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George Mason University General Chemistry 211 Chapter 11 Theories of Covalent Bonding

George Mason University General Chemistry 211 Chapter 11 Theories of Covalent Bonding Acknowledgements Course Text: Chemistry: the Molecular Nature of Matter and Change, 6 th edition, 2011, Martin S. Silberberg, McGraw-Hill

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George Mason University General Chemistry 211 Chapter 11 Theories of Covalent Bonding

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  1. George Mason University • General Chemistry 211 • Chapter 11 • Theories of Covalent Bonding • Acknowledgements • Course Text: Chemistry: the Molecular Nature of Matter and Change, 6th edition, 2011, Martin S. Silberberg, McGraw-Hill • The Chemistry 211/212 General Chemistry courses taught at George Mason are intended for those students enrolled in a science /engineering oriented curricula, with particular emphasis on chemistry, biochemistry, and biology The material on these slides is taken primarily from the course text but the instructor has modified, condensed, or otherwise reorganized selected material.Additional material from other sources may also be included. Interpretation of course material to clarify concepts and solutions to problems is the sole responsibility of this instructor.

  2. Molecular Structure - Summary • Atomic theory • Molecular Weight (MW) – Neutrons + Protons • Mass, Atomic Mass units, Law of Definite Proportions • Moles, Chemical Equations, Stoichiometry • Gas Laws, Thermodynamics (reaction energy) • Quantum Theory – waves vs particles, electronic structure of atoms energy absorption, emission electronic energy levels quantum numbers, electron shells • Periodicity – orbital diagrams Pauli exclusion principle Aufbau Principle for populating subshells

  3. Molecular Structure - Summary • Bonding – Valence electrons Periodic table Ionic Bonds Covalent Bonds Electronic Configuration Lattice Energy, Born-Haber cycle, Bond energy • Geometry – Lewis diagrams Resonance, Octet Rule Formal Charge (valence electrons – unbonded electrons – ½ bonded electrons) • Valence-Shell Electron Pair Repulsion Model (VSEPR) Molecular Notation – AXaEb Xa – Bonding pairs Eb – Nonbonding pairs sum(a + b) determines geometry (linear, tetrahedral) if “b” > 0 molecule may form dipole (polar)

  4. Bond Theories • Quantum Numbers & Electron Configuration • In Chapters 8 & 9 an electron was defined as a unique set of 4 quantum numbers • The first 3 quantum numbers (n, l, ml) defined an atomic orbital, which could contain a maximum of 2 electrons (+1/2 & -1/2 spin (ms)) • Each orbital (s, p, d) has a unique shape: spherical (s), dumbell(p), pear shaped(d) • All of the orbitals defined by a unique set ofn, l, ml quantum numbers, have the same energy

  5. “p” orbitals “s” orbital “d” orbitals

  6. Bonding Theories • Valence Bond (VB) theory is one of two basic theories, along with Molecular Orbital (MO) theory, that were developed to use the methods of quantum mechanics to explain chemical bonding • Valence Bond Theory is a chemical bonding theory that explains the bonding between two atoms caused by the overlap of the half-filled atomic orbital from each atom • It focuses on how the atomic orbitals of the dissociated atoms combine to give individual chemical bonds when a molecule is formed • The two atoms from the bonding atoms share each other's unpaired electron to form a filled orbital to form a hybrid orbital and bond together.

  7. Bonding Theories • Molecular Orbital (MO) theory is a method for determining molecular structure in which electrons are not assigned to individual bonds between atoms, but are treated as moving under the influence of the nuclei in the whole molecule • In this theory, each molecule has a set of molecular orbitals, in which it is assumed that the molecular orbital wave function ψj may be written as a simple weighted sum of the n constituent atomic orbitals • A given Atomic Orbital (s, p, d) takes the form of a subset of “Molecular Orbitals  bonding &  antibonding bonds and  bonding &  antibonding bonds • Each has its own energy • Molecular Orbital orbitals cover the whole molecule

