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Chapter 9 Molecular Geometry And Bonding Theories 熊同銘 [email protected] TMHsiung ©2016 Chapter 09 Slide 1 of 81 第二次會考 1051207 (ch5-8) 積極性補強教學: 週一、週二17:30-20:30 週三、週四17:30-21:30 海事大樓412教室 http://moodle.ntou.edu.tw/ TMHsiung ©2016 Chapter 09 Slide 2 of 81 Contents 1. 2. 3. 4. 5. 6. 7. 8. Molecular Shapes The VSEPR Model Molecular Shape and Molecular Polarity Covalent Bonding and Orbital Overlap Hybrid Orbitals Multiple Bonds Molecular Orbitals Period 2 Diatomic Molecules TMHsiung ©2016 Chapter 09 Slide 3 of 81 1. Molecular Shapes Lewis structures is two-dimensional arrangement: Molecular shapes three-dimensional arrangement: TMHsiung ©2016 Chapter 09 Slide 4 of 81 1. ***** The VSEPR Model Valence Shell Electron Pair Repulsion (VSEPR) theory: A theory that allows prediction of the shapes of molecules or polyatomic ion based on the idea that electron domain˗ either as lone pair (nonbonding pair) or as bonding pair ˗ repel one another. • Electron domain geometry: The geometrical arrangement of electron domain in a molecule. • Molecular geometry: The geometrical arrangement of atoms in a molecule. TMHsiung ©2016 Chapter 09 Slide 5 of 81 i) ii) ***** VSEPR theory proceeding Write a best Lewis structure Determine VSEPR notation: ABnEm: A: Central atoms B: Terminal atoms E: Lone pairs electrons H2O for example: TMHsiung ©2016 AB2E2 Chapter 09 Slide 6 of 81 iii) Determine the electron geometry ***** An electron group can be: - either single bond or a multiple bond - a (resonance) hybrid bond - a lone pairs of electron - a unpaired single-electron Repulsion force in general: LP vs. LP > LP vs. BP > BP vs. BP * Lone Pairs (LP), Bonding Pairs (BP) Angle for repulsion forces: 90° > 120° > 180° For central (interior) atom belong to third-period or higher element with VSEPR notation such as AB5, AB4E, AB3E2, AB6, AB5E, AB4E2 require an expanded octet such as 3d orbital. Multiple bond occupy more space than single bond TMHsiung ©2016 Chapter 09 Slide 7 of 81 ***** iv) Determine the molecular geometry Structures for the central atom without lone-pair electrons (ABn type), electron geometry and molecular geometry are identical. Structures for the central atom with lone-pair electrons (ABnEm type) type), electron geometry and molecular geometry are different. TMHsiung ©2016 Chapter 09 Slide 8 of 81 Determine the molecular geometry of NH3 TMHsiung ©2016 Chapter 09 ***** Slide 9 of 81 ***** * Count only electron groups around the central atom. Each of the following is considered one electron domain: a lone pair, a single bond, a double bond, a triple bond, or a single electron. TMHsiung ©2016 Chapter 09 Slide 10 of 81 ***** TMHsiung ©2016 Chapter 09 Slide 11 of 81 ***** TMHsiung ©2016 Chapter 09 Slide 12 of 81 ***** TMHsiung ©2016 Chapter 09 Slide 13 of 81 The Five Basic Shapes (All electrons around the central atom are bonding group) Two Electron Domain (AB2): Linear TMHsiung ©2016 Chapter 09 Slide 14 of 81 Three Electron Domain (AB3): Trigonal Planar * double bond contains more electron density than the single bond TMHsiung ©2016 Chapter 09 Slide 15 of 81 Four Electron Domain (AB4): Tetrahedral Five Electron Domain (AB5): Trigonal Bipyramidal TMHsiung ©2016 Chapter 09 Slide 16 of 81 Six Electron Domain (AX6): Octahedral TMHsiung ©2016 Chapter 09 Slide 17 of 81 Example Determine the molecular geometry of NO3−. Solution NO3− has 5 + 3(6) + 1 = 24 valence electrons. The Lewis structure has three resonance structures: Use any one of the resonance structures to determine the number of electron groups around the central atom. The nitrogen atom has three electron domain. The electron domain geometry is trigonal planar: The molecular geometry is also trigonal planar. TMHsiung ©2016 Chapter 09 Slide 18 of 81 The Effect of Lone Pairs (Some electrons around the central atom are lone pairs) Three Electron