Information collected from

http://www.science.uwaterloo.ca/~cchieh/cact/c120/hybrid.html

http://www.elmhurst.edu/~chm/vchembook/210polarity.html

http://www.chemistrycoach.com/tutorials-1.htm

INTRODUCTION

We know the structure of the atom. We know that each atom is a compromise between electrostatic attraction between the electrons and the nucleus and electron-electron repulsion. Chemical bonds between atoms must have the same features.

The energy of interaction between the atoms changes with distance between the nucleii. There is an optimal distance for the chemical bond which is where this energy is at a minimum. The minimum energy with respect to the energy of dissociated fragments (r -> infinity) is called the bond energy.

The above picture is for the case of the Hydrogen molecule, but each particular chemical bond has its' own equilibrium distance and its' own bond dissociation energy. The bond lengths of the halogen molecules are used to determine an approximate radius for chemical (covalent) bonding of the halogen atoms. Perfect electron sharing is expected between atoms of the same type, so the bond in this case is perfectly covalent.

Why do atoms form covalent bonds? two major factors:

Delocalizing electrons over two atoms instead of one lowers the energy of the system.
Atoms with less than filled shell electron configurations can share valence electrons to fill their highest or valence subshell and thus gain quantum mechanical stability. G.N. Lewis counted the valence electrons with dots to show how the tendency to create a filled s and p subshell (8 electrons) influenced molecular stochiometery and structure. He called the tendency to have or share 8 electrons the 'Octet Rule'.

The 'Lewis Dot' symbology is simple. Draw atoms with their valence electrons only as dots, grouped in four possible pairs around the atom. Fill the four places around the atom as if they were four degenerate orbitals.

Now combine atoms together to form molecules by pairing electrons without changing the total number of electrons. Make an 'octet' around each atom in this way (except Hydrogen which can only support 2 valence electrons and heavy elements which can support 'super-octets' due to unfilled d- and f- orbitals). Replace all bonding pairs with a single line (non-bonded pairs of electrons or lone pairs are left as two dots). If more than one pair of electrons is shared between a given pair of atoms, a multiple bond has formed. Draw a solid line for each pair of bonding electrons in the multiple bond. Try to pair all the electrons in the structure (this is not possible if the number of valence electrons is odd).

Triumphs of Lewis dot structure:

Predicts multiple bonds
Explains stoichiometry of covalent molecules

Example Lewis structures:

Try this interactive builder of Lewis Dot Structures (http://www.stolaf.edu/depts/chemistry/courses/toolkits/121/js/lewis/)

Bond

A chemical bond is a mechanism that is used to chemically combine atoms. There are three types of bonds: metallic, ionic, and covalent.The mechanism is an electrostatic force of attraction between areas of positive and negative charge. The locations of the areas of charge will differ from system to system. These differences are responsible for the various types of bonds generally found in compounds. Bonds form as an attempt to stabilize a chemical system by releasing energy. The greater the amount of energy released during the formation of a bond, the more stable the bond will be. All bond formation processes involve the use of valence level electrons.

The bond forming process is always exothermic. If two atoms can release energy by forming a bond, then the atoms will be more stable by staying together than they would be as individual atoms. As a result, the atoms remain in the bonded condition. If two atoms gain energy in an attempt to form a bond, then the bond will NOT form. They need the benefit derived from a reduction of energy, not a gain of energy.

Bond Energy

Bond Energy is the amount of energy released when a bond forms. It is a direct measure of the amount of stability gained when two atoms establish a chemical bond. Inversely, bond energy corresponds to the amount of energy that is required to break a bond. The amount that is required to break a bond is exactly equal to the amount released when the bond formed. The magnitude of the bond energy corresponds to the vertical drop that appears in a potential energy well at the lowest point, or most stable position, in the curve. An equation that represents a bond formation process would appear as

A + B = AB + Energy.

The energy term corresponds to the energy released, or bond energy

Bond Length

Bond Length is the average distance between the centers of two bonded atoms. Because bonded atoms experience some vibration, moving towards and away from each other, the distance between bonded atoms will vary slightly over a period of time. The term Bond Length specifically refers to the average positions of the two atoms during the harmonic vibrations that they undergo. On the Potential Energy Well, the Bond Length is the position on the horizontal coordinate that corresponds to the bottom of the well, or the position of lowest energy for the system.

Bond Mechanism

The Bond Mechanism is the actual force that holds bonded atoms together. The mechanism differs from the bond motivation. The motivation explains WHY atoms would like to bond. Mechanism refers to the force that keeps them together after they have bonded. In all cases, regardless of bond type, the mechanism is an electrostatic force of attraction (Coulombic Force). The primary difference between the various types of bonds is the location of the charged areas that are responsible for establishing the electrostatic forces. For instance, in ionic systems the electrostatic force is established between the cation and the anion. In covalent types of systems, the electrostatic force is established between the positive nuclei and the negative electron cloud that exists between the nuclei.

Covalent versus Ionic Bonding

In our early discussion of chemical compounds, we said that if a non-metal and a metal bond, one or more electrons will be transferred from the metal to the nonmetal and the resulting ions stick by electrostatics. This is an extreme case of unequal sharing of electrons, but leads to the same kind of octet configuration of the atoms involved in the bond. Take LiF, for example:

How evenly or not the bonding electrons are shared will determine the polarity of the bond and the nature of the interaction. What determines how the electrons are shared is the relative electronegativity (electron greed) of the bonding atoms. The degree of polarity or degree of ionic bonding of any given bond can vary continuosly zero to nearly 100%. We normally say that bonds between atoms with electronegativity difference (DEN )greater than 1.7 are ionic, although this really means only more than about half ionic in character. Here are some examples of the bonds formed with different electronegativity differences, DEN,between the atoms:

Bond Energetics

Since we are treating the chemical bond as largely depending only upon the nature of the two atoms in contact through the bond, perhaps we can use this idea to determine the overall stability of a molecule by adding up its bond energies. This assumes that all chemical bonds between the same pair of atoms of the same type are approximately equal in properties. Namely, in this case, we will assume all C-H bonds take about the same amount of energy to break, regardless of the molecule they are in.

The hypothetical state of a molecule after all its bonds are broken can be used as a 'reference', just like we used the standard states of the elements as a reference for the Enthalpies of Formation of molecules. Thus the energetics of a chemical transformation can be estimated from the bonds broken and formed in the reaction

A specific example can be made from our old familiar combustion of methane reaction. We calculated the enthaly change during this transformation before from traditional thermochemcial methods. We can do this agian by using the average bond enthalpies of C-H, C=O, {O=O}, and O-H bonds

So, the Heat of Formation of new molecule, or the Heat of Reactions of a given transformation can be estimated by using average bond energies and the above thermochemical analysis. This is not as accurate as using directly measured heats of formation (which is not an approximation!) but is sometimes very useful as a starting guess.

Other average properties of bonds are also useful. For instance, the equilibrium bond length of a given type of bond is usually pretty constant from molecule to molecule. Therefore, average bond lengths can be used to predict parts of the structure of new and unknown molecules.

IONIC BONDING

The common table salt, NaCl, is a representative of an important class of compounds called salts. A salt consists of positive and negative ions, Na⁺ and Cl^- in NaCl. Salts such as KCl, CsCl, CaCl₂, CsF, KClO₄ NaNO₃, and CaSO₄ are generally considered ionic compounds, which are composed of (positive) cations and (negative) anions. When they dissolve in water, the solutions contain hydrated positive and negative ions.

A salt is produced in a neutralization reaction or in a direct reaction. For example, NaCl solid can be obtained by

NaOH + HCl = H₂O + NaCl (solid after evaporation of solvent)
2 Na + Cl₂(g) = NaCl (solid) (burning metallic sodium in a chlorine gas.)

Ionic Bonding

When a highly electronegative atom and an electropositive one are bonded together, an electron is transferred from the electropositive atom to the electronegative atom to form a cation and an anion, respectively. The cation, being a positively charged ion, is attracted to the negatively charged anion as described by Coulomb's law:

Figure 1.1: Coulomb's law states that oppositely charged species attract each other.

A negative energy means there is an attractive interaction between the particles in the above expression. If the charges on the two ions are opposite in sign, they will attract each other. Conversely, if two charges are similar, they repel each other. Using this knowledge we can construct a graph of energy versus distance for two oppositely charges ions. At large distances, there is a negligible energy of attraction between the two ions, but as they are brought closer together, they are attracted to one another. Coulomb's law may seem to predict that the ions should be as close as possible to achieve a minimal energy state. However, the graph of energy versus distance1.2 shows that the ions are actually repelled at small distances. To explain this observation, remember that the ions' nuclei are both positively charged. When the nuclei approach each other, they repel strongly--accounting for the steep rise in potential as the ions get closer than the bond length.

Figure 1.2: Plot of potential energy versus distance for oppositely charged ions

The depth (y-axis) of the minimum in the potential energy curve above represents the bond strength, and the distance (x-axis) at the energy minimum is the bond length. Using Coulomb's law and the bond length, one can actually predict with some accuracy the strength of an ionic bond. Performing a series of these calculations you find that ionic compounds formed by ions with larger charges create stronger bonds and that ionic compounds with shorter bond lengths form stronger bonds.

Crystal Lattices

Ionic compounds do not usually exist as isolated molecules, such as LiCl, but as a part of a crystal lattice--a three dimensional regular array of cations and anions. Ionic compounds form lattices due to the contributing coulombic attractions of having each cation surrounded by several anions and each anion surrounded by several anions. An example of a crystal lattice is shown in Figure 1.3:

Figure 1.3: An ionic crystal lattice

As you can see in the above figure, each lithium ion is surrounded by six chlorine atoms and vice versa. By virtue of the arrangement of the ions in the lattice, the lattice is lower in energy than it would be if the ions were separated into isolated LiCl molecules.

Lattice Enthalpy

Bond enthalpies provide a measure of the strength of covalent bonds. Ionic bonding is an electrostatic attraction between oppositely charged ions. The attraction acts in all directions, resulting in a giant ionic lattice containing many ions. For ionic compounds the corresponding enthalpy is the lattice enthalpy (also called the lattice energy). Lattice enthalpy indicates the strength of the ionic bonds in an ionic lattice.

The standard molar lattice enthalpy is the energy required to convert one mole of a solid ionic compound into its constituent gaseous ions under standard conditions.

e.g. NaCl (s) Na⁺ (g) + Cl^- (g)

Born-Haber cycle

This is an application of Hess’s Law and can be used to calculate lattice energies.

Lattice enthalpies cannot be determined directly by experiment and must be calculated indirectly using Hess’s Law and other enthalpy changes that can be found experimentally. The energy cycle used to calculate a lattice enthalpy is the Born-Haber cycle.

The basis of a Born-Haber is the formation of an ionic lattice from its elements.

In general for an ionic compound a Born-Haber cycle can be written as:

Na⁺ (g) + Cl^- (g)

ΔH_e.a.