  8. Valence Bond Theory • Valence Bond Theory is an attempt to explain the Covalent bond from a Quantum Mechanical view • All orbitals of the same type (s, p, d, f) have the same energy • According to this theory, a bond forms when two atomic orbitals (s/s s/p p/p) “overlap” • The space formed by the overlapping orbitals has a capacity for two electrons that have opposite spins, +1/2 & -1/2 (exclusion principle) Note: Each orbital forming the bond has at least one unfilled slot to accommodate the electron being shared from the other bonding orbital • The bond strength depends on the attraction of the nuclei for the shared electrons

  9. Valence Bond Theory • Valence bond theory (con’t) • The greater the orbital overlap, the stronger (more stable) the bond • The extent of the overlap depends on the shapes and directions of the orbitals • An s orbital is spherical, but p and d orbitals have more electron density in one direction than in another • Whenever possible, a bond involving p or d electrons will be oriented in the direction that maximizes overlap

  10. Valence Bond Theory Hydrogen, H2 1s1 Hydrogen Fluoride, HF [He]2s22p5 To maximize overlap, half-filled H 1s and F 2p orbitals overlap along the long axis of the 2p orbital Fluorine, F2 [He] 2s22p5 In F2, the half-filled 2 px orbital on one F atom points end to end toward the half-filled 2px of the other F to maximize overlap

  11. Hybrid Orbitals • One might expect the number of bonds formed by an atom would equal its unpaired electrons • Chlorine, for example, generally forms one bond as it has one unpaired electron - 1s22s22p5 • Oxygen, with two unpaired electrons, usually forms two bonds - 1s22s22p4 • However, Carbon, with only two unpaired electrons, generally forms four (4) bonds C (1s22s22p2) [He] 2s22p2 The four bonds come from the 2 (2s) paired electrons and the 2 (2p) unpaired electrons For example, Methane, CH4, is well known The uniqueness of these bonds is described next

  12. Hybrid Orbitals • Linus Pauling proposed that the valence atomic orbitals in a molecule are different from those of the isolated atoms forming the molecule • Quantum mechanical computations show that if specific combinations of orbitals are mixed mathematically, “new” atomic orbitals are obtained • The spatial orientation of these new orbitals lead to more “stable” bonds and are consistent with observed molecular shapes • These new orbitals are called: “Hybrid Orbitals”

  13. Hybrid Orbitals • Types of Hybrid Orbitals • Each type has a unique geometric arrangement • The hybrid type is derived from the number of s, p, d atomic orbitals used to form the Hybrid

  14. sp Hybrid Orbitals • SP Hybridization • 2 electron groups surround central atom • Linear shape, 180o apart • VB theory proposes the mixing of two nonequivalent orbitals, one “s” and one “p”, to form two equivalent “sp” hybrid orbitals • Orientation of hybrid orbitals extend electron density in the bonding direction • Minimizes repulsions between electrons • Both shape and orientation maximize overlap between the atoms

  15. “sp” Hybrid Orbitals hybrid orbitals Ex: BeCl2 The Be-Cl bonds in BeCl2 are neither spherical (s orbitals) nor dumbell (p orbitals) The Be-Cl bonds have a hybrid shape In the Beryllium atom the 2s orbital and one of the 2p orbitals mix to form 2 sp hybrid orbitals Each Be Hybrid sp orbital overlaps a Chlorine 3p orbital in BeCl2 Beryllium Hybrid Orbital Diagram orbital box diagrams

  16. “sp2” Hybridization • sp2 - Trigonal Planar geometry (Central atom bonded to three ligands) • The three bonds have equivalent hybridized shapes • The sp2 hybridized orbitals are formed from: 1 “s” orbital and 2 “p” orbitals Note: Of the 4 orbitals available (1 s & 3 p) only the s orbital and 2 of the p orbitals are used to form hybrid orbitals Note: Unlike electron configuration notation, hybrid orbital notation uses superscripts for the number of atomic orbitals of a given type that are mixed, NOTfor the number of electrons in the orbital, thus, sp2 (3 orbitals), sp3 (4 orbitals), sp3d (5 orbitals)

  17. “sp2” Hybridization Hybrid Orbital Diagram BF3 The 3 B-F bonds are neither spherical nor dumbell shaped They are all of identical shape In Boron, the “2s” orbital and two of the “2p” orbitals mix to form 3 sp2 hybrid orbitals, each containing one the 3 total valence electrons Each of the Boron hybrid sp2 orbitals overlaps with a 2p orbital of a Fluorine atom Boron (B) 1s22p1 Forms 3 sp2 hybrid orbitals BF3

