1. Types of bonding

Much of the variety and complexity of matter is due to the existence of compounds. The constituent atoms in a compound are not free to move independently. Instead, their electrons interact to hold the compound together. The different properties of compounds are due to the different ways in which the electrons interact to form the chemical bonds. The types of bond that exist are ionic, covalent, co-ordinate and metallic.

2. Ionic Bonding

Ionic bonds (or electrovalent bonds) are formed when oppositely charged ions are held together by electrostatic attraction.

Positively charged ions are formed when atoms lose electrons. For example, sodium (₁₁Na, 1s² 2s² 2p⁶ 3s¹) loses its outermost electron to form a sodium ion (₁₁Na⁺, 1s² 2s² 2p⁶):

Na Na⁺ + e^-

The Na⁺ ion is isoelectronic with the noble gas ₁₀Ne. With electronic configuration ns² np⁶ (1s² for He), the noble gases have a full outer shell of electrons and it seems probable that it is this electronic configuration that makes them stable, that is, chemically unreactive. By losing its single outer electron, sodium can also obtain this stable configuration.

Negatively charged ions are formed when atoms gain electrons. For example chlorine (₁₇Cl, 1s² 2s² 2p⁶ 3s² 3p⁵) accepts an electron into its outermost energy level to form a chloride ion (₁₇Cl^-, 1s² 2s² 2p⁶ 3s² 3p⁶):

Cl + e^- Cl^-

By gaining an electron, chlorine becomes isoelectronic with the noble gas argon, ₁₈Ar. Again, the full outer shell brings with it stability.

The sodium atom cannot lose an electron unless another atom will accept it. It can, however, give an electron to a chlorine atom. The transfer of the electron from sodium to chlorine forms two ions with full outer electron shells (figure 1.1). The electrostatic attraction between oppositely charged ions holds the ions Na⁺ and Cl^- together. The electrostatic attraction is the chemical bond in the compound sodium chloride. It is called an ionic bond or electrovalent bond. Sodium chloride is an ionic or electrovalent compound.

[D.R.B1]

Figure 1.1 The formation of sodium chloride.

3. Energy Contributions to Ionic Bond Formation

The formation of ionic bond may be analysed into three steps:

• removal of an electron from A to form A⁺ (the ionisation energy of A)

• addition of an electron to B to form B^- (the electron-gain energy of B)

• electrostatic attraction between the oppositely charged ions A⁺ and B^-.

An ionic bond between atoms A and B will form only if it is energetically favourable overall. Similar considerations apply in ionic crystals except that larger numbers of interacting ions must be considered.

The energy of bond formation will be favourable if A has a low ionisation energy (so that it is easy to remove electrons); if B has a large, exothermic electron-gain energy (so that energy is released when B^- is formed); and if the ions are close enough together to maximise the mutual attraction and overcome the energy required for ionisation.

Atoms with low ionisation energies have outer (valence) electrons that can be removed easily and they can be expected to participate in ionic bonding. Once the valence electrons have been lost, further ionisation would take so much energy that it would not be recovered from increasing attraction. Therefore, core electrons do not play any part in ionic or (for analogous reasons) covalent bonding. The elements with the lowest ionisation energies are those in which the outer electrons are far from the nucleus and are well shielded from the full nuclear charge by inner electrons. These include the larger Group 1 and Group 2 metals such as Rb, Cs and Ba.

Atoms with exothermic electron-gain energies accept an added electron into a gap in the valence shell where it is strongly attracted by a large effective nuclear charge. Once the outer shell is full, an added electron must enter a new shell more distant and more shielded from the nucleus. A closed-shell anion (e.g. Cl^-) thus has a strongly endothermic electron-gain energy. Any further addition of electrons would not be recovered from increased electrostatic attraction. The electron-gain energy will be highest for atoms in which the outer electrons are close to the nucleus and shielded little from the nuclear charge. These include the smaller Group 16 and Group 17 elements such as F, O and Cl.

Ionic bonds are likely to form between elements on the left and elements on the right of the Periodic Table, electron transfer occurring until all atoms have gained or lost enough electrons to reach closed-shell configurations. In 1916, G. N. Lewis formulated this as the octet rule:

atoms have a tendency to form a stable octet of electrons

In modern parlance, ‘stable octet’ means an outer electronic configuration of ns² np⁶.

The word tendency should not be misinterpreted. The energy of a gas phase O^2- ion is greater than that of a gas phase O atom. It is only formed because the overall energy change, including the interactions in a solid ionic compound, is favourable.

Similarly, Group 1 and 2 metals do not want to lose electrons and Group 16 and 17 elements do not want to gain electrons. The electrostatic attraction between the resulting ions is large enough to overcome the energy required to form the ions.