Na⁺ (g) + Cl (g)

ΔH_I.E.

Na (g) + Cl (g) ΔH_latt.= U

ΔH_diss.

Na (g) + ½ Cl₂ (g)

ΔH_sub. ΔH_F^θ

Na (s) + ½ Cl₂ (g) NaCl (s)

Applying Hess’s Law

ΔH_sub. + ΔH_I.E. + ΔH_diss. + ΔH_e.a. - ΔH_latt. – ΔH_f^θ = 0

According to Hess’s Law

ΔH_latt. = (-ΔH_F^θ) + ΔH_sub. + ΔH_I.E. + ΔH_diss. + ΔH_e.a.

ΔH_f^θ = enthalpy of formation of MX (s)

ΔH_sub. = enthalpy of sublimation of M (s)

ΔH_I.E. = ionisation energy

ΔH_diss. = dissociation energy of X₂ (g)

ΔH_e.a.= electron affinity of X (g)

ΔH_latt. = lattice energy

Consider the reaction between sodium and chlorine to form sodium chloride.

Na (s) + ½ Cl₂ (g) NaCl (s)

The reaction can be considered to occur by means of the following steps:

· Vaporization of sodium

Na (s) Na (g) ΔH_sub.

The standard enthalpy of sublimation or vaporisation is the enthalpy change when one mole of sodium atoms are vaporised. This is an endothermic process and can be determined experimentally.

· Ionization of sodium

Na (g) Na⁺ (g) + e^- ΔH_I.E

The standard enthalpy of ionisation is the energy required to remove one mole of electrons from one mole of gaseous atoms. This is endothermic and can be determined by spectroscopy.

· Dissociation of chlorine molecules

Cl₂ (g) 2Cl (g) ΔH_diss.

The standard bond dissociation enthalpy is the energy required to dissociate one mole of chlorine molecules into atoms (i.e. to break one mole of bonds). This is also endothermic and can be determined by spectroscopy.

· Ionization of chlorine atoms

Cl (g) + e^- Cl^- (g) ΔH_e.a.

The electron affinity of chlorine is the energy released when one mole of gaseous chlorine atoms accepts one mole of electrons forming one mole of chloride ions.

· Reaction between the ions

Na⁺ (g) + Cl^- (g) NaCl (s) -ΔH_latt.

This is the reverse of the lattice energy. The standard lattice enthalpy is the energy absorbed when one mole of solid sodium chloride is separated into its gaseous ions. It has a positive value and cannot be determined experimentally.

Use of Lattice Energies

· The melting points of ionic solids depend on their lattice enthalpies.. The greater the lattice energy the higher the melting point of the compound.

	NaF	NaCl	NaBr	NaI
ΔH_latt. kJ mol^-1	915	781	743	699
m. pt. ^oC	995	808	750	662

· Solubility of ionic compounds is usually governed by its lattice energy. In general the higher the lattice energy the lower the solubility.

(See enthalpy of solution below)

· A comparison of calculated and theoretical lattice energies gives an indication of the degree of covalent character in an ionic compound. The greater the difference between the two values the more covalent the compound.

Compound	Theoretical lattice energy kJ mol^-1	Calculated lattice energy (via Born-Haber cycle) kJ mol^-1
NaCl	766	776
NaBr	731	742
NaI	686	699
AgCl	768	890
AgBr	759	877
AgI	736	867

The close agreement between the theoretical and experimental values for the alkali metal halides provides strong evidence that the simple ionic model of a lattice, composed of discrete spherical ions with an even charge distribution, is a very satisfactory one.

For the silver halides the theoretical values are about 15% less than the experimental values based on the Born-Haber cycle. This indicates that the simple ionic model is not very satisfactory.

When there is a large difference in electronegativity between the ions in a crystal , as in the case of the alkali metal halides then the ionic model is satisfactory. However as the difference in electronegativity gets smaller, as in the case of the silver halides, the bonding is stronger than the ionic model predicts. The bonding in this case is not purely ionic but intermediate in character between ionic and covalent. The ionic bonds have been polarised (Fajans rules) giving some covalent character.

Trends in lattice enthalpy explained in terms of ionic radius and charge.

Consider the ionisation of an ionic solid MX.

MX (s) ® Mⁿ⁺ (g) + X^n- (g)

The ease of separation of the ions and hence the lattice energy is determined by the size of the ions and their charge.

	Group I					Group II
	Li	Na	K	Rb	Cs	Be	Mg	Ca	Sr	Ba
F	1029	915	813	779	735	3456	2883	2583	2427	2289
Cl	849	776	710	685	676	2983	2489	2197	2109	2049
Br	804	742	671	656	644	2895	2416	2125	2046	1937
I	753	699	643	624	607	2803	2314	2038	1954	1841

Effect of ionic size

As the ionic radius of both Mⁿ⁺ and X^n- the lattice energy decreases. The attractive force between the ions decreases and they become easier to separate.

e.g. LiBr 804 kJ mol^-1 BeCl₂ 2983 kJ mol^-1

NaBr 742 MgCl₂ 2489

KBr 671 CaCl₂ 2197

RbBr 656 SrCl₂ 2109

CsBr 644 BaCl₂ 2049

As we descend both Groups I and II the lattice energies become less positive.

For any given metal the lattice energy also decreases in passing from the fluoride to the iodide.

e.g. NaF 915 kJ mol^-1 SrF₂ 2427 kJ mol^-1

NaCl 776 SrCl₂ 2109

NaBr 742 SrBr₂ 2046

NaI 699 SrI₂ 1954

This is due to an increase in ionic size from F^- to I^- which increases the internuclear distance. There is a corresponding decrease in attractive force and hence lattice energy.

When the internuclear distances are about equal, as for RbF and LiI for example, then the lattice energies are almost equal.

Effect of ionic charge

As the charge on Mⁿ⁺ increases there is a greater attractive force between the ions and lattice energies increase. In addition, the decrease in size of M^{n+ with} increasing charge increases the attractive force between the ions and also increases the lattice energy.

The ionic radius of the Na⁺ and Ca²⁺ ions are very similar. However the lattice energy of CaCl₂ is about 3 times that of NaCl.

NaCl 776 kJ mol^-1 CaCl₂ 2197 kJ mol^-1

This is due to the increased charge on the metal ion giving greater electrostatic attraction.

In general Group II halides have a lattice energy about three times that of the equivalent Group I halide.

Beryllium halides have considerable covalent character and the lattice energies are bigger than expected.

Enthalpy of solution related to lattice enthalpy and enthalpy of solvation of simple ionic salts.

When an ionic solid dissolves two enthalpy changes are involved:

- The ionc lattice must be broken down and the ions separated.

The energy required is the lattice enthalpy.

NaCl (s) ® Na⁺ (g) + Cl^- (g) ΔH_lattice

This is an endothermic process.

- The separate ions interact with the solvent molecules. If the solvent is polar, the charged ions can be attracted to one end of the polar solvent molecules. The energy released is called the enthalpy of solvation.

When the solvent is water the enthalpy change is called the enthalpy of hydration.

This process is exothermic.

Na⁺ (g) + Cl^- (g) + solvent ®Na⁺ (aq) + Cl^- (aq) ΔH_solvation

The difference between the two is called the enthalpy of solution.

ΔH_lattice

NaCl (s) + (aq) Na⁺ (g) + Cl^- (g

ΔH_solution ΔH_hydration

Na⁺ (aq) + Cl^- (aq)

Applying Hess’s Law ΔH_solution = ΔH_lattice + ΔH_hydration

The enthalpy of solution can be exothermic or endothermic depending on the size of the lattice energy (ΔH +ve) and the solvation (hydration) energy (ΔH -ve).

e.g. for NaCl

ΔH_lattice = +776 kJ mol^-1

ΔH_hydration = -772 kJ mol^-1

Therefore ΔH_solution = +4 kJ mol^-1

The enthalpy of solution is the energy change when one mole of solute is dissolved in a solvent to form an infinitely dilute solution.

Some values for enthalpies of hydration are given below.

H⁺	Li⁺	Na⁺	K⁺	Rb⁺	Cs⁺
-1075	-449	-390	-306	-281	-248
	Be²⁺	Mg²⁺	Ca²⁺	Sr²⁺	Ba²⁺
	-2425	-1891	-1562	-1414	-1273
		Al³⁺
		-4613

Properties of ionic compounds:

Ionic solids are poor conductors of electricity and heat.
Ionic solids are hard and brittle.
Ionic solids can be melted to form liquids that are an electrical conductors.
Ionic solids that are water soluble, dissolve to form solutions that are electrical conductors. ( Not all ionic substances are water soluble.) In aqueous solution, an ionic compound dissociates into its ions.

This means that when NaCl is dissolved in water, the solution contains Na⁺ ions and Cl^- ions.
The dissociated ions in aqueous solution gives the solution the ability to conduct electricity. Therefore, ionic compounds dissolved in water makes strong electrolytes.

The smallest unit of an ionic compound is a formula unit. The mass of this formula unit is called the formula mass.

The formula unit of sodium chloride is NaCl. It has a formula mass is 58.44 amu/formula unit.
The formula unit of sodium chloride is NaCl₂. It has a formula mass is 95.21 amu/formula unit.

Ionic solids are generally high melting. The strong attractions between the cations and the anions in ionic solids are responsible for their high melting points. For ionic compounds, melting points typically range from 300^oC to 1000^oC.

Why ionic substances are the way they are?

Ionic solids are rigid because the multiple interactions between oppositely charged ions hold the charged particles in relatively fixed positions. Electrical conductivity depends on ions being able to move freely. The conduction of heat depends partly on the movement of electrons in a substance. Electric charge is "locked" in the lattice positions of the ions in the solids. This means there is poor mobility of charges and poor conductivity of electricity and heat.

Ionic solids are brittle and hard because the electrostatic attractions in the solid again hold the ions in definite positions. The electrostatic attractions must be overcome to move the ions. When the ions in the solid are shifted by some very strong force the positions of ions shift so that like charged ions are close together. This results in strong repulsions and the like charged ions move apart. This causes the solid to shatter and not simply deform like a metal. Try crushing a few grains of salt in the bowl of a spoon with anoterh spoon. The particles do not deform, they shatter.

Iionic solids melt when the ions have enough energy to slide past one another. They are mobile and can act to carry electrical charge through the liquid. This explains why a molten ionic substance conducts electricity, but a solid ionic material doesn't. The ions move through the liquid to carry charge from one place to another.

The dissolving process is like a tug of war. Soluble ionic substances are ripped apart by the solvent when the solid is dissolved. The solvent pulls the ions out of the solid and breaks the forces holding the crystal together. The solvent isolates the ions in an envelope of solvent particles. The ions are free to move and carry electric charge through the solution.

Nonsoluble ionic solids are held together so tightly that the ions cannot be pulled out of the lattice by the solvent. The attractive forces in the solid are stronger than the attractions between the solvent and the ions. The solvent can't pull the ions out of the crystal.

