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These notes were written for the old IB syllabus (2009). The new IB syllabus for first examinations 2016 can be accessed by clicking the link below.

### 14.2 - Hybridisation

14.2.1: Describe sigma and pi bonds. Treatment should be restricted to: sigma bonds electron distribution has axial symmetry around the axis joining the two nuclei, pi bonds resulting from the combination of parallel 'p' orbitals, double bonds formed by a sigma and a pi bond, triple bonds formed by a sigma and two pi bonds.

#### Orbitals

An orbital is a region of space in which there is a 99% probability of finding an electron with a specific quantity of energy. The shape plotted out by this probability is accepted to be the region of space where the electron is, as this makes discussions of electrons and their movements much easier to understand.

For example electrons with the lowest energy are 99% likely to be within a region of spherical shape around the nucleus of an atom. It is convenient for us to describe this region of space as the orbital in which a maximum of two electrons may be housed. We call it an 's' orbital. If it is the lowest energy level, then it is designated 1s.

#### Sigma bonds

When two s orbitals overlap, the electrostatic forces of attraction for the nucleus of one atom will attract the electrons of the other atom and vice versa. This produces an overall force that holds the two nuclei together. We call this a chemical bond.

If two s orbitals directly overlap then the bond formed is linear between the two nuclear centres and is called a sigma bond.

Sigma bonds are produced by any direct orbital overlap along the axis joining the two nuclear centres together.

Although it is convenient to show this overlap using two 1s orbitals, in fact this is the exception rather than the rule. Direct orbital overlap usually happens by overlap of a hybridised orbital with a 1s orbital (in hydrogen) or between two hybridised orbitals.

#### 'pi' bonds

When a sigma bond is formed by direct orbital overlap and this brings two parallel 'p' orbitals into close proximity then these can overlap sideways (laterally) to form a region of electron density that is not directly between the two nuclear centres but which nevertheless contributes to bonding. This is called a pi bond.

It should be emphasised that a pi bond can only form after a sigma bond has already formed. It is always part of a double or triple bond.

#### Double and triple bonds

As stated above a pi bond can only form after a sigma bond. Consequently the pi bond must be part of a double (or triple) bond system. Whenever there is a double bond it is made up of one sigma (direct orbital overlap) bond and one pi (lateral orbital overlap) bond.

Triple bonds have two pi bonds arranged at 90º to one another brought about by the lateral overlap of one pair of py orbitals and one pair of pz orbitals.

Summary:

• Double bonds - 1 sigma and 1 pi bond
• Triple bonds - 1 sigma and 2 pi bonds

14.2.2: Explain Hybridization in terms of the mixing of atomic orbitals to form new orbitals for bonding. Students should consider sp, sp2 and sp3 hybridization, and the shapes and orientation of these orbitals. TOK: Is hybridisation a real process or a mathematical device?

#### Hybridisation

Hybridisation means making something new from an amalgamation or combination of other parts. A hybrid plant is one made from two different plants blended together. The hybrid shows the characteristics of both plants.

In terms of chemistry we refer to the hybridisation of atomic orbitals to explain the change that seems to happen between the atomic orbitals in an uncombined atom and the orbitals used by the same atom when bonding.

We are familiar with the orbitals in an atom and their different shapes. The 's' orbital is spherical about the nucleus and the 'p' orbitals are like double headed balloons arranged along the axis of (imaginary) three dimensional coordinates.

 's' orbitals 'p' orbitals

However, it is apparent that the shapes of these orbitals are inadequate to explain the orientation of the bonds produced in molecules. The 'p' orbitals are oriented at 90º to one another and yet there are few molecules that show a bond angle of 90º (in fact the bond angle 90º does appear in some of the larger moolecules but that is due to different reasons).