4. Crystals

One feature of ionic compounds is that they form crystals. The crystals of sodium chloride are perfect cubes. In a solution of sodium chloride, the sodium ions and chloride ions move about independently of other ions. When the solution is evaporated to the point of crystallisation, the ions move much closer to each other. A sodium ion attracts chloride ions, as shown in figure 4.1.(a). Each chloride ion attracts other sodium ions, and a three-dimensional arrangement of ions called a crystal structure is built up [figure 4.1.(b)]. There is no pair of Na⁺ and Cl^- ions that could be regarded as a molecule of sodium chloride. The formula NaCl represents the ratio in which ions are present in the crystal structure. A pair of ions Na⁺Cl^- is called a formula unit of sodium chloride.

Figure 4.1 The arrangement of ions in a sodium chloride crystal.

Figure 4.2 Electron density map for sodium chloride.

The crystal is uncharged because the number of sodium ions is equal to the number of chloride ions. The bonds between the positive and negative ions are strong. This is why solid sodium chloride does not conduct electricity and is not electrolysed. In the solid, the ions cannot move out of their positions in the three-dimensional structure. When the salt is melted or dissolved, the ions are free to move and can travel towards the electrodes.

An impressive demonstration of the existence of ions is the use of X ray analysis to obtain electron density maps. The one for sodium is shown in figure 4.2. It consists of regions of charge which are isolated from other regions of charge. This is the picture one would expect from a structure consisting of separate Na⁺ and Cl^- ions. The technique is now sufficiently advanced to show that there are ten electrons, not eleven, associated with each sodium nucleus: the species present is Na⁺ not Na.

5. Ionic Radii

The distance between the centres of ions in a crystal is the sum of the cationic radius and the anionic radius. Pauling apportioned the interionic distance in KCl (0.314nm) between the K⁺ and the Cl^- ions. These are isoelectronic (have the same number of electrons). He assumed that the radius of each ion is inversely proportional to its effective nuclear charge. Pauling obtained values for the ionic radii: K⁺, 0.133nm and Cl^-, 0.181nm. Ionic radii appear to be additive. By substituting these ionic radii in other compounds containing K⁺ and Cl^-, values for the ionic radii of a number of ions can be obtained. Some of these are shown below (O =0.13nm = 130pm):

6. The Metallic Bond

Modern technology is based on the use of metals. There must be some feature of the bond between metal atoms that gives metals their special properties. Many metals are strong and can be deformed without breaking; many are malleable (can be hammered) and ductile (can be drawn out into wires). They are shiny when freshly cut and good conductors of heat and electricity. Any theory of metallic bonding must account for all these features.

The outer shell electrons of a metal (the valence electrons) are relatively easily removed, with the formation of metal cations. When two metals approach closely, as in a metal structure, their outer shell orbitals overlap and combine. They form a set of new orbitals surrounding both atoms called molecular orbitals. If a third atom approaches, its atomic orbitals can overlap with those of the first two atoms to form another molecular orbital. For a large number of atoms, a large number of molecular orbitals are formed, extending over three dimensions. As a consequence of the multiple overlapping of atomic orbitals, the outer electrons from each atom come under the influence of a very large number of atoms. They are free to move through the structure and are no longer located in the outer shell of any one atom: they are delocalised. The removal of the electron leaves behind metal cations. The reason why the cations are not pushed apart by the repulsion between them is that, in a pair of cations, each cation is attracted to the delocalised electron cloud between them (figure 6.1).

This theory of the metallic bond explains the physical properties of metals. If a stress is applied to a metal, the structure can change in shape without fracturing (figure 6.1).

Figure 6.1 Deformation of a metal structure.

The high thermal conductivity of metals is accounted for. When heat is supplied to one end of the metal, the kinetic energy of the electrons is increased. The increase is transmitted through the system of delocalised electrons to other parts of the metal.

Electrical conductivity can also be explained. If a potential difference is applied between the ends of a metal, the delocalised electron cloud will flow towards the positive potential.

The shiny appearance (lustre) of metals fits in with the theory of the nature of the metallic bond. The metal contains a large number of molecular orbitals at a large number of different energy levels. When photons of light fall on to the metal, the energy associated with the photons can be absorbed by the electrons, exciting them to higher energy levels. A large number of transitions between energy levels is possible, with a whole range of frequencies of light being absorbed. As electrons return to lower energy levels, light is emitted and makes the metal shine.