Ionic compound formula	Ionic compound name	Melting point in degrees celsius	Solubility g per 100 g water superscript is temperature
LiCl	lithium chloride	613	45 g cold water, 128 g¹⁰⁰
NaCl	sodium chloride	801	209 g cold water, 284 g ¹⁰⁰
KCl	potassium chloride	776	35 g cold water, 57 g ¹⁰⁰
RbCl	rubidium chloride	715	77 g cold water, 139 g¹⁰⁰
MgF₂	magnesium fluoride	1396	0.0076 g cold water, insoluble ¹⁰⁰
MgCl₂	magnesium chloride	708	54 g cold water, 72 g¹⁰⁰
MgBr₂	magnesium bromide	695-700	101 g cold water, 126 g ¹⁰⁰
MgI₂	magnesium iodide	greater than 700	100 g ⁰cold water, 165 g ¹⁰⁰

What properties distinguish ionic compounds from covalent compounds?

Many differences in properties of ionic and molecular materials stem from the fundamentally different nature and strength of forces that hold these materials together. The attractive forces between positive and negative ions are much stronger than the attractive forces between neutral molecules. You can use that fact to explain differences in the following properties for ionic and molecular compounds:

· Electrical conductivity of the compound in aqueous solution. Ionic compounds conduct electricity when dissolved in water, because the dissociated ions can carry charge through the solution. Molecular compounds don't dissociate into ions and so don't conduct electricity in solution.

· Electrical conductivity of the compound in liquid form. Ionic compounds conduct electricity well when melted; metallic solids do as well. Covalent molecular compounds do not, because they usually don't transfer electrons unless they react.

· Hardness. Molecular solids are usually much softer than ionic materials. Ionic crystals are harder but often quite brittle. Squeezing an ionic crystal can force ions of like charge in the lattice to slide into alignment; the resulting electrostatic repulsion splits the crystal.

· Melting points and boiling points. In an ionic compound, the forces of attraction between positive and negative ions are strong and high temperatures are required to overcome them. The melting and boiling points of ionic compounds are usually very high. A smaller amount of energy is required to overcome the weak attractions between covalent molecules, so these compounds melt and boil at much lower temperatures than metallic and ionic compounds do. In fact, many compounds in this class are liquids or gases at room temperature.

· Enthalpies of fusion and vaporization The enthalpy of fusion is the amount of heat required to melt one mole of the compound in solid form, under constant pressure. The enthalpy of vaporization is the amount of heat required to vaporize one mole of the compound in liquid form, under constant pressure. These properties are typically 10 to 100 times smaller for molecular compounds than they are for ionic compounds.

COVALENT BONDING

Lewis Dot Structures

G.N. Lewis used dots to represent the valence electrons in his teaching of chemical bonding. He eventually published his theory of chemical bonding in 1916. He put dots around the symbols so that we see the valence electrons for the main group elements. Formation of chemical bonds to complete the requirement of eight electrons for the atom becomes a natural tendency.

Using Lewis dot structures and the octet rule, we can predict the electronic structure of covalently bonded molecules.

Diatomic Molecules

These molecules are called homonuclear diatomic molecules, since all atoms are the same. They are also non-polar molecules.

Below is an example of the polar HCl molecule.

Chlorine is more electronegative than Hydrogen so HCl has a polar covalent bond.

For diatomic oxygen, the Lewis dot structure predicts a double bond.

Actually, this is not quite right. While the Lewis diagram correctly predict that there is a double bond between O atoms, it incorrectly predicts that all the valence electrons are paired (i.e. it predicts that each valence electron is in an orbital with another electron of opposite spin). We know this is not right because substances that contain unpaired electrons exhibit a behavior called paramagnetism. Paramagnetic substances are attracted to a magnet. For example, Iron metal is paramagnetic, and it can be picked up with a magnet. On the other hand, blackboard chalk is not paramagnetic, so it cannot be picked it up with a magnet. When we pour liquid nitrogen through the poles of a magnet, we see that it just passes through. Nitrogen is not paramagnetic, thus it doesn't have any unpaired electrons.

On the other hand, if we pour liquid O₂ through the poles of the magnet, a solid O₂ bridge forms because liquid O₂ is paramagnetic. In the next chapter, we will learn a more advanced theoretical approach to chemical bonding called molecular orbital theory that can predict double bonds and unpaired electrons for O₂. In general, the Lewis-dot structures have the advantage that they are simple to work with, and very often present a good picture of the electronic structure.

For a diatomic Nitrogen, the Lewis-dot structure is:

This triple bond between nitrogens is very strong. The strength of the this triple bond makes the N₂ molecule very stable against chemical change. It is often called an inert gas.

There is a relationship between the number of shared elelctron pairs and the bond length.

The distance between bonded atoms decrease as the number of shared e^- pairs increase.

Rules for Lewis Dot Structures

Count the number of valence e^- each atom brings into the molecule.

For ions, the charge must be taken into account.

Put electron pairs about each atom such that there are 8 electrons around each atom (octet rule).

One exception is H (surrounded by only 2e^-s).

Sometimes it's necessary to form double and triple bonds. Only C, N, O, and S (rarely Cl) will form multiple bonds.

Exceptions to the Octet Rule

If there is not enough electrons to follow the octet rule, then the least electronegative atom is left short of electrons.

e.g. BeF₂ number of valence e^- = 2+ 2(7) = 16 e^- or 8 pairs.

Neither Be or F form multiple bonds readily and Be is least electronegative so

2. If there are too many electrons to follow the octet rule, then the extra electrons are placed on the central atom.

How can this happen?

The octet rule arises because the s and p orbitals can take on up to 8 electrons. However, once we reach the third row of elements in the periodic table we also have d-orbitals, and these orbitals help take the extra electrons.

NOTE: You still need to know how the atoms are connected in a polyatomic molecule before using the Lewis-Dot structure rules.

We can write Lewis dot structures that satisfy the octet rule for many molecules consisting of main-group elements, but the octet rule may not be satisfied for a number of compounds. For example, the dot structures for NO, NO₂, BF₃ (AlCl₃), and BeCl₂ do not satisfy the octet rule.

^.N:::O:

compare
with

:C:::O:

.
N
// \
:O: :O:
' '

..
:F:
|
B
/ \
:F: :F:
' ' ' '

. . . .
:Cl : Be : Cl:
' ' ' '

The above are structures for the gas molecules. The solids of AlCl₃ and BeCL₂ are polymeric with bridged chlorides.

. . . .
:Cl: :Cl: :Cl:
\ / \ /
Al Al
/ \ / \
:Cl: :Cl: :Cl:
. . . .

Polymeric
solid
structures

:Cl: :Cl: :Cl:
/ \ / \ / \
Be Be
\ / \ / \ /
:Cl: :Cl: :Cl:

Aluminium chloride, AlCl₃, is a white, crystalline solid, and an ionic compound. However, it has a low melting point of 465 K (192°C), and the liquid consists of dimers, Al₂Cl₆, whose structure is shown above. It vaporizes as dimers, but further heating gives a monomer that has the same structure as the BF₃.

In compounds PF₅, PCl₅, :SF₄, ::ClF₃, :::XeF₂ and :::I₃^-, the center atoms have more than 10 electrons instead of 8. In compounds SF₆, IOF₅, :IF₅, BrF₅, ::XeF₄, PF₆^- etc, the center atoms have 12 electrons.

The formulas given above follows a systematic pattern according to the positions of the elements on the periodic table. As the number of atoms bonded to it decreases, the number of unshared electrons increase.

Formal Charge

The formal charge on any atom in a Lewis structure is a number assigned to it according to the number of valence electrons of the atom and the number of electrons around it. The formal charge of an atom is equal to the number of valence electrons, N_v.e. subtract the number of unshared electrons, N_us.e. and subtract half of the bonding electrons, ½ N_b.e..

Formal charge = N_v.e. - N_us.e. - ½ N_b.e.

Some practice of assigning formal charge is necessary before you master this technique. Some examples of drawing Lewis structure and assigning formal charge are given below.

The formal charge is a hypothetical charge from the dot structure. The formal charges in a structure tell us the quality of the dot structure.

Formal charge rules

Often, many Lewis dot structures are possible. These are possible resonance structures, but often we should write a reasonable one, which is stable. The formal charge guides us about the stability of the dot structure. The guidance are called formal charge rules

Formulas with the lowest magnitude of formal charges are more stable.
More electonegative atoms should have negative formal charges.
Adjacent atoms should have opposite formal charges.

Example 1.

Draw Lewis dot structure for SO₂

Solution

Put down number of valence electrons:

..
: O :

..
: S :

..
: O :

Put all atoms together to make a molecule and check to see if it satisfy the octet rule.

.. .. .. : O : : S : : O :	<= octet rule not satisfied
0 0 0	formal charge

Adjust bonding electrons so that octet rules apply to all the atoms

.. .. .. : O : S : : O : ''	<- octet rule satisfied
-1 +1 0	formal charge

Since the left O has 6 unshared plus 2 shared electrons, it effectively has 7 electrons for a 6-valence-electron O, and thus its formal charge is -1.

Formal charge for O = 6 - 6 - (2/2) = -1.
Formal charge for S = 6 - 2 -(6/2) = +1.

There is yet another structure that does not satisfy the octet rule, but it's a reasonable structure:

.. .. .. : O : S : O : ' ' ' '	<- octet rule satisfied
-1 +2 -1	formal charge

Resonance Structures

When several structures with different electron distributions among the bonds are possible, all structures contribute to the electronic structure of the molecule. These structures are called resonance structures. A combination of all these resonance structures represents the real or observed structure. The Lewis structures of some molecules do not agree with the observed structures. For such a molecule, several dot structures may be drawn. All the dot structures contribute to the real structure. The more stable structures contribute more than less stable ones.

For resonance structures, the skeleton of the molecule (or ion) stays in the same relative position, and only distributions of electrons in the resonance structures are different.

Let us return to the SO₂ molecule. The molecule has a bent structure due to the lone pair of electrons on S. In the last structure that has a formal charge, there is a single S-O bond and a double S=O bond. These two bonds can switch over giving two resonance structures as shown below.

.. S / \ :O: :O: ' ' ' '	«	.. S // \ :O: :O: ' '	«	.. S / \\ :O: :O: ' '	«	.. S // \\ :O: :O:
1		2		3		4

..
S
/.' ^'' '.\
:O: :O:

In structure 1, the formal charges are +2 for S, and -1 for both O atoms. In structures 2 and 3, the formal charges are +1 for S, and -1 for the oxygen atom with a single bond to S. The low formal charges of S make structures 2 and 3 more stable or more important contributors. The formal charges for all atoms are zero for structure 4, given earlier. This is also a possible resonance structure, although the octet rule is not satisfied. Combining resonance structures 2 and 3 results in the following structure:

Example 2.

