Lattice Energy Remember, IE and EA are for adding/removing an electron to/from an atom in the gaseous state. Ionic compounds are usually solids. The release of energy on forming the solid, called the lattice energy is the driving force for the formation of ionic compounds. Because of high lattice energies, ionic solids tend to be hard and have high melting points. Ionic compounds are insulators in the solid state, because electrons are localized on the ions, but conduct when molten or in solution, due to flow of ions (not electrons). Lattice energies can be calculated using Hess’s law, via a Born-Haber Cycle.

Figure 9.6 The Born-Haber cycle for lithium fluoride

Calculating Lattice Energy Step 1: Convert elements to atoms in the gas state e.g. for Li, Li (s)  Li (g)  H 1 =  H atomization for F, 1/2 F 2 (g)  F (g)  H 2 = 1/2 (Bond Energy) Step 2: Electron transfer to form (isolated) ions Li (g)  Li + (g) + e –  H 3 = IE 1 F (g) + e –  F – (g)  H 4 = EA 1 Step 3: Ions come together to form solid Li + (g) + F – (g)  LiF (s)  H 5 = Lattice Energy Overall: Li (s) + 1/2 F 2 (g)  LiF (s)  H =  H f =  (  H 1–5 ) Lattice Energy =  H f – (  H 1 +  H 2 +  H 3 +  H 4 )

Periodic Trends in Lattice Energy Coulomb’s Law charge A X charge B electrostatic force  distance 2 (since energy = force X distance) charge A X charge B or, electrostatic energy  distance So, lattice energy increases, as ionic radius decreases (distance between charges is smaller). Lattice energy also increases as charge increases.

Figure 9.7 Trends in lattice energy

I. Bonding Theory A covalent H-H bond is the net result of attractive and repulsive electrostatic forces. When bringing together two atoms that are initially very far apart. Three types of interaction occur: (1) The nucleus-electron attractions (blue arrows) are greater than the (2) nucleus-nucleus and (3) electron-electron repulsions (red arrows), resulting in a net attractive force that holds the atoms together to form an H 2 molecule.

If the hydrogen atoms are too far apart, attractions are weak and no bonding occurs. A zero of energy when two H atoms are separated by great distances. A drop in potential energy (net attraction) as the two atoms approach each other. When the atoms are optimally separated, the energy is at a minimum. A minimum in potential energy at particular internuclear distance (74pm) corresponding to the stable H 2 molecule and the potential energy corresponds to the negative of the bond dissociation energy. If the atoms are too close, strong repulsions occur. A increase in potential energy as the atoms approach more closely. A graph of potential energy versus internuclear distance for the H 2 molecule.

II. Valence-Bond Theory 1)bond formation by overlapping orbitals: A description of covalent bond formation in terms of atomic orbital overlap is called the valence bond theory. It gives a localized electron model of bonding: core electrons and lone-pair valence electrons retain the same orbital locations as in the separated atoms, and the charge density of the bonding electrons is concentrated in the region of orbital overlap. 2) hybridization of atomic orbitals: How do a carbon with a s orbital and three p orbitals combined with four hydrogen (s orbitals) form four bonds and all four bonds are found to be  ?

Overlap of two half-filled orbitals leads to the formation of a covalent bond. 1s   1s-1s overlap gives a H – H single bond

F  2s2s2p2p  1s1s H The 1s-2p overlap gives a H – F single bond

Non-bonding electrons F  2s2s2p2p  1s1s H

F 2s2s2p2p  The 2p-2p overlap gives a F – F single bond F  2s2s2p2p 

F 2s2s2p2p  Non-bonding electrons F  2s2s2p2p  Each F atom has three pairs of non-bonding electrons.

Q.23 Identify the non-bonding electrons in O 2 molecules. Two 2p-2p overlaps give a O=O double bond O  2s2s2p2p  O  2s2s2p2p 

Q.23 Identify the non-bonding electrons in O 2 molecules. Each O atom has two pairs of non-bonding electrons. O  2s2s2p2p  O  2s2s2p2p  Non-bonding electrons

Overlap of an empty orbital with a fully-filled orbital leads to the formation of a co-ordinate covalent bond or dative bond

Represented by an arrow  pointing from the electron pair donor to the electron pair acceptor.

F 3 B NH 3

Hybridization In 1931, Linus Pauling proposed that the wave functions for the s and p atomic orbitals can be mathematically combined to form a new set of equivalent wave functions called hybrid orbitals. The mathematical process of replacing pure atomic orbitals with reformulated atomic orbitals for bonded atoms is called hybridization. In a hybridization scheme, the number of hybrid orbitals equals to the total number of atomic orbitals that are combined. The symbols identify the numbers and kinds orbitals involved.