Since the bonding in metals stems from the attraction of the metal cations to the delocalised electrons, it is not surprising that moving from sodium (one outer electron) through magnesium (two outer electrons) to aluminium (three outer electrons) the bonding gets gradually stronger. Thus the melting point and boiling point rise from sodium to aluminium:

	Na	Mg	Al
r/ gcm^-3	0.97	1.74	2.70
Mpt/°C	97.8	650	660
Bpt/°C	890	1110	2470
k/W^-1m^-1	0.218	0.224	0.382

The stronger bonding from Na to Al means that the atoms are pulled closer together in Al than in Na. This explains the increasing density: Na < Mg < Al.

The increase in the number of delocalised electrons in moving from Na to Al also accounts for the increasing thermal and electrical conductivity.

7. Covalent Bonding

Two models exist for the formation of covalent bonds. The valence bond method considers atomic orbitals in isolation from the rest of the molecule. For example, two atoms of chlorine combine to form a molecule, Cl₂. Both chlorine atoms have an incomplete outer (valence) atomic orbital (3p_z). The two atoms have to approach sufficiently closely for the valence atomic orbitals to overlap. The two electrons then occupy the same orbital- called a covalent bond- and have opposing spins. By sharing electrons each of the bonded atoms ‘completes its octet’ and gains a full outer shell of electrons (figure 7.1). Thus, a covalent bond is a shared pair of electrons.

Figure 7.1 Ways of representing the chlorine molecule.

A double bond or a triple bond is formed when two atoms share two or three pairs of electrons (figure 7.2).

Figure 7.2 Ways of representing the carbon dioxide and nitrogen molecules.

In carbon dioxide, the carbon atom shares two electrons with each of two oxygen atoms, in order to give each a full octet of valence electrons. As each shared pair of electrons is a covalent bond, the two pairs of shared electrons between carbon and oxygen constitute a double bond. The pairs of electrons on the oxygen atom which are not shared are described as ‘lone pairs’ of electrons.

The molecular orbital method considers the entire molecule as a unit. Each electron is under the influence of all the nuclei and every other electron in the molecule. Quantum mechanics are used to calculate the electron density throughout the molecule. The result of the calculation for the hydrogen molecule is shown in figure 7.3.

Figure 7.3 The electron density map for the hydrogen molecule.

There is a region of electron density between the two nuclei called the electron cloud. The attraction of both nuclei to this electron density holds the atoms together in the molecule. The electron density also shields the nuclei from one another, preventing the repulsions between the two positively charged nuclei from driving the atoms apart. The interatomic distance between nuclei in a molecule is the distance at which the repulsive forces are balanced by the attractive forces (figure 7.4).

Figure 7.4 Attraction and repulsion in the hydrogen molecule.

8. Electronegativity

H							He
2.1
Li	Be	B	C	N	O	F	Ne
1.0	1.5	2.0	2.5	3.0	3.5	4.0
Na	Mg	Al	Si	P	S	Cl	Ar
0.9	1.2	1.5	1.8	2.1	2.5	3.0
						Br	Kr
						2.8

Electronegativity is the power of an atom to attract electron density from a covalent bond. It can be calculated by various means and is usually given a number varying from 0.7 to 4.0. Small atoms with a large number of protons in the nucleus attract electron density most strongly. Therefore the electronegativity increases from left to right across a period in the Periodic Table and from the bottom to the top of a group. As the noble gas elements do not participate in covalent bonding, they cannot be assigned a value for electronegativity.

When a covalent bond exists between atoms of differing electronegativity the shared pair of electrons is displaced towards the most electronegative atom.

e.g. B is more electronegative than A.

The displacement of electron density makes the less electronegative atom slightly electron deficient (hence d+) and the more electronegative atom has a slight excess of electron density (hence d-). This charge separation creates an electric dipole and the molecule is described as polar. Two examples of molecules with polar bonds are:

and

The polarity of a bond can be measured in a unit called the Debye. Its magnitude depends on the difference in electronegativity between elements.

molecule	electronegativity difference	dipole/ Debye
HCl	0.9	1.03
HBr	0.7	0.78
HI	0.4	0.38

There is no sharp distinction between an ionic bond and a covalent bond (figure 8.1). The term ionic bond is used for bonds which are predominantly ionic. The term covalent bond is used for non-polar bonds such as C-I, and also bonds in which there is a considerable degree of polarity. Bonds such as C-Cl and C-O are termed polar covalent bonds. The curve relating the percentage of ionic character in a bond to the difference in electronegativity between the bonded atoms is given in figure 8.2.

Figure 8.1 Bond types

Figure 8.2 Curve relating the percentage of ionic character in a bond

to the difference in electronegativity between the bonded atoms

Approximate values for some covalent bonds are given in the following table.