Draw the resonance structures of NO₃^-

Solution

-1
:O:
||
N
/ \
:O: :O:
' ' ' '

. . -1
:O:
|
N
// \
:O: :O:
' '

. . -1
:O:
|
N
/ \\
:O: :O:
' '

The resonance structure is shown on the right here. Note that only the locations of double and single bonds change here. What are the formal charges for the N atoms? What are the formal charges for the oxygen atoms that are single bonded and double bonded to N respectively? Please work these numbers out.

· Formal charges: N, +1; =O, 0; -O, -1

· The most stable structure has the least formal charge.

· In a stable structure, adjacent atoms should have formal charges of opposite signs.

The more stable the structure, the more it contributes to the resonance structure of the molecule or ion. All three structures above are the same, only the double bond rotates.

GEOMETRY BASED ON PAIR REPULSION:

VALENCE SHELL ELECTRON PAIR REPULSION THEORY (VSEPR Approach)

In 1957 the canadian chemist R.J Gillespie (university Mc Master Hamilton, Ontario) took back british N. Sigdwick and H. Powell idea, and developped the theory of the valence shell electron pair repulsion VSEPR. This method prolongs in the geometrical shape aspect the description of the chemical bond by G. N. Lewis (1916).

Valence Shell Electron Pair Repulsion theory (VSEPR) is a set of rules whereby the chemist may predict the shape of an isolated molecule. It is based on the premise that groups of electrons surrounding a central atom repel each other, and that to minimize the overall energy of the molecule, these groups of electrons try to get as far apart as possible. Groups of electrons can refer to electrons that participate in a bond (single, double, or triple) to another atom, or to non-bonding electrons (e.g. lone pair electrons).

The ideal electronic symmetry of a molecule consisting of a central atom surrounded by a number of substituents (bonded atoms and non-bonding electrons) is characteristic of the total number of substituents, and is determined solely by geometric considerations -- the substituents are arranged so as to maximize the distances amongst them. VSEPR is useful for predicting the shape of a molecule when there are between 2 and 6 substituents around the central atom (the case of one substituent is not discussed because it is trivial -- the only possible shape for such a molecule is linear). That means that there are only five unique electronic geometries to remember. For each electronic geometry, there may be a number of different molecular geometries (the shape of the molecule when only bonded atoms, not non-bonding electrons are considered). Molecular geometries are really just special cases of the parent electronic geometry -- this will hopefully be evident from the models shown on the pages linked to this one.

The electrons in the valence shell of most stable molecules and ions are paired (some rare molecules like NO₂ have unpaired electrons). The Pauli principle shows that only the electrons which own opposite spin quantic numbers move in the same space region, because they are described by the same orbital. These electrons can be grouped together in pairs. In the Lewis model, the bond between two atoms is described by a bonding electron pair. The electron pairs no employed in a bond are lone pairs or non bonding electron pair. Afterwards X indicate an atom attached to the central atom A and E a non-bonding pair on the central atom. In first approximation, multiple bonds are treated like a single bond with only one shared pairs

	Atoms attached to A : X	Non-bonding pair on A : E
Number	n	m

The first approximation of the theory is to liken electron pairs to punctual electric charges. Each pair which belongs to the valence shell moves to a comparable distance from the atom centre, so on the same sphere whose the centre is the atom A. On this sphere, the position of the pairs is the consequence of their mutual repulsions. Although this is not an electrostatic interaction between punctual charges (because the behaviour of electrons are governed by quantum mechanics) we obtain a correct result if we search the arrangement that gives maximum distances between electron pairs. At this first level of approximation, we don't distinguish bonding and non bonding electron pairs. In these conditions, the arrangement that minimizes the pair repulsions depends only the sum (m + n), and so, if we stop at the number six, we see these following geometrical figures.

m + n	Overall geometry
2	Linear
3	Trigonal
4	Tetrahedral
5	Trigonal bipyramidal
6	Octahedral

For these five geometrical figures, we'll see more arrangements of the electron pairs. We'll see molecules with single or multiple bonds.

The different arrangement of pairs

1. Linear arrangement

For example, molecules with simple bonds :

Beryllium, an element of the second column of the periodic classification, has for electronical configuration : [He] 2s². It has two single bonds with two atoms in BeCl₂.

For example, molecules with multiple bonds :

2. Trigonal arrangement

We distinguish two families :

AX₃	AX₂E
Trigonal planar	Bent

For example, molecules with single bonds :

B	Sn
[He] 2s² 2p¹	[Kr] 4d¹⁰ 5s² 5p²

Molecules with multiple bonds :

S	O	N
[Ne] 3s²3p⁴	[He] 2s² 2p⁴	[He] 2s² 2p³

3. Tetrahedral

We distinguish three families :

AX₄	AX₃E	AX₂E₂
Tetrahedral	Trigonal pyramidal	Bent

For example molecules with simple bonds :

Si	P	O
[Ne] 3s² 3p²	[Ne] 3s² 3p³	[He] 2s² 2p⁴

For example molecules with multiple bonds :

P	S
[Ne] 3s² 3p¹	[Ne] 3s² 3p⁴

4. Trigonal bipyramidal

The corners of the bipyramid aren't equivalent. We can split in axial (a) or equatorial (e) corners.

The problem can be resolve if we refine the hypothesis of the method. The non bonding and bonding pairs can be differently treated, indeed the position in the space of bonding pairs is controlled by the field of the two bonding atoms, but the position of non bonding pairs is controlled by only one atom : the central atom. And so, the volume of a non bonding E is higher than this of bonding S. The repulsion between pairs follows the order:

E-E (x) > E-S (y) > S-S (z)

A practical parameter to assess the importance of the repulsion between the pairs is the angle a between the directions of these pairs. This parameter allow to compare the energies of the two arrangements (1) and (2) when we count the interactions with the previous inegalities. If we only count the interactions when a £ 90° (we disregard the other one) we obtain :

Arrangement (1)	Arrangement (2)
The pair E acts with 2 atomes X	The pair E acts with 3 atomes X

The first arrangement is stabler than the second. The molecules that belong to this first arrangement, are called "disphenoïd" molecules, like SF₄. Experimentally we don't know stereoisomer for this molecule.

A same study for the other possible trigonal bipyramidal shapes, shows that the lone pairs must preferably occupy the equatorial positions.

AX₅	AX₄E	AX₃E₂	AX₂E₃
Trigonal bipyramidal	Seesaw	T-shaped	Linear

For example molecules with single bonds :

P	S	Cl	I
[Ne] 3s² 3p³	[Ne] 3s² 3p⁴	[Ne] 3s² 3p⁵	[Kr] 4 d¹⁰ 5s² 5p⁵

Molecules and ions with multiple bonds :

S	I
[Ne] 3s² 3p⁴	[Kr] 4 d¹⁰5s² 5p⁵

5. Octahedral arrangement

We observe these families :

AX₆	AX₅E	AX₄E₂
Octahedral	Square pyramidal	Square planar

For example, molecules with single bonds :

S	Br	I
[Ne] 3s² 3p⁴	[Kr] 3 d¹⁰ 4s² 4p⁵	[Kr] 4 d¹⁰ 5s² 5p⁵

Molecules with multiple bonds :

I	Xe
[Kr] 4 d¹⁰ 5s² 5p⁵	[Kr] 4 d¹⁰ 5s² 5p⁶

Type	Bond Angle	Example	Lewis Diagram	Structure
AB₂: Linear	180^o	BeH₂
AB₃: Trigonal Planar	120^o	AlH₃
AB₄: Tetrahedral	109.5^o	CH₄
AB₅: Trigonal Bipyramidal	90^o, 120^o, 180^o	PCl₅
AB₆: Octahedral	90^o, 180^o	SF₆

Second order effects

Influence of the nature of electron pairs on the angles between bonds

It's logical to admit that the non-bonding pairs, less confined in the internuclear space than bonding pairs, occupy a higher volume. And so, we see a diminution of the angles between the bonds when we observe in the order CH₄, NH₃ and H₂O.


109,5°	107°	104,5°

We observe the same evolution for the ionic derivatives of NH₃ :

NH₄⁺	NH₃	NH₂^-
109,5°	107°	104°

Influence of the volume of the multiple bonds

The geometric form depends only on s bond. So we can class the molecules with p bonds in the same groups that these with only s bonds. But the volume occupied by the electrons depends on the number of p bonds, and then we observe a diminution of the opposite angle of the p bond.

For example in the trigonal arrangement, the molecules like HCHO and COCl₂ have an angle between single bonds inferior to 120°.


115,8°	111,3°

In the tetraedric arrangement we observe a diminution of the angle between single bonds when in this order the central atom owns only single bonds, one double bond and one triple bond like in : SiF₄, POF₃ and NSF₃.


109,5°	102°	98°

In the trigonal bipyramidal arrangement the angle FOF is inferior to 120° in SOF₄.

110°

Influence of the difference of electronegativity between atoms

There are two cases :

The first appears when for a same central atom we compare the angles between bonds with atoms X whose electronegativity increases like : PI₃, PBr₃, PCl₃, PF₃.

c (I)	c (Br)	c (Cl)	c (F)
2,66	2,96	3,16	3,98

c (I) < c (Br) < c (Cl) < c (F)


102°	101,5°	100,3°	97,8°

We observe a decrease of these angles. Indeed, the bonding electron pairs are moved near X which have a higher electronegativity than A, and then, confined near X, these pairs exert lower repulsions and the angles decrease.

The second case appears when for same bonding atoms X, we compare the angles between bonds for central atoms A whose electronegativity increases like AsH₃, PH₃, NH₃.

c (As)	c (P)	c (N)
2,17	2,19	3,04

c (As) < c (P) < c (N)


91,58°	93,83°	107°

We observe an increase of these angles. Indeed, the bonding electron pairs are moved near A which has an higher electronegativity than X and then confined near A these pairs exert higher repulsions and the angles increase.

Addition of the two effects : volume and electronegativity

The two effects seen can partially add or compensate. In molecules like C₂H₄ and C₂F₂H₂, the angles between simple bonds are lower than 120°. This is because the volume of the double bonds is higher than the volume of single bonds. In C₂F₂H₂ this diminution is higher than in C₂H₄ because F has an electronegativity higher than H and then the bonding pairs confined near F exert lower repulsions.


118°	109°

Non equivalence between axial and equatorial positions in trigonal bipyramidal geometry

We have already seen, that the equatorial and axial positions aren't equivalent in molecules like PF₅ or PCl₅. The interaction between bonding electron pairs in equatorial position is less than in axial position. So there is a decrease of the length for the equatorial bonds and an increase for the axial bonds.

Bond	P-Cl_éq	P-Cl_ax
d (nm)	0,202	0,214

The non equivalence between axial and equatorial positions is visible when the bonding atoms X are different. For example, in PF₃Cl₂, Cl has a lower electronegativity than F and the electron pair that provides the bond between P and Cl occupies a higher volume than this between P and F and so, the molecule with Cl in equatorial positions is the stablest.