Domain with Lone Pairs AB2E TMHsiung ©2016 Chapter 09 Slide 19 of 81 Four Electron Domain with Lone Pairs AB3E AB2E2 TMHsiung ©2016 Chapter 09 Slide 20 of 81 * Effect of Lone Pairs on Molecular Geometry TMHsiung ©2016 Chapter 09 Slide 21 of 81 Five Electron Domain with Lone Pairs AB4E AB3E2 AB2E3 TMHsiung ©2016 Chapter 09 Slide 22 of 81 Six Electron Domain with Lone Pairs ***** AB5E AB4E2 TMHsiung ©2016 Chapter 09 Slide 23 of 81 Sample Exercise 9.1 Use the VSEPR model to predict the molecular geometry of (a) O3, (b) SnCl3–. Solution (a) electron domains geometry: trigonal planar molecular geometry: bent electron domains geometry: tetrahedral molecular geometry: trigonal-pyramidal (b) TMHsiung ©2016 Chapter 09 Slide 24 of 81 Sample Exercise 9.2 Use the VSEPR model to predict the molecular geometry of (a) SF4, (b) IF5. Solution (a) electron domains geometry: trigonal bipyramid TMHsiung ©2016 molecular geometry: seesaw-shaped Chapter 09 Slide 25 of 81 Continued (b) electron domains geometry: octahedral TMHsiung ©2016 molecular geometry: square pyramidal Chapter 09 Slide 26 of 81 Representing Molecular Geometries on Paper Examples: TMHsiung ©2016 Chapter 09 Slide 27 of 81 Shapes of Larger Molecules Example: acetic acid TMHsiung ©2016 Chapter 09 Slide 28 of 81 ***** Sample Exercise 9.3 Eyedrops for dry eyes usually contain a water-soluble polymer called poly(vinyl alcohol), which is based on the unstable organic molecule vinyl alcohol: Predict the approximate values for the H—O—C and O—C—C bond angles in vinyl alcohol. Solution H—O—C angle is slightly less than 109.5゜. O—C—C angle is slightly greater than 120゜. TMHsiung ©2016 Chapter 09 Slide 29 of 81 ***** Memo for VSEPR Without lone-pair electrons VSEPR Notation AB2 AB3 AB4 Electron Geometry Linear Trigonal planar Tetrahedral Molecular Geometry Linear Trigonal planar Tetrahedral AB5 AB6 Trigonal bipyramidal Octahedral Trigonal bipyramidal Octahedral TMHsiung ©2016 Chapter 09 Slide 30 of 81 With lone-pair electrons ***** VSEPR Notation AB2E AB3E AB2E2 AB4E Electron Geometry Trigonal planar Tetrahedral Tetrahedral Trigonal bipyramidal Molecular Geometry Bent Trigonal pyramidal Bent Seesaw AB3E2 AB2E3 AB5E AB4E2 Trigonal bipyramidal Trigonal bipyramidal Octahedral Octahedral T-shaped Linear Square pyramidal Square planar TMHsiung ©2016 Chapter 09 Slide 31 of 81 3. Molecular Shape and Molecular Polarity Bond dipole versus Molecular dipole Bond dipole: A separation of positive and negative charge in an individual bond. Molecular dipole: • For diatomic molecule: molecular dipole is identical to bond dipole. • For a molecule consisted by three or more atoms, molecular dipole is estimated by the vector sum of individual bond dipole moment (overall dipole moment). TMHsiung ©2016 Chapter 09 Slide 32 of 81 Polar molecule versus Nonpolar molecule Polar molecule: A molecule in which the molecular dipole is nonzero. Nonpolar molecule: A molecule in which the molecular dipole is zero. Molecular polarity prediction • Draw the Lewis structure for the molecule and determine its molecular geometry. • Determine if the molecule contains polar bonds by electronegativity values. • Determine if the polar bonds add together to form a overall dipole moment. TMHsiung ©2016 Chapter 09 Slide 33 of 81 ***** Examples CO2 Molecular geometry: linear Overall dipole moment: m = 0 D Nonpolar molecule H2 O Molecular geometry: bent Overall dipole moment: m = 1.85 D Polar molecule TMHsiung ©2016 Chapter 09 Slide 34 of 81 X. VB versus MO Quantum-Mechanical Approximation Technique Perturbation theory (used in valence bond theory): A complex system (such as a molecule) is viewed as a simpler system (such as two atoms) that is slightly altered or perturbed by some additional force or interaction (such as the interaction between the two atoms). Variational method (used in molecular orbital theory): The energy of a trial function (educated function) within the Schrodinger equation is minimized. TMHsiung ©2016 Chapter 09 Slide 35 of 81 Schrodinger equation revisited H = E • H (Hamiltonian operator), a set of mathematical operations that represent the total energy (kinetic and potential) of the electron within the atom. • E is the actual energy of the electron. • is the wave function , a mathematical function that describes the wavelike nature of the electron. Perturbation theory: Approach by small changes to a known system in which Hamiltonian operator is modified. Variational method: Approach by combining systems of comparable weighting in which wave function is modified. TMHsiung ©2016 Chapter 09 Slide 36 of 81 Valence bond theory versus molecular orbital theory Valence bond theory (VB): An advanced model of chemical bonding in which electrons reside in quantum-mechanical orbitals localized on individual atoms that are a hybridized blend of standard atomic orbitals; chemical bonds result from an overlap of these orbitals. Molecular orbital theory (MO): An advanced model of chemical bonding in which electrons reside in molecular orbitals delocalized over the entire molecule. In the simplest version, the molecular orbitals are simply linear combinations of atomic orbitals. TMHsiung ©2016 Chapter 09 Slide 37 of 81 4. Covalent Bonding and Orbital Overlap Valence bond theory describes that covalent bonds are formed when atomic orbitals on different atoms overlap. Simple Atomic Orbitals (AO’s) Overlap • A covalent bond is formed by the pairing of two electrons with opposing spins in the region of overlap of atomic orbitals between two atoms. • This overlap region has a high electron charge density. • The overall energy of the system is lowered. TMHsiung ©2016 Chapter 09 Slide 38 of 81 Formation of the H2 molecule as atomic orbitals overlap. TMHsiung ©2016 Chapter 09 Slide 39 of 81 Acceptable simple Atomic Orbitals (AO’s) Overlap Bonding in H2S for example • Predicted H˗S˗H angle is 90o, actual H˗S˗H angle is 92o, therefore, the simple AO overlap is acceptable for H2S molecule. TMHsiung ©2016 Chapter 09 Slide 40 of 81 Unacceptable simple Atomic Orbitals (AO’s) Overlap C Example: CH4 • Ground-state electron configuration of C for example, it should form only 2 bonds • Actually, the central atom of H2S, H2O, NH3, and CH4, are sp3 hybridization TMHsiung ©2016 Chapter 09 Slide 41 of 81 ***** 5. Hybrid Orbitals Hybridization: A mathematical procedure in which standard atomic orbitals are combined to form new, hybrid orbitals. • • • Hybridizing is mixing different types of orbitals in the valence shell to make a new set of degenerate orbitals such as sp, sp2, sp3, sp3d, sp3d2. Hybrid orbitals minimize the energy of the molecule by maximizing the orbital overlap in a bond. Those central atoms are available hybridized, however, those terminal atoms are supposed to be unhybridized. TMHsiung ©2016 Chapter 09 Slide 42 of 81 General statements regarding hybridization ***** • Hybridization is employed for central atom only, thus, the hybrid orbital describes the electron geometry for central atom. • Number of hybrid orbitals = Number of standard atomic orbitals combined = Number of σ bond + Number of lone pairs. • Number of hybridization obitals of a central atom = 2 → sp; = 3 → sp2; = 4 → sp3; = 5 → sp3d; = 6 → sp3d2. • Hybrid orbitals may overlap with standard atomic orbitals or with other hybrid orbitals to form σ bond. • Molecular geometry is described by the relative atomic position around central atom. TMHsiung ©2016 Chapter 09 Slide 43 of 81 sp3 hybridization (C for example) one s orbital with three p orbitals combine to form four sp3 hybrid orbitals (degenerate). TMHsiung ©2016 Chapter 09 Slide 44 of 81 TMHsiung ©2016 Chapter 09 Slide 45 of 81 ***** Examples of sp3 hybridization (for central atom) Central Moleatom cule Standard orbitals Hybrid Orbital σ C H H C H H 