Bond	C-I	C-H	C-Cl	C-F
Ionic character/ %	0	4	6	40

9. Covalent Radii

The distance between the nuclei of covalently bonded atoms is the sum of their covalent radii. Covalent radii, which are also called atomic radii, are additive. The sum of the covalent radii of chlorine and hydrogen gives the length of the covalent bond in hydrogen chloride (figure 9.1).

Figure 9.1 Covalent radii for hydrogen and chlorine

10. Polarisation of Ionic Bonds

In an ionic lattice, if the ions are perfectly spherical, the bonds are said to be ‘perfectly ionic’. This is true for calcium fluoride, CaF₂ (figure 10.1).

Figure 10.1 The electron density map for calcium fluoride

When a large negative ion in a lattice is adjacent to a positive ion which is small and highly charged, the electron cloud around the negative ion is usually distorted so that it is no longer spherical. A positive ion with a high charge to size ratio attracts electron density from neighbouring anions as shown in figure 10.2. The large negative ion is distorted and polarised. Some electron density is concentrated between the ions and the bond begins to resemble a covalent bond in which an electron pair is localised between two atoms.

Figure 10.2 Distorted ions in LiI

In lithium iodide, the small lithium ion has a high charge to size ratio and the large, polarisable iodide ion is distorted by it. The bonding in lithium iodide is said to be ‘ionic with covalent character’.

The Al³⁺ ion also has a very large charge to size ratio. It attracts electrons so strongly that AlCl₃ is a covalent molecule that exists in the forms shown in figure 10.3.

Figure 10.3 Aluminium chloride

The Al₂Cl₆ molecule is formed when two AlCl₃ molecules link with co-ordinate bonds (see §11) formed by donation of lone pairs from two of the chlorine atoms.

Across Period 3 from Na to Si, the type of bonding in the chlorides changes as follows:

NaCl	MgCl2	AlCl3	SiCl4
ionic	ionic with some covalent character	covalent	covalent

11. The Coordinate Bond

A coordinate bond is a covalent bond in which the shared pair of electrons is provided by only one of the bonded atoms. One atom is the donor, the other is the acceptor, and the bond is sometimes called the dative covalent bond. Once formed, a coordinate bond is identical to a covalent bond.

For an atom to act as a donor it must have at least one pair of unshared electrons (a lone pair) in its outer shell. The acceptor must have at least one vacant orbital in its outer shell. It may be a metal cation or a transition metal atom or an atom in a molecule.

Figure 11.1 Coordinate bond formation.

It is sometimes convenient to use the symbol to highlight a coordinate bond in a molecule, the arrow pointing from the donor towards the acceptor:

12. Intermolecular Forces

Covalent molecules are attracted to each other by intermolecular forces. In order of strength these forces are:

All species, even noble gases, are attracted to each other by van der Waals forces.

Polar molecules contain atoms with different electronegativities and, in addition to attraction by van der Waals forces, these molecules attract each other by permanent dipole-dipole forces.

Molecules which contain hydrogen covalently bonded to a nitrogen or an oxygen or a fluorine atom are attracted to each other by hydrogen bonding.

13. Van der Waals Forces

These are temporary, induced dipole-dipole attractions. At any instant in time the electron distribution in a non-polar covalent molecule may be unsymmetrical due to the fluctuating movement of electrons. This leads to a temporary dipole which induces an opposite dipole in a second molecule. The second molecule is therefore attracted to the first molecule:

The dipoles are temporary but the net attraction which they produce is permanent.

The ease with which an electron cloud is distorted, and therefore the ease with which a dipole is induced, is called polarisability. Polarisability increases with number of electrons in a molecule, and the magnitude of van der Waals forces therefore increases with molar mass. The shape of a molecule is another factor: elongated molecules are more easily polarised than compact, symmetrical molecules. Figure 13.1. illustrates these effects. The ellipses represent the boundary of the electron density in each molecule. The d+ and d- charges shown are temporary and fluctuate around the molecule with time.

Figure 13.1 Van der Waal forces in alkanes

Pentane and 2,2-dimethylpropane have the same molecular formula (C₅H₁₂) and the same molar mass but the molecules of the branched chain alkane, due to their more spherical nature, cannot pack together as closely and therefore their induced dipoles are weaker. The boiling point of the branched chain isomer is therefore less than that of the straight chain alkane.

Figure 13.2 Van der Waals forces in liquid argon

If a pair of molecules are far apart, there will be no induction of dipoles and no attractive forces between them. If the molecules move to close together, repulsion between electron shells will predominate over the induction effect and drive the molecules apart. Figure 13.2 shows how closely argon atoms can approach in the liquid state. Half the distance between the atoms at their closest distance is called the van der Waals radius of the atom.