  18. sp3 Hybrid Orbitals • sp3 (4 bonds, thus, Tetrahedral geometry) • The sp3 hybridized orbitals are formed from: 1 “s” orbital and 3 “p” orbitals • Example” • Carbon is the basis for “Organic Chemistry” • Carbon is in group 4 of the Periodic Chart and has 4 valence electrons – 2s22p2 • The hybridization of these 4 electrons is critical in the formation of the many millions of organic compounds and as the basis of life as we know it • The following slides show 3 different forms of the electronic structure and explains why the hybridized form reflects the observed structure of organic compounds

  19. sp3 Hybrid Orbitals 2p 2p This structure implies different shapes and energies for the “s” and “p” bonds in carbon compounds. Observations indicate that all fours bonds are equivalent 2s 2s Energy 1s 1s C atom (ground state) C atom (promoted)

  20. sp3 Hybrid Orbitals • One bond on Carbon would form using the 2s orbital while the other three bonds would use 3 2p orbitals • This does not explain the fact that the four bonds in CH4appear to be identical • Valence bond theory assumes that the four available atomic orbitals (2s22p2) in carbon combine to make four equivalent “hybrid” orbitals

  21. Hybrid Orbitals • Hybrid orbitals are orbitals used to describe bonding that is obtained by taking combinations of atomic orbitals of an isolated atom • In the case of Carbon, one “s” orbital and three “p” orbitals, are combined to form 4sp3 hybrid orbitals • The carbon atom in a typical sp3 hybrid structure has 4 bonded pairs and zero unshared electrons, therefore, Tetrahedral structure AXaEb (a + b) 4 + 0 = AX4 • The four sp3 hybrid orbitals take the shape of a tetrahedron

  22. Hybridization of Carbon in CH4 2s 4 sp3 orbitals formed 2p sp3 sp3 C-H bonds Energy 1s 1s 1s C atom (ground state) C atom (hybridized state) C atom (in CH4)

  23. Spatial Arrangement ofsp3 Hybrid Orbitals Shape of sp3 hybrid orbital different than either s or p

  24. sp3d Hybrid Orbitals • sp3d (5 molecules, thus, Trigonal Bypyramidal geometry) • Molecules with central atoms from Period 3 or higher, can utilize “d” orbitals in the formation of hybrid orbitals • The sp3d hybridized orbitals are formed from: 1 “s” orbital, 3 “p” orbitals, 1 “d” orbital PCl5 AXaEb AX5E0 hybrid orbitals – 5 (sp3d) : : F : : : : F F : P : : : : F : F : : :

  25. sp3d Hybrid Orbitals Hybridized Orbital Diagram for PCl5 • 5 equivalent (hybrid) orbitals are required • The one 3s orbital, the 3 3p orbitals and one of the unused 3d orbitals of the Phosphorus atom mix to form the 5 sp3d hybrid orbitals • The remaining 4 empty 3d orbitals (unhybridized) are not used

  26. Diagrams of Hybrid Orbitals Showing their Spatial Arrangements

  27. Hybrid Orbitals • To obtain the bonding description of any atom in a molecule, you proceed as follows: • Write the Lewis electron-dot formulafor the molecule • From the Lewis formula, use the VSEPR theory to determine the arrangement of electron pairsaround the central atom, i.e., the geometry • From the geometric arrangement (AXaEb) of the electron pairs, obtain the hybridization type • Assignvalence electronsto the hybrid orbitals of this atom one at a time, pairing only when necessary • Form bonds to the central atom by overlapping singly occupied orbitals of other atoms with the singly occupied hybrid orbitals of the central atom

  28. Oxygen Atom Bonding in H2O 2s Energy 4 sp3 Hybridized Orbitals 2p sp3 sp3  H O H  lone pairs O-H bonds a + b 2 + 2 = 4 Tetrahedral AX2E2 bent Tetrahedral 1s 1s 1s OCentral Atom (ground state) O atom (hybridized state) O atom (in H2O)