(a) NH 4 + By Lewis model, the structure is  4 single bonds are formed, one of them is a dative bond.

By VB Theory, Three 2p-1s(half-filled) overlaps lead to the formation of three N – H single bonds. N  2s2s2p2p  3H  H+H+ 1s1s1s1s

By VB Theory, One 2s(fully-filled)-1s(vacant) overlap leads to the formation of one N  H dative bond. N  2s2s2p2p  3H  H+H+ 1s1s1s1s

(b) HCN By Lewis model, the structure is H-C  N  one H-C single bond and one C  N triple bond.

By VB Theory, C  Only 2 single bonds can be formed.  Promotion of a 2s electron to a 2p orbital.  2s2s2p2p C*  2s2s2p2p 

 The overlap of one orbital (?) of C* with an 1s orbital of H gives the C-H single bond.  Overlaps of three orbitals (???) of C* with three 2p orbitals of N give the C  N triple bond. C*  2s2s2p2p  N  2s2s2p2p  H  1s1s

 The 2s electrons on N are non-bonding electrons.  The energy released by forming a stronger triple bond outweighs the energy required for promoting an electron from a 2s orbital to a 2p orbital. C*  2s2s2p2p  N  2s2s2p2p  H  1s1s

(c) SO 2 By Lewis model, the three possible structures are O  S=O, O=S  O, O=S=O Most stable no separation of charge.

By VB Theory,  Only two single bonds can be formed.  One 3p electron has to be promoted to a 3d orbital.  Expansion of Octet. S  3s3p 

By VB Theory, S  3s3p  S*  3s3p  3d octet expansion

 Overlaps of two half-filled orbitals (??) of S* with two half-filled 2p orbitals of an oxygen atom give a S=O double bond. A total of two S=O bonds are formed with two O atoms 2O  2s2s2p2p  S*  3s3p  3d

Non-bonding electrons : S* 3s 2 ; O 2s 2 and 2p 2 2O  2s2s2p2p  S*  3s3p  3d

The energy released by forming of two stronger double bonds outweighs the energy required for promoting an electron from a 3p orbital to a 3d orbital. S  3s3p  S*  3s3p  3d octet expansion

The Concept of Resonance According to VB theory, the two less stable structures of SO 2, O  S=O and O=S  O do ‘exist’. Each of these structures contributes in certain extent to the real structure of SO 2.

If represents the wave function of the real structure of SO 2 molecules, then where are the wave functions of the three possible structures and a > b = c > 0

In other words, the real structure of SO 2 is the resonance hydrid of the three possible structures. O=S=O  O  S=O  O=S  O More contributionLess contribution

Q.24 S  3s3p  O  2s2p  O*  2s2p A S=O double bond is formed by 3p(half-filled)-2p(half-filled) overlaps between S and O. O=S  O

Q.24 S  3s3p  O  2s2p  O*  2s2p O=S  O A O  S dative bond is formed by 3p(fully-filled)-2p(empty) overlap between S and O*

Q.24 S  3s3p  O  2s2p  O*  2s2p O=S  O Formation of dative bond is not favourable because the two unpaired 2p electrons in O are forced to pair up to give O*

(d) SF 2, SF 4, SF 6 Most stable Lewis Structure SF 6 SF 4 SF 2 Molecule F-S-F

By VB Theory, Only two S-F single bonds can be formed by 3p-2p overlaps between one S atom and two F atoms  SF 2 is formed. S  3s3p  F  2s2p  F-S-F

By VB Theory, To form four S-F single bonds in SF 4, a 3p electron in S has to be promoted to a 3d orbital. S  3s3p  F  2s2p  S*  3s3p  3d

By VB Theory, To form six S-F single bonds in SF 6, a 3s electron in S* has to be promoted to a 3d orbital. S  3s3p  F  2s2p  S**  3s3p  3d 

By VB Theory, S  3s3p  S**  3s3p  3d  The energy released by forming more single bonds outweighs the energy required for promoting 3s and 3p electrons to 3d orbitals.

Q.25 Most stable Lewis Structure XeF 6 XeF 4 XeF 2 Molecule F-Xe-F

By VB Theory, To form two Xe-F bonds in XeF 2, a 5p electron in Xe has to be promoted to a 5d orbital. Xe  5s5p  F 2s2p  Xe*  5s5p  5d

By VB Theory, To form four Xe-F bonds in XeF 4, a 5p electron in Xe* has to be promoted to a 5d orbital. Xe*  5s5p  5d Xe**  5s5p  5d 

By VB Theory, To form six Xe-F bonds in XeF 6, a 5p electron in Xe** has to be promoted to a 5d orbital. Xe**  5s5p  5d  Xe***  5s5p  5d 

By VB Theory, Xe**  5s5p  5d  Xe***  5s5p  5d  The energy released by forming more single bonds outweighs the energy required for promoting 5p electrons to 5d orbitals.