14. Permanent Dipole-Dipole Forces

Molecules with permanent dipoles attract each other:

The permanent dipoles are stronger than temporary ones and therefore permanent dipole- permanent dipole intermolecular forces are stronger than intermolecular van der Waals forces.

In the solid state, polar molecules interact to form an ordered arrangement in which the partial positive (d+) charges are adjacent to partial negative (d-) charges (figure 14.1).

Figure 14.1 The process of dissolution

Polar solids dissolve in polar solvents (i.e. like dissolves like). The energy required to break up the crystal is recovered when energy is released as polar solute molecules interact with polar solvent molecules. This interaction is called solvation (figure 14.1); if the solvent is water, it is called hydration.

15. Hydrogen Bonding

This is the name given to the strongest type of intermolecular force between neutral molecules. It is a special case of a permanent dipole- permanent dipole force which exists between a lone pair of electrons on a nitrogen, oxygen, or fluorine atom and a hydrogen atom which has a strong partial positive (d+) charge because it is attached to an atom with a large electronegativity (N, O, or F). The electronegative atom pulls electron density away from the hydrogen so that, on the side opposite the bond, the hydrogen appears almost like an unshielded proton. Two examples of hydrogen bonding are:

The nucleus of a hydrogen-bonded hydrogen atom is always in line with the nuclei of the two electronegative elements on either side. Hydrogen bonds are much weaker than covalent bonds- typically between 5% and 10% of the strength of a covalent bond (≈ 20kJmol^-1). Nevertheless, this intermolecular force is strong enough to cause anomalously high melting and boiling points for some compounds (figure 15.1).

Figure 15.1 Graphs of melting temperature against period number (left) and boiling temperature against period number (right)

The boiling and melting points of hydrides generally increase down a group in the Periodic Table. The melting and boiling points of H₂O, NH₃ and HF go against this trend and are therefore higher than expected due to hydrogen bonding.

When the molar masses of carboxylic acids are found from measurements in the vapour phase, the values are often up to twice the values expected from the formula. The molecules are thought to dimerise through the formation of hydrogen bonds:

Water is a hydrogen-bonded association of water molecules. A substance such as ethanol, C₂H₅OH, will dissolve in water as molecules of ethanol can displace water molecules in the association:

Compounds such as chloroethane, C₂H₅Cl, do not form hydrogen bonds with water ad are only slightly soluble.

The bonds in water, H₂O, are inclined at approximately the tetrahedral angle (≈109°). The lone pairs occupy the other apices of the tetrahedron. Liquid water contains associations of water molecules. In ice, the arrangement of molecules is similar, but the regularity extends throughout the whole structure. The structure spaces the molecules further apart than they are in liquid water. This is why, when water freezes, it expands by 9%, and why ice is less dense than water at 0°C. The underlying structure of ice resembles that of diamond figure 15.2).

Figure 15.2 Hydrogen bonding in ice

The fact that ice is less dense than water at 0°C explains why ponds and lakes freeze from the surface downwards. Water reaches its maximum density at 4°C. As it cools further, the water at the surface becomes less dense and therefore stays on the top of the slightly warmer water until it freezes. The layer of ice on the surface helps to insulate the water underneath from further heat loss. Fish and plants survive under the ice in Canadian lakes and rivers for months.

Hydrogen bonding is important in protein molecules. Proteins consist of long polyamide chains. A single protein molecule contains many hydrogen bonds. They are one of the forms of interaction that hold the protein in a three-dimensional arrangement described as the secondary structure of the protein. Figure 15.3 shows an a helix- a spiral which, looking away from you, is spiralling in a clockwise direction.

Figure 15.3. A protein chain with the a helical structure

Hydrogen bonding is also important in the famous double helix of DNA. Chromosomes are the bodies in the nuclei of the cells of living organisms which carry genetic information. They contain macromolecular substances called nucleic acids. There are two types: ribonucleic acid, RNA, and deoxyribonucleic acid, DNA. The macromolecular chains in DNA are of the type:

where P is a phosphate group and S is the sugar deoxyribose. B is one of the four bases: adenine, thymine, cytosine and guanine. DNA consists of two macromolecular strands spiralling round each other in a double helix (figure 15.4). The strands are held together by hydrogen bonding between the bases: B^........B.

Figure 15.4. The double helix

Of the four bases, thymine can pair up with adenine by hydrogen bonding and cytosine can form hydrogen bonds with guanine (figure 15.5). The double helix brings these base pairs into contact so they can form the bonds that keep the structure intact.