  29. Practice Problem What hybrid orbitals of Sulfur are involved in the bonding in Sulfur Trioxide (SO3)? a. sp b. sp2 c. sp3 d. sp2d e. sp3d2 Ans: b A B C  D  O O     O   S S S       O O O O     O O       fcS = 6-0-1/2(12) fcS = 0 (preferred form) fcS = +3 fcS = +2 fcS = +1 O   Total Valence e- - 3 x 6 + 6 = 24 Bonded Pairs 3 x 2 = 6 Distribute e- about O atoms = 3 x 6 = 18 Unshared e- about S atom = 24 - 6 -18 = 0 Move e- pairs from O to S to form alternative forms of SO3 Compute formal charge on S; select form with least formal charge (D) AXaEb = 3 + 0 = 3 = AX3 (trigonal Planar) 3 O-S hybridized orbitals are required: one “s” orbital blended with 2 “p” orbitals (sp2) S   O O  

  30. Sulfur Trioxide – Hybrid Orbitals 3s 3p 3p 3p VSEPR – AX3 Trigonal Planar 3 sp2 orbitals required sp2 sp2 S atom (in SO3) S atom (ground state) S atom (hybridized state)

  31. Nitrogen Atom Bonding in NH3 2s Energy 4 sp3 orbitals required 2p sp3 sp3 lone pair N-H bonds a + b 3 + 1 = 4 Tetrahedral AX3E1 trigonal pyramidal  Tetrahedral H N H H 1s 1s 1s N atom (ground state) N atom (hybridized state) N atom (in NH3)

  32. Multiple Bonds • Types of Covalent Bond & Orbital Overlap • Orbitals can overlap two ways Side to Side or End to End • Two types of Covalent Bonds: Sigma Bonds (C-C) pi ()Bonds (C=C) • Multiple Bonds Ethane Tetrahedral (both carbons) Ethylene Trigonal planar(both carbons) Acetylene Linear (both carbons) 109.5o 120o 180o sp3 sp2 sp double bond acts as single electron group triple bond acts as single electron group

  33. Multiple Bonds • End-to-End overlap & Sigma Bonds • The C – C bond in Ethane (C2H6) involves overlap of 1 sp3 orbital from each carbon • Each of the six (6) C – H bonds involves the overlap of a Carbon sp3 and a Hydrogen 1 s orbital • All bonds involve overlap of one end of orbital with the end of the other orbital • The bond formed from end-to-end overlap is called a “sigma bond” (symbol - )

  34. Multiple Bonding • According to Valence Bond theory, one hybrid orbitalis needed for each bond (whether a single or multiple) and for each lone pair • For example, consider the molecule: Ethene (or Ethylene) H H C C H H

  35. Multiple Bonding • Each Carbon atom is bonded to three other atoms and no lone pairs, which indicates the need for three hybrid orbitals • This implies AX3E0 (Trigonal) sp2 hybridization 1 2s & 2 2p orbitals • The third 2p orbital is left unhybridizedand lies perpendicular to the plane of the trigonal sp2 hybrids • The following slide represents the sp2 hybridization of the Carbon atoms

  36. Multiple Bonding 2s 1s 1s (unhybridized) 2p 2p sp2 Energy C atom (ground state) C atom (hybridized)

  37. Multiple Bonding • Each carbon atom is sp2 hybridized • Each of the carbon atom’s 4 valence electrons fill ½ its 3 sp2 orbitals and its unhybridized 2p orbital, which lies perpendicular to sp2 plane • Two sp2 orbitals of each carbon form C – H sigma () bonds by overlapping the 1 s orbitals of the two H atoms • The 3rd sp2 orbital of one carbon forms a C – C () bond with the sp2 orbital of the other carbon with end-to-end overlap • A pi () bond is formed when the two unhybridized 2p orbitals (one from each carbon) overlap side-to-side, forming two regions of electron density, one above and one below the -bond axis • A double bond always consists of: one -bond and one bond

  38. Multiple Bonding • Two of the sp2 hybrid orbitals of each carbon overlap end-to-end with the 1s orbitals of the 2 hydrogen atoms forming a sigma bond • The remaining sp2 hybrid orbital, one on each carbon, overlap end-to-end to form a sigma bond