PCl₅	PF₃Cl₂

Remark : The same effect is observed in the octahedral arrangement. For AX₅E molecules like BrF₅ (square pyramidal), we observe a small diminution of the angle between bonds Br-F_eq and Br-F_ax (85° instead of 90°) due to a higher volume occupied by the non-bonding pair and the axial bond is longer that the equatorial ones.

Bond	Br-F_eq	Br-F_ax
d (nm)	0,177	0,168

Limits of VSEPR method

The VSEPR method often permits the correct prediction for the local arrangement of electron pairs arround an atom when this one is the central atom without ambiguity but for complex molecules it's more difficult to forsee the global geometry. For example it's impossible to forsee that C₂H₄ is a flat molecule or that in (allenes) the substituants are in perpendicular plane.

Morever, molecules aren't static objects, this is clear in molecules with pyramidal atoms like NH₃ or PH₃ . It exists some phenomenons more complex too, like the exchange between axial and equatorial positions in trigonal bipyramidal geometry (Berry's pseudo-rotation).

References

R. J Gillespie et R. S Nyholm - Quart. Rev., 1957, 11, 339.
R. J Gillespie - Actualité chimique, 1973, 4, 27.
R. J Gillespie - Molecular geometry, 1972. Van Nostrand Reihold, Londres.
G. Fontaine - Bulletin de l'union des physiciens n° 591 p. 559-568.
J. Sala- Pala - Bulletin de l'union des physiciens n° 648 p. 201-244.
N. N Greenwood and A. Earnshaw - Chemistry of the elements Pergamon Press 1984.

Links

VSEPR Theorie - Caroline Röhr, Universität Freiburg
VSEPR - by M. Lerner, Oregon State University
VSEPR - by Mark Winter, University of Sheffield
VSEPR - by John J. Nash, Purdue University

http://www.faidherbe.org/site/cours/dupuis/vseprev.htm

http://www.towson.edu/~ladon/lewis.html

http://www.chemistry.ohio-state.edu/~grandine/teaching/Chem121/lectures/LewisDot/LewisDot.html

ATOMIC ORBITAL APPROACH TO BONDING: THE VALENCE BOND THEORY

This second approach is also called the Atomic Orbital Approach to Bonding. The basic premise of this theory is that bonds are formed when atoms get close enough so that atomic orbitals on the individual atoms will be able to overlap so that the three dimensional probability regions share a common volume. This effectively increases the probability of finding bonding electrons between the two atoms. It also effectively results in the lowering of the energy state of the molecular system making the molecule more stable as a result of the overlap. The greater the overlap, the greater is the strength of the bond.

Pure Atomic Orbital Overlap

The simplest of these bonds involve the overlap of two "s" orbitals as in the example when two Hydrogen atoms get close enough to bond. The "s" orbitals overlap to form a "sigma" bond between the two "s" orbitals.

A second type of overlap is between two "p" orbitals to form a sigma bond between two "p" orbitals. An example is the p-p overlap between two Chlorine atoms.

A third type of sigma overlap is the overlap between an "s" orbital and a "p" orbital such as when a Hydrogen atom's "s" orbital overlaps with a "p" orbital of another atom like a Chlorine atom.

The valence bond theory (VB theory) or the molecular orbital theory (MO theory) explains why and how electrons are shared between atoms. The VB theory imagines individual atoms, each with its own orbitals and electrons coming together and forming covalent bonds of the molecule. The MO theory looks at the molecule as a collection of positive nuclei surround by electrons occupying sets of molecular orbitals.
A bond between two atoms is formed when a pair of electrons is shared by two overlapping orbitals, according to the VB theory. For example, in a hydrogen molecule, the two 1s orbitals from each H atoms overlap and share electrons.

The basis for the Valence Bond theory: Sigma (s) bonds form by head on overlap of unhybridized, s-orbital-s-orbital, p-orbital-p-orbital, s-orbital-p-orbital and hybridized, (sp, sp²,sp³, sp³d and sp³d²) orbitals, strong bonds will form.
pi (p)-bonds form by side-ways overlap of unhybridized p- and d-orbitals, weak bonds will from.
Molecular Geometry (three dimensional structure) can be determined by the number of s-bonds and the lone pairs on the central atom. These lone pairs will also be accommodated in hybridized orbitals.

Orbitals used in bond formation	s-bond, showing the head on overlap of atomic orbitals
s-orbital - s-orbital
s-orbital - p-orbital
p-orbital - p-orbital

Orbitals used in bond formation	p-bond, showing the side-ways overlap of atomic orbitals
p_y-orbital - p_y-orbital	overlap also illustrated like so

MOLECULAR POLARITY

Polarity is a physical property of compounds which relates other physical properties such as melting and boiling points, solubility, and intermolecular interactions between molecules.

For the most part, there is a direct correlation between the polarity of a molecule and number and types of polar or non-polar covalent bonds which are present.

In a few cases, a molecule may have polar bonds, but in a symmetrical arrangement which then gives rise to a non-polar molecule such as carbon dioxide.

Polarity results from the uneven partial charge distribution between various atoms in a compound. Atoms, such as nitrogen, oxygen, and halogens, that are more electronegative have a tendency to have partial negative charges. Atoms, such as carbon and hydrogen, have a tendency to be more neutral or have partial positive charges.

Electrons in a polar covalent bond are unequally shared between the two bonded atoms, which results in partial positive and negative charges. The separation of the partial charges creates a dipole. The word dipole means two poles: the separated partial positive and negative charges. A polar molecule results when a molecule contains polar bonds in an unsymmetrical arrangement.

Nonpolar molecules are of two types. Molecules whose atoms have equal or nearly equal electronegativities have zero or very small dipole moments. A second type of nonpolar molecule has polar bonds, but the molecular geometry is symmetrical allowing the bond dipoles to cancel each other.

What are polar covalent Bonds?

· Polar covalent bonds are a particular type of covalent bond.

· In a polar covalent bond, the electrons shared by the atoms spend a greater amount of time, on the average, closer to the Oxygen nucleus than the Hydrogen nucleus. This is because of the geometry of the molecule and the great electronegativity difference between the Hydrogen atom and the Oxygen atom.

· The result of this pattern of unequal electron association is a charge separation in the molecule, where one part of the molecule, the Oxygen, has a parital negative charge and the Hydrogens have a partial positive charge.

· You should note this molecule is not an ion because there is no excess of proton or electrons, but there is a simple charge separation in this electrically neutral molecule.

· Water is not the only molecule that can have polar covalent bonds. Examples of other molecules that have polar covalent bonds are Peptide bonds and amines .

The biological consequence of polar covalent bonds is that these kinds of bonds can lead to the formation of a weak bond called a hydrogen bond.

What is electronegativity? It is a measure of an atom's attraction for electrons in the covalent bond. You would be right if you said the halogen elements (fluorine, chlorine, iodine, etc) have some of the highest electronegativities, since they want to get one more electron to achieve an octet state. Look at the following periodic table and notice how electronegativities vary in a consistent manner across each column and row.

When two different atoms are covalently bonded, the atom with the higher electronegativity will attract the shared electrons stronger than the other atom can. This bond is known as a polar bond. As the difference in electronegativities of the atoms in a bond increase, so does its polarity. The more polar a bond becomes, the more ionic it is likely to be. You know that NaCl, table salt, is ionic; notice the difference in electronegativities, which is about 2.3. The following figure illustrates how the covalent and polar character increase. Typically, bonds with differences in electronegativities of less than 1.7 are said to be of covalent character.

Lets look at a polar molecule for an example. A good example is HCl, hydrogen chloride gas. The difference in electronegativities is about 1.0, suggesting polar character. At any point in time, the chlorine atom will attract the shared pair more strongly than the hydrogen atom; at this point, a dipole-moment exists within the atom.

Now look at methane, which has four equal hydrogen bonds. Because the symmetrical distribution of the polar bonds in the molecule cancels out the effects of the bond polarity, methane remains neutral. If we were to replace one hydrogen with a chlorine atom (forming chloromethane), the chlorine atom would attract the shared pair of electrons more strongly than the hydrogen opposite to it. Thus, the molecule becomes slightly polar.

Have you ever noticed that oil does not dissolve in water? A few things to remember are that most but not all organic compounds (compounds containing carbon and hydrogen) are non polar. Also, if we look at a water molecule, we can see that there is a lack of symmetrical electron distribution around the molecule. Because of this, water has been shown to be polar. We all know that salt dissolves in water. Why? Because like dissolves like, thus water, being polar, dissolves polar substances. Now we know why cooking oil simply floats on water and does not dissolve.

We have almost come to the end of our quest. One last section remains; the discussion of how covalent molecules exist at room temperature.

HYBRIDIZATION THEORY OF ATOMIC ORBITALS

The valence-bond approach considers the overlap of the atomic orbitals (AO) of the participation atoms to form a chemical bond. Due to the overlapping, electrons are localized in the bond region.

The overlapping AOs can be of different types, for example, a sigma bond may be formed by the overlapping the following AOs.

Chemical bonds formed due to overlap of atomic orbitals
*s-s*	*s-p*	*s-d*	*p-p*	*p-d*	*d-d*
H-H Li-H	H-C H-N H-F	H-Pd in palladium hydride	C-C P-P S-S	F-S in SF₆	Fe-Fe

However, the atomic orbitals for bonding may not be "pure" atomic orbitals directly from the solution of the Schrodinger Equation. Often, the bonding atomic orbitals have a character of several possible types of orbitals. The methods to get an AO with the proper character for the bonding is called hybridization. The resulting atomic orbitals are called hybridized atomic orbitals or simply hybrid orbitals.

We shall look at the shapes of some hybrid orbitals first, because these shapes determine the shapes of the molecules.

Hybridization of atomic orbitals

The solution to the Schrodinger Equation provides the wavefunctions for the following atomic orbitals:

1s, 2s, 2p, 3s, 3p, 3d, 4s, 4p, 4d, 4f, etc.

For atoms containing two or more electrons, the energy levels are shifted with respect to those of the H atom. An atomic orbital is really the energy state of an electron bound to an atomic nucleus. The energy state changes when one atom is bonded to another atom.

Quantum mechanical approaches by combining the wave functions to give new wavefunctions are called hybridization of atomic orbitals. Hybridization has a sound mathematical fundation, but it is a little too complicated to show the details here. Leaving out the jargons, we can say that an imaginary mixing process converts a set of atomic orbitals to a new set of hybrid atomic orbitals or hybrid orbitals.

At this level, we consider the following hybrid orbitals:

sp
sp²
sp³
sp³d
sp³d²

The sp hybrid atomic orbitals

The sp hybrid atomic orbitals are possible states of electron in an atom, especially when it is bonded to others. These electron states have half 2s and half 2p characters. From a mathematical view point, there are two ways to combine the 2s and 2p atomic orbitals:

sp₁ = 2s + 2p
sp₂ = 2s - 2p

These energy states (sp₁ and sp₂) have a region of high electron probability each, and the two atomic orbitals are located opposite to each other, centered on the atom. The sp hybrid orbitals are represented by this photograph.