Figure 15.5 Hydrogen bonding of base pairs in DNA

16. The Nature of Gases, Liquids and Solids

Gases are made up from particles which move with rapid random motion. The size of the particles and any intermolecular forces can be ignored unless the particles are close together at high pressure or at low temperature.

In liquids the particles are in a state of order which is intermediate between that of a gas and that of a solid. At any instant in time the arrangement of particles resembles a somewhat disordered solid. Over a period of time the disordered regions allow all the particles in a liquid to move through the liquid. The particles are held together by forces similar to those in a solid.

In solids the particles remain in fixed positions about which they can vibrate. The forces which hold the particles together can be ionic attractions, covalent bonds, hydrogen bonds, permanent dipole-permanent dipole forces and van der Waals forces.

The separation of particles in liquids is only about 10% more than in solids. In gases the separations are much larger.

Energy is required to change a solid into a liquid at its melting point. The energy is used to partially overcome the forces which hold the particles together. This energy is called the enthalpy of fusion.

More energy is needed to change phase from liquid into a gas than to change from a solid into a liquid. The energy is used to completely overcome the forces which hold the particles together so that the particles can be completely separated. This energy is called the enthalpy of vaporisation.

17. Types of Crystal

A solid with a regular shape which contains particles organised in a regular structure is called a crystal. Crystals can be classified according to the type of bonding between the particles.

18. Metallic Crystals

Metal atoms pack closely together in a regular structure. There is no way of packing spheres so that they fill all of the space completely without leaving gaps between them. Arrangements in which the gaps are kept to a minimum are called close-packed arrangements. X ray studies have revealed three main types of metallic structures. In the hexagonal close-packed (hcp) structure (e.g. magnesium and zinc), and the face-centred-cubic (fcc) close-packed structure (e.g. copper and gold) the metal atoms occupy 74% of the space. In the body-centred-cubic (bcc) structure (e.g. sodium and potassium), the atoms occupy 68% of the total volume. Only one metal, polonium, is known to have the simple cubic structure, a cube with a metal atom at each corner. Its co-ordination number is 6, and so the structure is relatively loosely packed.

Figure 18.1 shows a face-centred-cubic close-packed structure. Since every atom is in contact with 12 others, it is said to have a co-ordination number of 12. The high co-ordination number in these structures arises from the non-directed nature of the metallic bond.

Also shown in figure 18.1 is the unit cell. A unit cell is the smallest part of the crystal that contains all the characteristics of the structure. The whole structure can be generated by repeating the unit cell in three directions.

Figure 18.1 Face-centred-cubic close-packed structures

The less closely packed body centred cubic structure is shown in figure 18.2. With one atom at each of the eight corners of a cube and one in the centre touching these eight, the co-ordination number is 8.

Figure 18.2 Body-centred-cubic structure

19. Ionic crystals

Ionic compounds- such as the alkali metal halides- have ions that are arranged in a regular three-dimensional structure. The melting and boiling temperatures of ionic compounds are high, owing to the strong forces of electrostatic attraction between the ions in the crystal. The crystals of alkali metal halides are cubic in shape, and X ray analysis shows two kinds of structures. The structure of sodium chloride is shown in figure 19.1.

The best arrangement of ions in a structure, being the one with lowest energy, is the one which allows the greatest number of contacts between oppositely charged ions without pushing together ions of the same charge. Many structures are close-packed arrangements of anions, with the smaller cations occupying holes (interstices) in the structures. Sodium chloride has a face-centred-cubic close-packed lattice of chloride ions (radius, 0.181nm), which is expanded to accommodate sodium ions (radius, 0.098nm) in the lattice of anions. There are six sodium ions surrounding each chloride ion: the co-ordination number of chlorine is 6. Similarly, there are six chloride ions surrounding each sodium ion: the co-ordination number of sodium is 6. The structure is fully described as two interpenetrating face-centred cubes, with 6: 6 co-ordination.

Figure 19.1 The sodium chloride structure

Figure 19.2 The caesium chloride structure

The caesium chloride structure (figure 19.2) is different. Since the caesium ion (radius, 0.168nm) is larger than the sodium ion, a larger number of chloride ions can surround it. The structure is described as two interpenetrating simple cubes, with 8: 8 co-ordination. Both the caesium ions and the chloride ions adopt simple cubic lattices which interpenetrate so that each cube of chloride ions has caesium ion at its centre and vice versa.

Ionic crystals are brittle. Figure 19.3 shows what happens when an ionic crystal is subjected to stress. A slight dislocation in the crystal structure brings similarly charged ions together. Repulsion between the two like charges fractures the crystal. This is unlike the effect of stress on a metallic crystal, where deformation does not result in fracture (§6).