E.g. sp 3 signifies one s and three p orbitals are combined. Mixing one s orbital with three p orbitals yields four equivalent sp 3 hybrid orbitals.

The formation of four sp 3 hybrid orbitals by combination of an atomic s orbital with three atomic p orbitals. Each sp 3 hybrid orbital has two lobes, one of which is larger than the other. The four large lobes are oriented toward the corners of a tetrahedron at angles of 109.5°.

The bonding in methane. Each of the four C-H bonds results from head-on (s) overlap of a singly occupied carbon sp 3 hybrid orbital with a singly occupied hydrogen 1s orbital. Sigma bonds are formed by head-to-head overlap between the hydrogen s orbital and a singly occupied sp 3 hybrid orbital of carbon.

sp 2 hybridization E.g. the molecular geometry is trigonal planar with bond angle = 120°. To explain its geometry, we can use the following rational. sp 2 signifies one s and two p orbitals are combined.

sp hybridization Now consider BeCl 2 which has linear molecular geometry determined experimentally. In hybridization scheme that best describes this compound is that The combination of one s and one p orbital gives two sp hybrid orbitals oriented 180° apart. Two unhybridized p orbitals remain and are oriented at 90° angles to the sp hybrids.

sp 3 d hybrid Orbitals To described hybridization scheme to correspond to the 5- and 6- electron-group geometries of VSEPR theory, we need to go beyond s and p orbitals and traditionally this meant including d orbitals. We can achieve the five half-filled orbitals and trigonal-bipyramidal molecular geometry through the hybridization of one s, three p and one d orbitals of valence shell into five sp 3 d hybrid orbitals.

sp 3 d 2 hybrid Orbitals In the same way, we can achieve the six half-filled orbitals and octahedral geometry through the hybridization of one s, three p and two d orbitals of valence shell into six sp 3 d 2 hybrid orbitals.

Molecular Orbital Theory The goal of molecular orbital theory is to describe molecules in a similar way to how we describe atoms, that is, in terms of orbitals, orbital diagrams, and electron configurations.

Forming a Covalent Bond Molecules can form bonds by sharing electron –Two shared electrons form a single bond Atoms can share one, two or three pairs of electrons –forming single, double and triple bonds Other types of bonds are formed by charged atoms (ionic) and metal atoms (metallic).

Atomic and Molecular Orbitals (cont’d) Orbital Mixing –When atoms share electrons to form a bond, their atomic orbitals mix to form molecular bonds. In order for these orbitals to mix they must: Have similar energy levels. Overlap well. Be close together. This is and example of orbital mixing. The two atoms share one electron each from there outer shell. In this case both 1s orbitals overlap and share their valence electrons.

Energy Diagram of Sigma Bond Formation by Orbital Overlap

Examples of Sigma Bond Formation

Atomic and Molecular Orbitals In atoms, electrons occupy atomic orbitals, but in molecules they occupy similar molecular orbitals which surround the molecule. The two 1s atomic orbitals combine to form two molecular orbitals, one bonding (  ) and one antibonding (  *). This is an illustration of molecular orbital diagram of H 2. Notice that one electron from each atom is being “shared” to form a covalent bond. This is an example of orbital mixing.

Molecular Orbital Theory Each line in the diagram represents an orbital. The molecular orbital volume encompasses the whole molecule. The electrons fill the molecular orbitals of molecules like electrons fill atomic orbitals in atoms

Molecular Orbital Theory Electrons go into the lowest energy orbital available to form lowest potential energy for the molecule. The maximum number of electrons in each molecular orbital is two. (Pauli exclusion principle) One electron goes into orbitals of equal energy, with parallel spin, before they begin to pair up. (Hund's Rule.)

Molecular Orbital Diagram (H 2 )

MO Diagram for O 2

Molecular Orbital Diagram (HF)

Molecular Orbital Diagram (CH 4 ) So far, we have only look at molecules with two atoms. MO diagrams can also be used for larger molecules.

Molecular Orbital Diagram (H 2 O)

Conclusions Bonding electrons are localized between atoms (or are lone pairs). Atomic orbitals overlap to form bonds. Two electrons of opposite spin can occupy the overlapping orbitals. Bonding increases the probability of finding electrons in between atoms. It is also possible for atoms to form ionic and metallic bonds.