming the same number of molecules overall as we started with. Hence, the entropy change will be small. In forming [Ni(en)3]2+, three en molecules are used to replace six water molecules, so there are more product molecules than there are reactant molecules. This leads to greater disorder in the system, and a much larger, positive, entropy change, which is favourable. Therefore, the value of β is greater for [Ni(en)3]2+ than it is for [Ni(NH3)6]2+. Thus, the chelate effect is entropic in nature. This has long been exploited by nature to handle metal ions in biochemical processes.

Another important concept in the stability of complexes is the relative 'hardness' or 'softness' of the metal ions and the donating atoms of its ligand. Complexes can be described as being made up of a cationic metal ion, that can accept electrons, and is therefore a Lewis acid, surrounded by electron donating ligands, that are Lewis bases.

Metal ions and their ligands can be divided into two broad categories:

  1. 'Hard' acids and bases.
  2. 'Soft' acids and bases.

Hard metal ions are those which are small and compact, holding their electrons close, and so are not easily polarisable. These include the ions of the alkali and alkaline earth metals and the lighter and highly charged transition metal and ions, such as Ti4+, Fe3+, Co3+ and Al3+. The donating atoms of hard ligands are also small, electronegative and so non-polarisable, for example, nitrogen and oxygen, containing ligands such as amines and alkoxides and lighter halides such as fluoride.

Soft metal ions are larger and are much more polarisable. These include the heavier transition metals, such as Hg2+, Pt2+, Pt4+, Ag+ and also low valent (+1) metal ions or zero valent (neutral) metal atoms like Cu+. Soft ligands contain donating atoms that are similarly large and polarisable, such as those containing sulphur, phosphorus or heavier halides such as iodide. The general rule for the stability of complexes is that hard metals prefer hard ligands and soft metals prefer soft ligands (table 4).

Table 4: Relative stability of complexes of soft and hard metal ions for ligands containing donor atoms for groups 15, 16 and 17 of the periodic table.
Complexes of "Hard" Metal ions,
eg Ti4+, Co3+
LigandsComplexes of "Soft" Metal ions,
eg Pt2+, Hg2+, Ag+

Organometallic Chemistry

An important area of inorganic chemistry that has expanded enormously over the past four or five decades is organometallic chemistry. This deals with compounds in which ligands that are organic groups bind directly to a metal atom or ion through carbon atoms. The term applies to metal-carbon bonded compounds of the alkali and alkaline earth metals, the transition metals and the metallic elements of the p block. Although not thought of as metals, carbon bonded compounds of boron, silicon and phosphorus can also be classed as organometallic.

Organometallic chemistry might appear to be the border between mainstream inorganic chemistry and organic chemistry. Organometallic compounds have colossal importance in industry as catalysts for the production of many important bulk chemicals and many organometallic compounds are used as reagents in organic synthesis.

Organometallic compounds of highly electropositive metals, such as sodium, are mainly ionic - they contain carbanions, which contain in turn negatively charged carbon atoms. These tend to be highly reactive and sensitive to air and moisture. Many of the organometallic compounds of the transition metals and the p block are much more stable and covalent, having metal-carbon σ-bonds. For example, Re(CH3)6 (figure 4).

The ligand that is ubiquitous in the organometallic chemistry of the later transition metals is the carbonyl ligand, CO, which, when free of the metal, is better known as 'carbon monoxide'. Carbonyl complexes are known for most of the transition metals, for example, a classic example being hexacarbonyl chromium, Cr(CO)6 (figure 4).

Organometallic chemistry also gives several examples of types of molecule that involve unique bonding interactions between the metal and π bonds of organic molecules. A vast number of complexes are known containing alkenes (where the metal forms a three membered ring by interacting with the C=C double bond, the first recorded example being Ziese's complex, PtCl3(H2C=CH2, see figure 4), alkynes and also other organic molecules with extended π systems, including ring molecules like benzene, C6H6, where the metal ion bonds to all six carbon atoms and sits above the ring.

A famous complex of this type latter type which contains two cyclopentadienyl ligands, C5H5-, a ring similar to benzene, is ferrocene, Fe(C5H5)2. In this complex the ligands are parallel to each other, sandwiching an Fe2+ ion between them. The organometallic chemistry is individual groups and elements are discussed in the relevant sections.

Figure 4: Some examples of organometallic complexes. H3 O O C CH3 C C |/ |/  H3C-Re-CH3 OC-Cr-CO /| /|  H3C C C C H3 O O   Cl |  Cl-Pt+-Cl |  H2C=CH2 Zeise's Complex

Some Key Thermodynamic Definitions

  • Ionisation enthalpy - the energy required to completely remove and electron from an atom in the gas phase

  • Lattice enthalpy - the energy given out when a crystalline lattice is formed from the constituent anions and cations in the gas phase

  • Hydration/solvation enthalpy - the energy given out forming a hydrated ion with a solvent shell around it from the bare ion

  • Electron affinity - the energy given out when a neutral atom accepts an electron to form an anion in the gas phase

  • Activation energy - the minimum amount of energy that is required to make a chemical reaction proceed

1A picometre (pm) is a length of 10-12 metres.

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