20. Molecular crystals

Some solids are held together by weak attractions between individual molecules. They are described as molecular crystals or molecular solids and are said to have a molecular structure. The intermolecular forces may be van der Waals forces, dipole-dipole forces , or hydrogen bonds. At very low temperatures, even the noble gases may be solidified. Solid argon can be formed but the intermolecular forces are very weak and the solid melts at -170°C. Figure 20.1 shows the face-centred cubic structure of solid argon and the face-centred cubic structure of solid iodine.

Iodine is a molecular solid up to a temperature of 30°C. The atoms are covalently bonded in pairs as I₂ molecules. Operating between molecules are the much weaker van der Waals forces. As a result of the regular arrangement of molecules, iodine is a crystalline solid with regular faces, which give a shiny appearance. When solid iodine is heated, the van der Waals forces are overcome and individual I₂ molecules are set free. The vapour phase, which is purple, consists of individual I₂ molecules. Bromine and chlorine adopt similar structures at lower temperatures.

21. Macromolecular crystals

A number of solids have the kind of crystals described as macromolecular or giant molecular. Covalent between atoms bind all the atoms into a giant molecule. Diamond, an allotrope of carbon, is one of the hardest substances known and has a macromolecular structure (figure 21.1). Each carbon forms covalent bonds to four other carbons. The structure that results is very strong. Diamond remains a solid up to a temperature of 3500°C, at which it sublimes.

Figure 19.3 An ionic structure is easily fractured

Figure 20.1 The structures of solid argon and solid iodine

Other solids with a diamond-like structure are silicon carbide (SiC)_n and boron nitride (BN)_n. The formula unit BN is isoelectronic with CC. Silicon(IV) oxide, SiO₂ (silica), also forms a three-dimensional structure. The silicon atoms are each covalently bonded to four oxygens. The oxygen atoms are each covalently bonded to two silicons (figure 21.2). This structure occurs in quartz which remains solid up to a temperature of 1700°C.

Figure 21.1 The structure of diamond

Figure 21.2 The structure of silicon(IV) oxide

Graphite, another allotrope of carbon, has a layered structure. Within each layer, every carbon uses three of its valence electrons to form covalent bonds with three other carbon atoms. A network of coplanar hexagons is formed with a C-C bond distance of 0.142nm. Between layers, the distance is 0.335nm. The weak van der Waals forces of attraction between the layers allow one layer of bonded atoms to slip over another layer. The structure (figure 21.3) accounts for the properties of graphite. It is a lubricant whereas diamond is abrasive. The fourth valence electron participates in a delocalised cloud of electrons similar to the metallic bond. They enable graphite to conduct electricity and are responsible for its shiny appearance.

Figure 21.3 The structure of graphite

22. Chain Structures

Some substances exist in chain-like structures. One example is sulphur(VI) oxide, which crystallises in long shiny needles. Another example is beryllium chloride. Their structures shown in figure 22.1.

Figure 22.1. The structures of (SO₃)_n and (BeCl₂)_n.

23. Some Physical Properties of Crystals

Type of crystal	Tm & Tb (relative value)	Electrical conductivity when solid	Electrical conductivity when molten	Solubility in water
Ionic	high	non conductor	good	variable but often good
Macromolecular	very high	non conductor (except graphite)	non conductor	insoluble
Molecular	low	non conductor	non conductor	variable
Metallic	usually high	good	good	insoluble

24. Shapes of Molecules

Ionic bonds are the electrostatic attractions that exist between oppositely charged ions. Since ions radiate a spherically symmetrical positive or negative field, ionic bonds are non-directional.

Covalent bonds involve overlap of atomic orbitals to from molecular orbitals. The more the atomic orbitals overlap, the more stable will be the molecular orbital formed. The strongest bonds will be formed if the atoms approach in such a way that there is maximum overlap between atomic orbitals. It follows that a covalent bond will have a preferred direction. A covalent molecule will have a shape which is determined by the angles between the bonds joining the atoms together.

A simple theory accounting for the shapes of molecules was put forward by Sidgwick and Powell in 1940 although it was later modified slightly by Gillespie and Nyholm. Their valence-shell electron-pair repulsion (VSEPR) theory pointed out that the arrangement of electron pairs around a central atom depends on the number and type of electron pairs in its valence shell. Between an electron pair and any other electron pair, there is an electrostatic repulsion which forces the orbitals as far apart as possible in three-dimensional space.

The number of valence-shell electron pairs is calculated by taking into consideration:

• the number of valence electrons originally in the central atom

• the number of additional shared electrons in covalent or coordinate bonds

• the loss or gain of electrons if the species is a positive or a negative ion.