H-Be-H

1s 1s
H sp₁ Be sp₂ H
1s 1s

For example, the molecule H-Be-H is formed due to the overlapping of two 1s orbitals of 2 H atoms and the two sp hybridized orbitals of Be. Thus, the H-Be-H molecule is linear. The diagram here shows the overlapping of AOs in the molecule H-Be-H.

The ground state electronic configuration of Be is 1s²2s², and one may think of the electronic configuration "before" bonding as 1s²sp². The two electrons in the sp hybrid orbitals have the same energy.

You may say that the concept of hybridizing AOs for the bonding is just a story made up to explain the molecular shape of Cl-Be-Cl. You are right! The story is lovely and interesting, though.

In general, when two and only two atoms bond to a third atom and the third atom makes use of the sp hybridized orbitals, the three atoms are on a straight line. For example, sp hybrid orbitals are used in the central atoms in the molecules shown on the right.

The sp² hybrid orbitals

The energy states of the valence electrons in atoms of the second period are in the 2s and 2p orbitals. If we mix two of the 2p orbitals with a 2s orbital, we end up with three sp² hybridized orbitals. These three orbitals lie on a plane, and they point to the vertices of a equilateral triangle as shown here.

When the central atom makes use of sp² hybridized orbitals, the compound so formed has a trigonal shape. BF₃ is such a molecule.

Not all three sp² hybridized orbitals have to be used in bonding. One of the orbitals may be occupied by a pair or a single electron. If we do not count the unshared electrons, these molecules are bent, rather than linear. The three molecules shown together with the BF₃ molecule are such molecules.

Carbon atoms also makes use of the sp² hybrid orbitals in the compound H₂C=CH₂. In this molecule, the remaining p orbital from each of the carbon overlap to form the additional pi, p, bond.

Other ions such as CO₃^2-, and NO₃^-, can also be explained in the same way.

The sp³ hybrid orbitals

Mixing one s and all three p atomic orbitals produces a set of four equivalent sp³ hybrid atomic orbitals. The four sp³ hybrid orbitals points towards the vertices of a tetrahedron, as shown here in this photograph.

When sp³ hybrid orbitals are used for the central atom in the formation of molecule, the molecule is said to have the shape of a tetrahedron.

The typical molecule is CH₄, in which the 1s orbital of a H atom overlap with one of the sp³ hybrid orbitals to form a C-H bond. Four H atoms form four such bonds, and they are all equivalent. The CH₄ molecule is the most cited molecule to have a tetrahedral shape. Other molecules and ions having tetrahedral shapes are SiO₄^4-, SO₄^2-,

As are the cases with sp², hybrid orbitals, one or two of the sp³ hybrid orbitals may be occupied by non-bonding electrons. Water and ammonia are such molecules.

The C, N and O atoms in CH₄, NH₃, OH₂ (or H₂O) molecules use the sp³ hybrid orbitals, however, a lone pair occupy one of the orbitals in NH₃, and two lone pairs occupy two of the sp³ hybrid orbitals in OH₂. The lone pairs must be considered in the VSEPR model, and we can represent a lone pair by E, and two lone pairs by E₂. Thus, we have NH₃E and OH₂E₂ respectively.

The VSEPR number is equal to the number of bonds plus the number of lone pair electrons. Does not matter what is the order of the bond, any bonded pair is considered on bond. Thus, the VSEPR number is 4 for all of CH₄, :NH₃, ::OH₂.

According the the VSEPR theory, the lone electron pairs require more space, and the H-O-H angle is 105 deegrees, less than the ideal tetrahedral angle of 109.5 degrees.

The dsp³ hybrid orbitals

The five dsp³ hybrid orbitals resulted when one 3d, one 3s, and three 3p atomic orbitals are mixed. When an atom makes use of fice dsp³ hybrid orbitals to bond to five other atoms, the geometry of the molecule is often a trigonalbipyramidal. For example, The molecule PClF₄ displayed here forms such a structure. In this diagram, the Cl atom takes up an axial position of the trigonalbipyramid. There are structures in which the Cl atom may take up the equatorial position. The change in arrangement is accomplished by simply change the bond angles. This link discusses this type of configuration changes of this molecule.

Some of the dsp³ hybrid orbitals may be occupied by electron pairs. The shapes of these molecules are interesting. In TeCl₄, only one of the hybrid dsp³ orbitals is occupied by a lone pair. This structure may be represented by TeCl₄E, where E represents a lone pair of electrons. Two lone pairs occupy two such orbitals in the molecule BrF₃, or BrF₃E₂. These structures are given in a VSEPR table of 5 and 6 coordinations.

The compound SF₄ is another AX₄E type, and many interhalogen compounds ClF₃ and IF₃ are AX₃E₂ type. The ion I₃^- is of the type AX₂E₃.

The d²sp³ hybrid orbitals

The six d²sp³ hybrid orbitals resulted when two 3d, one 3s, and three 3p atomic orbitals are mixed. When an atom makes use of six d²sp³ hybrid orbitals to bond to six other atoms, the molecule takes the shape of an octahedron, in terms of molecular geometry. The gas compound SF₆ is a typical such structure. This link provides other shapes as well.

There are also cases that some of the d²sp³ hybrid orbitals are occupied by lone pair electrons leading to the structures of the following types:

AX₆, AX₅E, AX₄E₂ AX₃E₃ and AX₂E₄
IOF₅, IF₅E, XeF₄E₂

No known compounds of AX₃E₃ and AX₂E₄ are known or recognized, because they are predicted to have a T shape and linear shape respectively when the lone pairs of electrons are ignored.

Molecular shapes of compounds

While the hybridized orbitals were introduced, in the foregoing discussion, Valence-shell Electron-pair Repulsion (VSEPR) Model were included to suggest the shapes of various molecules. Specifically, the VSEPR model counts unshared electron pairs and the bonded atoms as the VSEPR number. A single-, double- and tripple-bond is considered as 1. After having considered the hybridized orbitals and the VSEPR model, we can not take a systematic approach to rationalize the shapes of many molecules based on the number of valence electrons.

A summary in the form of a table is given here to account for the concepts of hybrid orbitals, valence bond theory, VSEPR, resonance structures, and octet rule. In this table, the geometric shapes of the molecules are described by linear, trigonal planar, tetrahedral, trigonal bypyramidal, and octahedral. The hybrid orbitals use are sp, sp², sp³, dsp³, and d²sp³.

The VSEPR number is the same for all molecules of each group. Instead of using NH₃E, and OH₂E₂, we use :NH₃, ::OH₂ to emphasize the unshared (or lone) electron pairs.

A summary of hybrid orbitals, valence bond theory, VSEPR, resonance structures, and octet rule.
Linear	Trigonal planar	Tetrahedral	Trigonal bipyramidal	Octahedral
sp	sp²	sp³	dsp³	d²sp³
BeH₂ BeF₂ CO₂ HCN HCºCH	BH₃ BF₃ CH₂O (>C=O) >C=C< CO₃^2- benzene graphite fullerenes •NO₂ N₃^- :OO₂ (O₃) :SO₂ SO₃	CH₄ CF₄ CCl₄ CH₃Cl NH₄⁺ :NH₃ :PF₃ :SOF₂ ::OH₂ ::SF₂ SiO₄^4- PO₄^3- SO₄^2- ClO₄^-	PF₅ PCl₅ PFCl₄ :SF₄ :TeF₄ ::ClF₃ ::BrF₃ :::XeF₂ :::I₃^- (:::I I₂^-) :::ICl₂^-	SF₆ IOF₅ PF₆^- SiF₆^2- :BrF₅ :IF₅ ::XeF₄
• a lone odd electron : a lone electron pair

This table correlates a lot of interesting chemical concepts in order to understand the molecular structures of these compounds or ions. There are some intriguing chemical relationships among the molecules in each column for you to ponder.

Only Be and C atoms are involved in linear molecules. In gas phase, BeH₂ and BeF₂ are stable, and these molecules do not satisfy the octet rule. The element C makes use of sp hybridized orbitals and it has the ability to form double and triple bonds in these linear molecules.

Carbon compounds are present in trigonal planar and tetrahedral molecules, using different hybrid orbitals. The extra electron in nitrogen for its compounds in these groups appear as lone unpaired electron or lone electron pairs. More electrons in O and S lead to compounds with lone electron pairs. The five-atom anions are tetrahedral, and many resonance structures can be written for them.

Trigonal bipyramidal and octahedral molecules have 5 and 6 VSEPR pairs. When the central atoms contain more than 5 or 6 electrons, the extra electrons form lone pairs. The number of lone pairs can easily be derived using Lewis dot structures for the valence electrons.

In describing the shapes of these molecules, we often ignore the lone pairs. Thus, •NO₂, N₃^-, :OO₂ (O₃), and :SO₂ are bent molecules whereas :NH₃, :PF₃, and :SOF₂ are pyramidal. You already know that ::OH₂ (water) and ::SF₂ are bent molecules.

The lone electron pair takes up the equatorial location in :SF₄, which has the same structure as :TeF₄ described earlier. If you lay a model of this molecule on the side, it looks like a butterfly. By the same reason, ::ClF₃ and ::BrF₃ have a T shape, and :::XeF₂, :::I₃^-, and :::ICl₂^- are linear.

Similarly, :BrF₅ and :IF₅ are square pyramidal whereas ::XeF₄ is square planar.

The Centre Atom

A nice student asked a brilliant question.

Which atom in the formula is usually the center atom?

Usually, the atom in the center is more electropositive than the terminal atoms. However, the H and halogen atoms are usually at the terminal positions because they form only one bond.

Take a look at the chemical formulas in the table, and see if the above statement is true.

However, the application of VSEPR theory can be expanded to complicated molecules such as

    H H         H   O

    | |         |  //

  H-C-C=C=C-C=C-C-C

    |           |  \

    H           N   O-H

/ \

              H   H

By applying the VSEPR theory, one deduces the following results:

H-C-C bond angle = 109^o
H-C=C bond angle = 120^o, geometry around C trigonal planar
C=C=C bond angle = 180^o, in other words linear
H-N-C bond angle = 109^o, tetrahedral around N
C-O-H bond angle = 105 or 109^o, 2 lone electron pairs around O

HYBRIDIZATION AND ASSOCIATED MOLECULAR GEOMETRY

Hybridization	Orbitals (simplified)	Molecular Geometry
sp	one s + one p :: two sp hybrids	Linear
sp²	one s + two p's :: 3 sp² hybrids	Trigonal Planar
sp³	one s + three p's :: 4 sp³ hybrids	Tetrahedral
sp³d	one s + three p's + one d :: 5 sp³d hybrids	Trigonal Bipyramidal
sp³d²	one s + three p's + two d's :: 6 sp³d² hybrids	Octahedral

HYBRIDIZATION, LONE PAIRS AND ASSOCIATED MOLECULAR GEOMETRY
MOLECULAR GEOMETRY IS DETERMINED BY THE POSITIONS OF ATOMIC NUCLEI IN THREE DIMENSIONAL SPACE

Hybridization	Orbitals with LOne Pairs	Molecular Geometry
sp²	One Lone Pair in one of the sp² hybrids	Bent
sp³	One Lone Pair in one of the sp³ hybrids	Trigonal Pyramidal
sp³	Two Lone Pairs in two of the sp³ hybrids	Bent
sp³d	One Lone Pair in one of the sp³d hybrids	See Saw
sp³d	Two Lone Pairs in two of the sp³d hybrids	T-Structure
sp³d	Three Lone Pairs in three of the sp³d hybrids	Linear
sp³d²	One Lone Pair in one of the sp³d² hybrids	Square-pyramidal
sp³d²	Two Lone Pairs in two of the sp³d² hybrids	Square-planar

WHAT ARE THE PROPERTIES OF COVALENT COMPOUNDS?

