Covalent Bonding

London-Heitler Model of the Covalent Bond How does sharing a pair of electrons between two hydrogen atoms lead to a lower overall energy state?

Uses the mathematics of quantum mechanics to study the hydrogen molecule, H2 Begin with two hydrogen atoms infinitely faraway from each other - no interaction- zero energy As the two atoms approach each other, two sets of forces develop- attractive forces between the electron of one atom and the nucleus of the other and repulsive forces, nucleus to nucleus and electron to electron

Fig. 9.12

Both the attractive forces and the repulsive forces increase as the two atoms approach each other Initially, the attractive forces increase more rapidly than the repulsive forces leading to an overall lower energy state- more stable However, at a certain internuclear distance, the repulsive forces begin to increase faster than the attractive forces as the atoms approach each other

This creates an energy minimum, maximizing the attractive forces and minimizing the repulsive forces, at a certain internuclear distance- if the two nuclei move closer together or farther away from each other they move to higher energy states The model predicts a certain internuclear distance in the hydrogen bond (0.074 nm) and a certain bond energy (-432 kJ/mol) both of which are observed in real hydrogen molecules

Figure 9.11: Potential-energy curve for H2.

Figure 9.10: The electron probability distribution for the H2 molecule.

Covalent Bonding in Hydrogen, H2 Fig. 9.11

We say the orbitals overlap in space (1s-1s); both electrons are said to be in both orbitals at the same time or form one bonding orbital

While the London-Heitler model is the best model we have for the covalent bond applying it to more complicated molecules isn’t practical. We will use the Lewis model (G. N. Lewis) of the covalent bond that works with the concept of valence electrons- the number of electrons in the outermost energy level of an atom

Lewis Electron-Dot Symbols for Elements in Periods 2 & 3 Fig. 9.3

Octet Rule In the Lewis model atoms share valence electrons so as to get eight valence electrons Problem: Hydrogen only shares to get two valence electrons (duet rule) Atoms can share one pair of electrons, single bond, two pairs of electrons, double bonds, or three pairs of electrons, triple bonds

Formal Charge -Used to evaluate Lewis structures and look at how charge is distributed in a Lewis structure -Formal Charge = Valance electrons-(unshared electrons + 1/2 shared electrons)

Exceptions to the Octet Rule Electron deficient species (IA, IIA, IIIA elements) Free Radicals (odd electron species) Expanded Octets (more than 8 valence electrons)

Electron Deficient Species Elements in groups IA, IIA and IIIA, due to their low electronegativity, usually only form as many bonds as they have valence electrons IA: LiCH3 IIA: BeF2 IIIA: BF3

Free Radicals Species with an odd number of electrons Ex: NO, NO2 The odd electron (free radical electron) should end up on the least electronegative atom Impossible to give the atom with the free radical an octet but be sure to give it seven electrons

Expanded Octets Species with 10, 12, 14 or more valence electrons Always a central atom surrounded by single bonds or unshared pairs Central atom must be from the third period or below on the periodic table- requires d orbitals to form the bonds Ex. PCl5, SF6, IF7

Lewis Structures for Octet Rule Exceptions .. .. .. B Cl .. .. .. .. F .. .. .. .. F Cl .. .. F Each chlorine atom has 8 electrons associated. Boron has only 6! Each fluorine atom has 8 electrons associated. Chlorine has 10 electrons! . .. .. .. .. .. .. N .. .. Cl Be Cl .. .. .. O O Each chlorine atom has 8 electrons associated. The beryllium has only 4 electrons. NO2 is an odd electron atom. The nitrogen has 7 electrons.

Resonance When no single Lewis structure describes what is known about the molecule Ex. NO3-1

-None of the three structures accurately describes the ion -The real nitrate ion is best thought of as an average of its resonance forms -The actual bond energy is equal to a bond and a third, the actual bond length is a bond and a third -The extra pair of electrons are delocalized over the whole system

Nonpolar Bonds In the molecules H2 and F2 the two electrons are shared equally between the two nuclei- nonpolar covalent bond

Polar Bonds Unequal sharing of electrons Measured by DEN, difference in electronegativity Electron density is shifted towards the more electronegative atom and away from the less electronegative atom

Fig. 9.18

The Relation of Bond Order, Bond Length and Bond Energy Bond Bond Order Average Bond Average Bond Length (pm) Energy (kJ/mol) C O 1 143 358 C O 2 123 745 C O 3 113 1070 C C 1 154 347 C C 2 134 614 C C 3 121 839 N N 1 146 160 N N 2 122 418 N N 3 110 945 Table 9.4 (p. 344)

Fig. 10.2

Using bond energies to calculate H°rxn of methane Fig. 10.3

Molecular Geometry

Molecular Geometry- three dimensional shape of a molecule Geometry of diatomic molecules- 2 points define a straight line so the molecule is linear; no bond angle Ex. H2, F2, HF