The final shape is also modified if some of the electron pairs are lone (i.e. non-bonding) pairs. The lone pairs are more compact than bonding pairs so they repel more strongly leading to bond angles between bonding pairs that are smaller than those found in totally symmetrical shapes.

Linear molecules

The molecules of gaseous beryllium chloride, BeCl₂, are linear. Beryllium, in Group II of the Periodic Table, has two electrons in its valence shell, and forms two covalent bonds. A linear arrangement of the atoms (a bond angle of 180°) puts the atoms as far apart as possible:

Other linear molecules are:

The electron pairs in a multiple bond are assumed to occupy the position of one electron pair in a single bond.

Trigonal planar molecules

When there are three pairs of electrons around the central atom, the bonds lie in the same plane at an angle of 120° to one another. Three atoms form a triangle about the central atom, and the arrangement is described as trigonal planar. An example is boron trichloride, BCl₃. Boron, in Group III of the Periodic Table, has three valence electrons and forms three covalent bonds. In gaseous tin(II) chloride, SnCl₂, tin uses only two of its four electrons for bond formation. The remaining lone pair of electrons repels the bonding pairs and a trigonal planar arrangement of orbitals results, as shown in figure 24.1. The atoms, however, form a bent conformation.

Figure 24.1 The trigonal planar arrangement of electron pairs in BCl₃ and SnCl₂

Other structures based on a trigonal planar arrangement are ethene, the nitrate ion, and sulphur dioxide (figure 24.2).

Figure 24.2 The arrangement of electron pairs in CH₂CH₂, NO₃^-, and SO₂

Tetrahedral molecules

Four electron pairs adopt a tetrahedral configuration around a central atom. In a perfect tetrahedron the bond angles are 109.5° and this is the angle between bonds in molecules such as methane, CH₄, and the ammonium ion, NH₄⁺ (figure 24.3).

Figure 24.3 The tetrahedral arrangement of electron pairs in CH₄, NH₃, NH₄⁺, and H₂O

In many molecules, lone (non-bonding) pairs constitute some of the electron pairs in the valence shell of the central atom. Lone pairs are closer to the nucleus than bonding pairs and exert a greater repulsive force. Repulsion between electron pairs decreases in the order:

lone pair : lone pair > lone pair : bonding pair > bonding pair : bonding pair

Repulsion between the lone pair and the bonding pairs in ammonia, NH₃, makes the angle a in figure 24.3 greater than the tetrahedral angle (109.5°) and consequently the angle b is less than 109.5° and is nearer 107°. The four atoms in NH₃ form a trigonal pyramid. Similarly in water, H₂O, the repulsion of two lone pairs means that angles d and e are greater than 109.5°, and the angle f between the H-O-H bonds is 104.5°. The three atoms in water have a bent configuration.

Structures with five pairs of valence electrons

Structures with more than four pairs of electrons about the central atom may occur if the element is in the second short period or a later period. A molecule of gaseous phosphorus(V) chloride, PCl₅, with five bonding pairs of electrons, has the shape of a trigonal bipyramid. The angles between the bonds are 90° and 120°. Two Cl atoms occupy axial positions in the bipyramid and three occupy equatorial positions (figure 24.4). In sulphur(IV) fluoride, SF₄, a lone pair occupies the more spacious equatorial position to form a see-saw shaped molecule. The central chlorine atom in the molecule chlorine(III) fluoride, ClF₃, has two lone pairs and the molecule is T-shaped. In the I₃^- ion, three lone pairs occupy the equatorial positions. The molecule is linear.

Figure 24.4 The trigonal bipyramidal arrangement of valence-electron pairs in

PCl₅, SF₄, ClF₃, and I₃^-

Structures with six pairs of valence electrons

An example of a structure with six pairs of valence electrons around a central atom is sulphur(VI) fluoride, SF₆. Such molecules have an octahedral arrangement of electron pairs, with 90° bond angles (figure 24.5). The arrangement of atoms in IF₅ is square pyramidal as a lone pair is present in the iodine atom’s valence shell. In ICl₄^-, the four chlorine atoms are in a square planar configuration, with lone pairs occupying the axial positions of the octahedron.

Figure 24.5 The octahedral distribution

of the electron pairs in SF₆, IF₅, and ICl₄^-

Structures with seven pairs of valence electrons

A molecule like IF₇, with seven pairs of electrons around the central atom, has the pentagonal bipyramidal arrangement of bonds shown in figure 24.6.

Figure 24.6 The pentagonal bipyramidal shape of IF₇

Summary

---

[D.R.B1]