The classic molecule to consider is methane CH4. In this molecule the bond angles indicate that the shape of the molecule is a perfect tetrahedron with bond angles of 109º 28' (approximately 109,5º)

It seems that the orbitals used for bonding are arranged as far apart as possible suggesting that they have the same energy (degenerate). We know that the orbitals on the carbon atom do not have the same energy - the 2s orbital is of lower energy that the three 2p orbitals. Hybridisation is a model that allows us to combine the atomic orbitals and then produce four degenerate orbitals to be used for bonding. In order for the electrons to be ready for this process one of them must be promoted from the 2s orbital to the 2pz orbital as in the diagram.

 The 2s electron is promoted to the 2pz orbital and the four orbitals then undergo hybridisation to form four degenerate orbitals. As these new orbital have emerged from one s and three p orbitals they are called 'sp3' orbitals.

It should be emphasised at this point that this is the norm rather than the exception. It seems that all elements undergo this hybridisation process (or a similar one) when bonding. Logically, the 2s orbital is in no position to overlap directly with another orbital from another atom without interfering with the p orbitals. This hybridisation process allows the 2s electrons to be involved in bonding.

If we study the shape of the water molecule (section 14.1) we accept that the four electron pairs around the oxygen are tetrahedrally arranged. They have hybridised and the sp3 orbitals so formed overlap directly with the 1s orbitals of the two hydrogens. The two lone pairs on the oxygen remain in the sp3 orbitals that are not used in bonding.

#### Other types of hybridisation

Carbon can also bond to three other atoms instead of four (as in methane) and it seems that it hybridised its orbitals using only the 2s and two of the 2p orbitals to do this.

As can be seen this leaves an unaffected p orbital that is then used for lateral overlap pi bonding

This is the formation of a double bond in molecules such as ethene. The three sp2 hybrid orbitals are degenerate (same energy) and consequently arrange as far apart as possible in space i.e. at 120º to each other. This creates a trigonal shape that is planar leaving the remaining 2pz orbital to orientate itself above and below the plane of the other orbitals. This 2p orbital caln then laterally overlap with adjacent singly occupied 'p' orbitals on adjacent atoms.

In sp hybridisation, carbon bonds to two other atoms by hybridising the 2s and only one of the 2p orbitals to produce two sp orbitals arranged at 180º to one another. The remaining two 2p prbitals can overlap with suitable orbitals on adjacent atoms to produce pi systems. Examples include ethyne, the nitrogen molecule, hydrogen cyanide, and any other triple bond systems.

#### Other forms of hybridisation

Although not specifically required for the IB diploma, it should be mentioned that this hybridisation process can be extended to allow atoms to bond with more than four other atoms (octet expansion). In this case the hybridisation invariably involves one or more of the 'd' orbitals. Sulphur hexafluoride forms six attacments to the six fluorines and consequently needs six available orbitals. It gets these by promoting one electron from the 3s and 3px orbitals into two of the 3d orbitals. It can then hybridise the 3s, 3px, 3py, 3pz, and 3dxy, 3dxz orbitals into an octagonal arrangement each with one electron.

#### Summary

Atoms rearrange their atomic orbitals when bonding to produce orbitals with shapes more suitable for the bonding process. This is called hybridisation. It is performed by almost all atoms when bonding although carbon provided the easiest examples to show. It is easy to recognise the hybridisation used by simply observing the double or triple bonds.

Only single bonds = sp3 hybridisation

1 double bond = sp2 hybridisation

1 triple bond =sp hybridisation

Hybridisation animation

14.2.3: Identify and explain the relationships between Lewis structures, molecular shapes and types of hybridization (sp, sp2 and sp3).
Students should consider examples from inorganic as well as organic chemistry.

#### Lewis structures

These are diagrams (dot - cross drawings) that show all of the valence electrons around the atoms in a molecule. Although the "rules " for dcrawing these structures are not hard and fast, they do provide a useful guideline for arriving at the 'correct ' structure.