  39. Multiple Bonding • The remaining “unhybridized” 2p orbitals, one on each of the carbon atoms, overlap side-to-side, one on top of the sigma bond and one on the bottom of the sigma bond, forming a pbond • The carbon-carbon double bond is described as • ones bond and one bond The two electron pairs in a double bond act as a “single” electron group The electron pairs do not repulse each other because each electron pair occupies a distinct orbital, a specific region of electron density, thus repulsions are reduced

  40. Practice Problem Use valence bond theory to describe the bonding in CO2 Ans: 1. Draw Lewis structure 2. Determine hybridization 3. Draw diagram of hybrid atomic orbitals 4. Pair electrons (O) with hybrid C orbitals forming sigma bonds 5. Pair electrons (O) with unpaired p electrons in C atom to form pi () bonds Con’t on next slide

  41. Practice Problem (Con’t) Use valence bond theory to describe the bonding in CO2         O C O O C O O C O             2 bonding pairs 0 non-bonding pairs AXaEb = a + b = 2 + 0 = 2 (Linear) Hybridization – sp (2 hybrid orbitals required 2p p 2p C-O p (p)(unhybridized) 2s 1s 2s sp C-O sp () Hybridized Carbon Carbon atom 2s22p2 Oxygen atom 2s22p4

  42. Molecular Orbital (MO) Theory • Molecular Orbital (MO) theory is a theory of the electronic structure of molecules in terms of molecular orbitals, which may spread over several atoms or the entire molecule • MO theory explains the observed and computed energydifferences among orbitals, which Valence Bond theory does not • As atoms approach each other and their atomic orbitals overlap, molecular orbitals (MO) are formed • Note: Only outer (valence) Atomic orbitals (AO) interact enough to form Molecular Orbitals (MO) • Electron motions are complex making solutions to the Schroedinger equation approximations • Mathematically, the combination of atomic orbitals to form molecular orbitals involves adding or subtracting atomic wave functions

  43. Molecular Orbital (MO) Theory • Adding Wave Functions • Forms a “Bonding”() molecular orbital (MO) • Region of high electron density between nuclei • Electron charge between nuclei is dispersed over a larger area than in atomic orbitals (AO) • MO orbital energy is lower than in the AO because of the reduction in electron repulsion • Bonding MO is more stable than AO

  44. Molecular Orbital (MO) Theory • Subtracting Wave Functions • Forms a “Nonbonding”(*)molecular orbital • The node between the nuclei has most of the electron density outside the node with very little density (zero) between the nuclei • Thus, the electrons do not shield one nuclei from the other resulting in increased nucleus-nucleus repulsion • Therefore, the antibonding MO has a higher energy than the corresponding atom orbitals (AO) • When the antibonding orbital is occupied, the molecule is less stable than when the orbital is not occupied

  45. Molecular Orbital Theory • Example: The bonding of two Hydrogen atoms • s1s(bonding) molecular orbital is formed • s1s * (antibonding) molecular orbital is formed • The following slide illustrates the relative energies of the molecular orbitals (MO) compared to the original atomic orbitals (AO) • Because the energy of the two electrons in the bonding orbital is lower than the energy of the individual atoms, the molecule is stable

  46. Molecular Orbital Theory Atomic orbital Molecular Orbital Atomic orbital H atom H2 molecule H atom s1s* 1s 1s s1s More Stable

  47. Bonding and Antibonding Orbitals from 1s Hydrogen Atom Orbitals

  48. Bond Order • The term bond order refers to the number of electron pairs shared between two atoms • The bond order of a diatomic molecule is defined as one-half the difference between the number of electrons in bonding orbitals, nb, and the number of electrons in antibonding orbitals, na For example, try H2 and He2. Determine bond orders

  49. Bond OrderH2 H – 1s1 Bond Order BO = ½[(2) – (0)] = ½[2] = 1 Energy 1s* 1s 1s 1s

  50. Bond OrderHe2 He – 1s2 Bond Order BO = ½[(2) – (2)] = ½[0] = 0 Energy 1s* 1s 1s 1s

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