VSEPR Theory Valence Shell Electron Pair Repulsion Theory- electron pairs around a central atom want to be as far away from each other as possible Used to predict the shape of molecules

Species with just single bonds Two single bonds, BeF2 (180o bond angle, linear geometry) Three single bonds, BF3 (120o bond angle, planar geometry) Four single bonds, CH4 (109o bond angle, tetrahedral geometry) Five single bonds, PCl5 (120o, 90o bond angle, trigonal bipyramid geometry Six single bonds, SF6 (90o bond angle, octahedral geometry)

Balloon Analogy for the Mutual Repulsion of Electron Groups Two Three Four Five Six Number of Electron Groups Fig. 10.4

Fig. 10.5

Species with single bonds and unshared pairs Three single bonds and one unshared pair, NH3 (109o bond angle, pyramidal geometry) Two single bonds and two unshared bonds, H2O (109o bond angle, bent geometry) Two single bonds and one unshared pair, PbCl2 (120o bond angle, bent geometry)

Species with single bonds and unshared pairs- expanded octets Four single bonds and one unshared pair, SF4 (120o, 90o bond angle, distorted tetrahedral geometry) Three single bonds and two unshared bonds, ClF3 (90o bond angle, T-shaped geometry) Two single bonds, three unshared pairs, XeF2 (180o bond angle, linear geometry) Five single bonds, one unshared pair, BrF5 (90o bond angle, square pyramid geometry) Four single bonds, two unshared pairs, XeF4 (90o bond angles, square pyramid)

Fig. 10.6

The Two Molecular Shapes of the Trigonal Planar Electron-Group Arrangement Fig. 10.7

The Three Molecular Shapes of the Tetrahedral Electron-Group Arrangement Fig. 10.8

Bipyramidal Electron- Group Arrangement The Four Molecular Shapes of the Trigonal Bipyramidal Electron- Group Arrangement Fig. 10.10

The Three Molecular Shapes of the Octahedral Electron-Group Arrangement Fig 10.11

In VSEPR, double and triple bonds are equal to a single bond Ex. CO2 (180o bond angle, linear geometry) HCN (180o bond angle, linear geometry) SO2 (120o bond angle, bent geometry)

Polarity In Molecules A polar molecule is any molecule that orients itself in an electric field For a molecule to be polar it must have polarity in the bonds and a favorable geometry

Fig. 10.14

- - - - .. .. .. .. .. .. Polarity of CO2 and H2O + O O C O H H + + Water - H2O Carbon Dioxide - CO2 - - - + - .. .. .. .. O O C O .. .. H H + + A non- polar molecule A Polar molecule The bonds are polar, but the molecule is symmetrical, so that the molecule overall is non-polar. The bonds are polar, and the molecule is non-symmetrical.

Lewis structures say nothing about the energy and orbitals of bonding electrons Valence Bond Theory (Atomic Orbital Theory)- covalent bonds consist of a pair of electrons, of opposite spin, within an atomic orbital Maintains the orbital structure of isolated, gaseous atoms Direct overlap of atomic orbitals- sigma (s) bonds

Fig. 11.1

Problems occur with compounds: BeCl2, BF3, CH4 Two solutions: Scrap atomic orbitals and build up molecular orbitals unique to that molecule- Molecular Orbital Theory Modify atomic orbitals to fit what is known about the molecule experimentally use what is called hybridization- mixing or averaging atomic orbitals to give equivalent bonding orbitals Hybrid orbitals can only form sigma bonds or hold unshared pairs

The sp Hybrid Orbitals in Gaseous BeCl2 Fig. 11.2 A&B

Fig. 11.2 C&D

Fig. 11.3

Fig. 11.4

The sp3 Hybrid Orbitals in NH3 and H2O Fig. 11.5

The sp3d Hybrid Orbitals in PCl5 Fig. 11.6

The sp3d2 Hybrid Orbitals in SF6 Sulfur Hexafluoride -- SF6 Fig. 11.7

Use bond angle to predict hybridization 109o bond angle sp3 hybridization 120o bond angle sp2 hybridization 180o bond angle sp hybridization For expanded octets just add up the number of valence electrons 10 valence electrons sp3d 12 valence electrons sp3d2

Multiple Bonds, Pi (p) Bonding The second bond of a double bond and the the second and third bond of a triple bond are formed by p orbitals overlapping sideways to form a pi (p) bond Every single bond is a s bond One double bond is a p bond and a s bond One triple bond is two p bonds and a s bond Ex. Ethene, C2H4 and ethyne, C2H2

Fig. 11.9

Fig. 11.10

Fig. 11.11

Restricted Rotation of -Bonded Molecules A) Cis - 1,2 dichloroethylene B) trans - 1,2 dichloroethylene Fig. 11.12