Covalent compounds have the following properties (keep in mind that these are only general properties, and that there are always exceptions to every rule):

1) Covalent compounds generally have much lower melting and boiling points than ionic compounds.

As you may recall, ionic compounds have very high melting and boiling points because it takes a lot of energy for all of the + and - charges which make up the crystal to get pulled apart from each other. Essentially, when we have an ionic compound, we need to break all of the ionic bonds in order to make it melt.

On the other hand, when we have covalent compounds we don't need to break any bonds at all. This is because covalent compounds form distinct molecules, in which the atoms are bound tightly to one another. Unlike in ionic compounds, these molecules don't interact with each other much (except through relatively weak forces called "intermolecular forces"), making them very easy to pull apart from each other. Since they're easy to separate, covalent compounds have low melting and boiling points.

2) Covalent compounds are soft and squishy (compared to ionic compounds, anyway).

The reason for this is similar to the reason that covalent compounds have low melting and boiling points. When you hit an ionic compound with something, it feels very hard. The reason for this is that all of the ionic bonds which hold together the crystal tend to make it very inflexible and hard to move. On the other hand, covalent compounds have these molecules which can very easily move around each other, because there are no bonds between them. As a result, covalent compounds are frequently flexible rather than hard.

Think of it like this: Ionic compounds are like giant Lego sculptures. If you hit a Lego sculpture with your fist, it feels hard because all of the Legos are stuck very tightly to one another. Covalent compounds are more like those plastic ball pits they have at fast food playgrounds for little kids. While the balls themselves are held together very tightly (just like covalent molecules are held together tightly), the balls aren't really stuck to each other at all. As a result, when little kids jump into the ball pits they sink in rather than bouncing off.

3) Covalent compounds tend to be more flammable than ionic compounds.

The main reason that things burn is because they contain carbon and hydrogen atoms that can react to form carbon dioxide and water when heated with oxygen gas (that's the definition of a combustion reaction). Since carbon and hydrogen have very similar electronegativities, they are mostly found together in covalent compounds. As a result, more covalent compounds than ionic compounds are flammable.

There are a couple of exceptions to this rule. The first is with covalent compounds that contain neither carbon nor hydrogen. These tend not to burn, and if they do, they burn by mechanisms other than the classic combustion reaction. The other exception comes with ionic compounds referred to as "organic salts". These organic salts are ionic compounds in which the anion is basically a big covalent molecule containing carbon and hydrogen with just a very small ionic section. As a result, they burn even though they're technically ionic compounds.

4) Covalent compounds don't conduct electricity in water.

Electricity is conducted in water from the movement of ions from one place to the other. These ions are the charge carriers which allow water to conduct electricity. Since there are no ions in a covalent compound, they don't conduct electricity in water.

5) Covalent compounds aren't usually very soluble in water.

There's a saying that, "Like dissolves like". This means that compounds tend to dissolve in other compounds that have similar properties (particularly polarity). Since water is a polar solvent and most covalent compounds are fairly nonpolar, many covalent compounds don't dissolve in water. Of course, this is a generalization and not set in stone - there are many covalent compounds that dissolve quite well in water. However, the majority of them don't because of this rule.

INTERMOLECULAR FORCES

Intermolecular forces are generally much weaker than covalent bonds

Only 16 kJ/mol of energy is required to overcome the intermolecular attraction between HCl molecules in the liquid state (i.e. the energy required to vaporize the sample)
However, 431 kJ/mol of energy is required to break the covalent bond between the H and Cl atoms in the HCl molecule

Thus, when a molecular substance changes states the atoms within the molecule are unchanged.

The temperature at which a liquid boils reflects the kinetic energy needed to overcome the attractive intermolecular forces (likewise, the temperature at which a solid melts). Thus, the strength of the intermolecular forces determines the physical properties of the substance.

Attractive forces between neutral molecules

Dipole-dipole forces
London dispersion forces
Hydrogen bonding forces

Typically, dipole-dipole and dispersion forces are grouped together and termed van der Waals forces (sometimes the hydrogen bonding forces are also included with this group)

Attractive forces between neutral and charged (ionic) molecules

ion-dipole forces

Note that all of these forces will be electrostatic in nature

ION-DIPOLE

Involves an interaction between a charged ion and a polar molecule (i.e. a molecule with a dipole)
Cations are attracted to the negative end of a dipole
Anions are attracted to the positive end of a dipole
The magnitude of the interaction energy depends upon the charge of the ion (Q), the dipole moment of the molecule (u) and the distance (d) from the center of the ion to the midpoint of the dipole

Ion-dipole forces are important in solutions of ionic substances in polar solvents (e.g. a salt in aqueous solvent)

DIPOLE-DIPOLE FORCES

A dipole-dipole force exists between neutral polar molecules

Polar molecules attract one another when the partial positive charge on one molecule is near the partial negative charge on the other molecule
The polar molecules must be in close proximity for the dipole-dipole forces to be significant
Dipole-dipole forces are characteristically weaker than ion-dipole forces
Dipole-dipole forces increase with an increase in the polarity of the molecule

Boiling points increase for polar molecules of similar mass, but increasing dipole:

Substance	Molecular Mass (amu)	Dipole moment, u (D)	Boiling Point (°K)
Propane	44	0.1	231
Dimethyl ether	46	1.3	248
Methyl chloride	50	2.0	249
Acetaldehyde	44	2.7	294
Acetonitrile	41	3.9	355

LONDON DISPERSION FORCES

Nonpolar molecules would not seem to have any basis for attractive interactions.

However, gases of nonpolar molecules can be liquefied indicating that if the kinetic energy is reduced, some type of attractive force can predominate.
Fritz London (1930) suggested that the motion of electrons within an atom or non-polar molecule can result in a transient dipole moment

A Model To Explain London Dispersion Forces:

Helium atoms (2 electrons)

Consider the particle nature of electrons
The average distribution of electrons around each nucleus is spherically symmetrical
The atoms are non-polar and posses no dipole moment
The distribution of electrons around an individual atom, at a given instant in time, may not be perfectly symmetrical

Both electrons may be on one side of the nucleus
The atom would have an apparent dipole moment at that instant in time (i.e. a transient dipole)
A close neighboring atom would be influenced by this apparent dipole - the electrons of the neighboring atom would move away from the negative region of the dipole

Due to electron repulsion, a temporary dipole on one atom can induce a similar dipole on a neighboring atom

This will cause the neighboring atoms to be attracted to one another
This is called the London dispersion force (or just dispersion force)
It is significant only when the atoms are close together

The ease with which an external electric field can induce a dipole (alter the electron distribution) with a molecule is referred to as the "polarizability" of that molecule

The greater the polarizability of a molecule the easier it is to induce a momentary dipole and the stronger the dispersion forces
Larger molecules tend to have greater polarizability

Their electrons are further away from the nucleus (any asymmetric distribution produces a larger dipole due to larger charge separation)
The number of electrons is greater (higher probability of asymmetric distribution)

thus, dispersion forces tend to increase with increasing molecular mass

Dispersion forces are also present between polar/non-polar and polar/polar molecules (i.e. between all molecules)

HYDROGEN BONDING

A hydrogen atom in a polar bond (e.g. H-F, H-O or H-N) can experience an attractive force with a neighboring electronegative molecule or ion which has an unshared pair of electrons (usually an F, O or N atom on another molecule)

Hydrogen bonds are considered to be dipole-dipole type interactions

A bond between hydrogen and an electronegative atom such as F, O or N is quite polar:

The hydrogen atom has no inner core of electrons, so the side of the atom facing away from the bond represents a virtually naked nucleus
This positive charge is attracted to the negative charge of an electronegative atom in a nearby molecule
Because the hydrogen atom in a polar bond is electron-deficient on one side (i.e. the side opposite from the covalent polar bond) this side of the hydrogen atom can get quite close to a neighboring electronegative atom (with a partial negative charge) and interact strongly with it (remember, the closer it can get, the stronger the electrostatic attraction)

Hydrogen bonds vary from about 4 kJ/mol to 25 kJ/mol (so they are still weaker than typical covalent bonds.
But they are stronger than dipole-dipole and or dispersion forces.
They are very important in the organization of biological molecules, especially in influencing the structure of proteins

Water is unusual in its ability to form an extensive hydrogen bonding network

As a liquid the kinetic energy of the molecules prevents an extensive ordered network of hydrogen bonds
When cooled to a solid the water molecules organize into an arrangement which maximizes the attractive interactions of the hydrogen bonds

This arrangement of molecules has greater volume (is less dense) than liquid water, thus water expands when frozen
The arrangement has a hexagonal geometry (involving six molecules in a ring structure) which is the structural basis of the six-sidedness seen in snow flakes
Each water molecule can participate in four hydrogen bonds

One with each non-bonding pair of electrons
One with each H atom

METALLIC BOND

What is a metallic bond?

Metallic bonding in sodium

Metals tend to have high melting points and boiling points suggesting strong bonds between the atoms. Even a metal like sodium (melting point 97.8°C) melts at a considerably higher temperature than the element (neon) which precedes it in the Periodic Table.

Sodium has the electronic structure 1s²2s²2p⁶3s¹. When sodium atoms come together, the electron in the 3s atomic orbital of one sodium atom shares space with the corresponding electron on a neighbouring atom to form a molecular orbital - in much the same sort of way that a covalent bond is formed.

The difference, however, is that each sodium atom is being touched by eight other sodium atoms - and the sharing occurs between the central atom and the 3s orbitals on all of the eight other atoms. And each of these eight is in turn being touched by eight sodium atoms, which in turn are touched by eight atoms - and so on and so on, until you have taken in all the atoms in that lump of sodium.

All of the 3s orbitals on all of the atoms overlap to give a vast number of molecular orbitals which extend over the whole piece of metal. There have to be huge numbers of molecular orbitals, of course, because any orbital can only hold two electrons.

The electrons can move freely within these molecular orbitals, and so each electron becomes detached from its parent atom. The electrons are said to be delocalised. The metal is held together by the strong forces of attraction between the positive nuclei and the delocalised electrons.