Hydrogen can only share one pair of electrons (1 covalent bond)

Oxygen usually forms two covalent bonds, however it may share two pairs evenly OR accept a lone pair to form a dative coordinate bond (the same as a covalent bond except that both the electrons are provided by one atom)

The method for arriving at the Lewis structure is:

1. Count the number of valence electrons on the central atom (e.g. Phosphorus =5 from group 5)
2. Add one electron from each attached atom for each bond.
3. Count up the total number of electrons
4. Subtract the electrons used in forming the bonds
5. The number remaining will be the 'extra' electrons on the central atom

 Phosphorus Trichloride Phosphorus Trichloride animation Lewis structure The central atom is phosphorus therefore it has 5 valence electrons There are three chlorine atoms each providing one electron to bond = 3 electrons Total number of electrons = 8 Number of electrons used in bonding three chlorines = 3 x 2 = 6 This leaves 2 electrons unused (1 pair) that must go onto the phosphorus. Shape The central phosphorus then has four regions of electron density (three bonds and one lone pair) Electronically these four regions adopt a tetrahedral orientation but only three pairs are used for the bonding. The molecule is therefore pyramidal (with one invisible lone pair forming the apex of the electronic tetrahedron) animation needs chime plug in to be visualised

Lewis structures become difficult when the central atoms donates electron pairs. The only useful advice here is that when oxygen is attached to the central atom it can accept lone pairs from the central atom to make up its own octet (set of eight outer electrons) and that you should look out for this.

Examples are the oxides of phosphorus, sulphur and chlorine as well as their oxy-ions (phosphate, sulphate, sulphite, chlorate etc.)

 Sulphur dioxide SO2 Sulphur Dioxide animation The central sulphur provides 6 electrons Each oxygen can accept one pair of donated electrons from the sulphur making four electrons used However this gives the sulphur only six electrons in total in the outer shell. It is therefore appropriate to share another pair from one of the oxygens making an effective double bond and giving sulphur a complete octet. This picture suggests that the bonding between the sulphur and each of the oxygens is different. Bond measurements show us that this is not the case - this can be explained by the concept of resonance. This leaves the central sulphur with a lone pair It then has three regions of electron density and is electronically trigonal Only two of the regions are used in bonding therefore the molecule is angular (bent) SO2 animation needs chime plug in to be visualised

It should be clear from the above two examples that the hybridisation is determined by the number of molecular orbitals attached to the central atom. In the case of PCl3 it can clearly be seen that there are four regions of electron density and so the hybridisation adopted is sp3 (tetrahedral)

In the case of the SO2 there are only three regions of electron density and therefore sp2 hybridisation is adopted. This also leaves the remaining p orbital able to form a pi system with either of the oxygens and can then resonate between pi bonding with one oxygen and the other.

#### Summary

The relationship between the Lewis arrangement of electrons, the hybridisation, the resonance and the molecular shape supports the theories of bonding by linear combination of atomic orbitals and molecular orbital theory.

• The Lewis structure allows us to map out a probable arrangement of electrons around the atoms in the molecule.
• This in turn shows us the number of regions of electron density around the central atom which can be used to ascertain the hybridisation.
• From the hybridisation and the valence shell electron pair repulsion theory, we can predict the molecular shape (and the electronic shape from which it derives).
• The different valid Lewis structures that can be drawn give an idea about the possible resonances within the molecule.

#### Molecules and ions that should be studied in depth

 Molecule formula shape Nitrogen dioxide NO2 Sulphur dioxide SO2 Sulphur trioxide SO3 Phosphorus trichloride PCl3 Phosphine PH3 Ammonia NH3 Sulphur oxychloride SOCl2 Water H2O Carbon monoxide CO Carbon dioxide CO2 Xenon tetrafluoride XeF4 Phosphorus pentafluoride PF5 Xenon hexafluoride XeF6 Sulphur hexafluoride SF6 Hydrogen sulphide H2S Methane CH4 Ethane C2H4 Ethyne C2H2 Hydrogen cyanide HCN
 Ion formula shape Nitrate NO3- Nitrite NO2- Carbonate CO32- Phosphate PO43- Sulphate SO42- Sulphite SO32- Chlorate ClO3- Perchlorate ClO4- Chlorite ClO2- Cyanide CN-