This is sometimes described as "an array of positive ions in a sea of electrons".

If you are going to use this view, beware! Is a metal made up of atoms or ions? It is made of atoms.

Each positive centre in the diagram represents all the rest of the atom apart from the outer electron, but that electron hasn't been lost - it may no longer have an attachment to a particular atom, but it's still there in the structure. Sodium metal is therefore written as Na - not Na⁺.

Metallic bonding in magnesium

If you work through the same argument with magnesium, you end up with stronger bonds and so a higher melting point.

Magnesium has the outer electronic structure 3s². Both of these electrons become delocalised, so the "sea" has twice the electron density as it does in sodium. The remaining "ions" also have twice the charge (if you are going to use this particular view of the metal bond) and so there will be more attraction between "ions" and "sea".

More realistically, each magnesium atom has one more proton in the nucleus than a sodium atom has, and so not only will there be a greater number of delocalised electrons, but there will also be a greater attraction for them.

Magnesium atoms have a slightly smaller radius than sodium atoms, and so the delocalised electrons are closer to the nuclei. Each magnesium atom also has twelve near neighbours rather than sodium's eight. Both of these factors increase the strength of the bond still further.

Metallic bonding in transition elements

Transition metals tend to have particularly high melting points and boiling points. The reason is that they can involve the 3d electrons in the delocalisation as well as the 4s. The more electrons you can involve, the stronger the attractions tend to be.

The metallic bond in molten metals

In a molten metal, the metallic bond is still present, although the ordered structure has been broken down. The metallic bond isn't fully broken until the metal boils. That means that boiling point is actually a better guide to the strength of the metallic bond than melting point is. On melting, the bond is loosened, not broken.

The structure of metals

The arrangement of the atoms

Metals are giant structures of atoms held together by metallic bonds. "Giant" implies that large but variable numbers of atoms are involved - depending on the size of the bit of metal.

12-co-ordination

Most metals are close packed - that is, they fit as many atoms as possible into the available volume. Each atom in the structure has 12 touching neighbours. Such a metal is described as 12-co-ordinated.

Each atom has 6 other atoms touching it in each layer.

There are also 3 atoms touching any particular atom in the layer above and another 3 in the layer underneath.

This second diagram shows the layer immediately above the first layer. There will be a corresponding layer underneath. (There are actually two different ways of placing the third layer in a close packed structure, but that goes beyond the requirements of current A'level syllabuses.)

8-co-ordination

Some metals (notably those in Group 1 of the Periodic Table) are packed less efficiently, having only 8 touching neighbours. These are 8-co-ordinated.

The left hand diagram shows that no atoms are touching each other within a particular layer . They are only touched by the atoms in the layers above and below. The right hand diagram shows the 8 atoms (4 above and 4 below) touching the darker coloured one.

Dislocations

It would be misleading to suppose that all the atoms in a piece of metal are arranged in a regular way. Any piece of metal is made up of a large number of "crystal grains", which are regions of perfect regularity. At the grain boundaries atoms have become misaligned.

The grain boundaries are also known as dislocations.

The physical properties of metals

Melting points and boiling points

Metals tend to have high melting and boiling points because of the strength of the metallic bond. The strength of the bond varies from metal to metal and depends on the number of electrons which each atom delocalises into the sea of electrons, and on the packing.

Group 1 metals like sodium and potassium have relatively low melting and boiling points mainly because each atom only has one electron to contribute to the bond - but there are other problems as well:

· Group 1 elements are also inefficiently packed (8-co-ordinated), so that they aren't forming as many bonds as most metals.

· They have relatively large atoms (meaning that the nuclei are some distance from the delocalised electrons) which also weakens the bond.

Electrical conductivity

Metals conduct electricity. The delocalised electrons are free to move throughout the structure in 3-dimensions. They can cross grain boundaries. Even though the pattern may be disrupted at the boundary, as long as atoms are touching each other, the metallic bond is still present.

Liquid metals also conduct electricity, showing that although the metal atoms may be free to move, the delocalisation remains in force until the metal boils.

Thermal conductivity

Metals are good conductors of heat. Heat energy is picked up by the electrons as additional kinetic energy (it makes them move faster). The energy is transferred throughout the rest of the metal by the moving electrons.

Strength and workability

Malleability and ductility

Metals are described as malleable (can be beaten into sheets) and ductile (can be pulled out into wires). This is because of the ability of the atoms to roll over each other into new positions without breaking the metallic bond.

If a small stress is put onto the metal, the layers of atoms will start to roll over each other. If the stress is released again, they will fall back to their original positions. Under these circumstances, the metal is said to be elastic.

If a larger stress is put on, the atoms roll over each other into a new position, and the metal is permanently changed.

The hardness of metals

This rolling of layers of atoms over each other is hindered by grain boundaries because the rows of atoms don't line up properly. It follows that the more grain boundaries there are (the smaller the individual crystal grains), the harder the metal becomes.

Offsetting this, because the grain boundaries are areas where the atoms aren't in such good contact with each other, metals tend to fracture at grain boundaries. Increasing the number of grain boundaries not only makes the metal harder, but also makes it more brittle.

Controlling the size of the crystal grains

If you have a pure piece of metal, you can control the size of the grains by heat treatment or by working the metal.

Heating a metal tends to shake the atoms into a more regular arrangement - decreasing the number of grain boundaries, and so making the metal softer. Banging the metal around when it is cold tends to produce lots of small grains. Cold working therefore makes a metal harder. To restore its workability, you would need to reheat it.

You can also break up the regular arrangement of the atoms by inserting atoms of a slightly different size into the structure. Alloys such as brass (a mixture of copper and zinc) are harder than the original metals because the irregularity in the structure helps to stop rows of atoms from slipping over each other.

ACTIVITIES

1.- Calculate the lattice enthalpy of sodium chloride given

ΔH_f^θ (NaCl) = -411 kJ mol^-1

ΔH_sub. (Na) = 108.3 kJ mol^-1

ΔH_I.E. (Na) = 500 kJ mol^-1

ΔH_diss. (Cl) = 121 kJ mol^-1

ΔH_e.a. (Cl) = -364 kJ mol^-1

Answer ΔH_latt. = +776 kJ mol^-1

2. Draw Born-Haber cycles for each of the following ionic compounds and calculate their lattice enthalpies.

(Note : ΔH_at. of an element is the energy required to form one mole of gaseous atoms from the element.)

		M			X
Compound	ΔH_F^θ kJmol^-1		ΔH_at. kJmol^-1	ΔH_I.E. kJmol^-1	ΔH_at. kJmol^-1	ΔH_e.a. kJmol^-1
KBr	-392		+89	+420	+112	-342
BaCl₂	-860		+175	(1^st) +500 (2^nd) +1000	+121	-364

3.- The figures below give a list of lattice energies in kJ mol^-1. Try to find as many patterns and trends in the figures as you can.

RbF 779 CaI₂ 2038

BeF₂ 3456 CaCl₂ 2197

BaI₂ 1841 MgCl₂ 2489

MgBr₂ 2416 KCl 710

CaBr₂ 2125 NaF 915

CsI 607 LiF 1029

KBr 671 MgI₂ 2314

BaF₂ 2289 LiBr 804

CsBr 644 RbI 624

LiI 753 SrBr₂ 2046

BeI₂ 2803 NaBr 742

LiCl 849 SrCl₂ 2109

NaI 699 BeBr₂ 2895

BeCl₂ 2983 KF 813

CsCl 676 BaBr₂ 1937

KI 643 CaF₂ 2583

MgF₂ 2883 NaCl 776

RbCl 685 SrF₂ 2427

SrI₂ 1954 RbBr 656

CsF 735 BaCl₂ 2049

4. What would be the effect on lattice energy of increasing the charge on X^n- ? (i.e. forming a Group VI compound rather than a Group VII compound).

Describe and explain the trends.

5. Calculate the lattice energy for CaF_{2 (s)} from the following data: H_f(CaF₂) = -1215kJ/mol, H_vap (Ca) = 192.6kJ/mol, BE (F₂) = 159kJ/mol, IE₁ (Ca) = 590kJ/mol, IE₂ (Ca) = 1151.5kJ/mol, EA₁ (F) = -328kJ/mol.

11. Calculate the lattice enthalpy of sodium chloride given

ΔH_f^θ (NaCl) = -411 kJ mol^-1

ΔH_sub. (Na) = 108.3 kJ mol^-1

ΔH_I.E. (Na) = 500 kJ mol^-1

ΔH_diss. (Cl) = 121 kJ mol^-1

ΔH_e.a. (Cl) = -364 kJ mol^-1

Answer ΔH_latt. = +776 kJ mol^-1

12. Draw the Lewis dot structures and resonance structures for the following. Some hints are given.

CO₂ - :O::C::O: (plus two more dots for each of O)
NO₂ - ^.NO₂ (bent molecule due to the odd electron)
NO₂^- - :NO₂^- (same number of electron as SO₂)
HCO₂^- - H-CO₂
O₃ - (ozone, OO₂ same number of electron as SO₂)
SO₃ - (consider O-SO₂, and the resonance structures)
NO₃^-
CO₃^2-

Notice that some of the resonance structures may not satisfy the octet rule. The NO₂ molecule has an odd number of electrons, and the octet rule cannot be satisfied for the nitrogen atom.

13. Draw the Lewis dot structures and resonance structures for

HNO₃
H₂SO₄
H₂CO₃
HClO₄
C₅H₅N
NO₃^-
SO₄^2-
CO₃^2-
ClO₄^-
Benzene C₆H₆
Cl₂CO

The Octet rule should be applied to HNO₃, NO₃^-, H₂CO₃, CO₃^2-, C₅H₅N, C₆H₆, and Cl₂CO.

14. Draw the Lewis structure for the following molecules and verify their family and geometrical shape.

AX₂

COS, C₂H₂

15. Draw the Lewis structure for the following molecules and ions and verifiy their family and geometrical shape.

AX₃	AX₂E
BF₃, H₂CO , COCl₂ , C₂H₄ , (CO₃)^2-	SO₂

16. Draw the Lewis structure for the following molecules and ions. Verify their family and geometrical shape.

AX₄	AX₃E	AX₂E₂
CH₄ , (NH₄)⁺ , (S₂O₃)^2-	NH₃ , PH₃ , (H₃O)⁺	H₂O , H₂S , (NH₂)^-

17. Draw the Lewis structure for these following molecules or ions, and verify their family and geometrical shape.

AX₅	AX₄E
PF₃Cl₂ , XeO₃F₂	XeO₂F₂

http://www.sparknotes.com/chemistry/bonding/ionic/section1.html

http://www.science.uwaterloo.ca/~cchieh/cact/c120/dotstruc.html

http://www.sciencegeek.net/Activities/bornhaber.html

http://www.chem.uncc.edu/faculty/murphy/1251/slides/C19b/sld001.htm