2s O σ σ sp3 2p lone N σ Geometry σ σ σ .. H N H H H 2s 2p sp3 lone lone σ .. . O. H TMHsiung ©2016 2s σ sp3 2p Chapter 09 Slide 46 of 81 sp2 hybridization (B for example) one s orbital with two p orbitals combine to form three sp2 hybrid orbitals TMHsiung ©2016 Chapter 09 Slide 47 of 81 Examples of sp2 hybridization (for central atom) Central atom Molecule Standard orbitals B C F B F F H H 2s 2p H H 2s σ σ 2p sp2 σ C C Unhybridized Orbital Hybrid Orbital σ 2p σ σ σ π 2p sp2 lone ***** σ π .. .. N TMHsiung ©2016 H N N H 2s 2p Chapter 09 sp2 2p Slide 48 of 81 sp hybridization (Be for example) one s orbital with one p orbitals combine to form two sp hybrid orbitals TMHsiung ©2016 Chapter 09 Slide 49 of 81 ***** Examples of sp hybridization (for central atom) Central atom Molecule Standard orbitals Hybrid Orbital σ Be Cl Be Cl 2s 2p C TMHsiung ©2016 H C C H 2s 2p Chapter 09 σ sp σ Unhybridized Orbital σ sp 2p π π 2p Slide 50 of 81 Hypervalent Molecules (elements of period 3 and beyond may have more than octet electrons around central atom) sp3d hybridization, AsF5 for example TMHsiung ©2016 Chapter 09 Slide 51 of 81 Continued TMHsiung ©2016 Chapter 09 Slide 52 of 81 sp3d2 hybridization, SF6 for example TMHsiung ©2016 Chapter 09 Slide 53 of 81 Continued TMHsiung ©2016 Chapter 09 Slide 54 of 81 Procedure for Hybridization and Bonding Scheme ***** 1. Write the Lewis structure for the molecule. 2. Use VSEPR theory to predict the electron geometry about the central atom. 3. Select the correct hybridization for the central atom based on the electron geometry. 4. Sketch the molecule, beginning with the central atom and its orbitals. Show overlap with the appropriate orbitals on the terminal atoms. 5. Label all bonds using the σ or π notation followed by the type of overlapping orbitals. TMHsiung ©2016 Chapter 09 Slide 55 of 81 ***** Example for hybridization/electron geometry types versus molecular geometry Number of σ + lone Hybridization VSEPR notation Electron geometry Molecular geometry Example 2 sp AX2 Linear linear Cl-Be-Cl 3 sp2 AX3 AX2E Trigonal planar Trigonal planar Angular BCl3 SO2 4 sp3 AX4 AX3E AX2E2 Tetrahedral Tetrahedral Trigonal pyramidal Angular CH4 NH3 H2O 5 sp3d AX5 AX4E AX3E2 AX2E3 Trigonal bipyramidal Trigonal bipyramidal Seesaw T-shaped Linear PBr5 SF4 ClF3 XeF2 6 sp3d2 AX6 AX5E AX4E2 Octahedral Octahedral Square pyramidal Square planar SF6 BrF5 XeF4 TMHsiung ©2016 Chapter 09 Slide 56 of 81 6. ***** Multiple Bonds σ (sigma) bond: The first covalent bond formed by end-to-end overlap of standard or hybridized orbitals between the bonded atoms: s + s, s + p, p + p (end-to-end), s + hybrid orbital p + hybrid orbital, hybrid orbital + hybrid orbital π (Pi) bond: The second (and third, if present) bond in a multiple bond, results from side-by-side overlap of unhybridized p orbitals: p + p (side-by-side) TMHsiung ©2016 Chapter 09 Slide 57 of 81 σ bonding and π bonding * The electron density on internuclear axis, π bond less than σ bond. Therefore, π bond makes weaker overlap than σ bond. TMHsiung ©2016 Chapter 09 Slide 58 of 81 Single Bond and Multiple Bonds - Single bonds: Double bond: Triple bond: TMHsiung ©2016 one σ bond one σ bond and one π bond one σ bond and two π bonds Chapter 09 Slide 59 of 81 VB theory of bonding in ethylene (H2C=CH2) example of sp2 hybridization and a double bond • Lewis structure • A π-bond has two lobes (above and below plane), but is one bond, side-by-side overlap of 2p–2p TMHsiung ©2016 Chapter 09 Slide 60 of 81 Continued • All six atoms in C2H4 lie in the same plane TMHsiung ©2016 Chapter 09 Slide 61 of 81 VB theory of bonding in Acetylene (HCCH) example of sp hybridization and a triple bond • Lewis structure • Two π-bonds from 2p–2p overlap forming a cylinder of πelectron density around the two carbon atoms TMHsiung ©2016 Chapter 09 Slide 62 of 81 Continued TMHsiung ©2016 Chapter 09 Slide 63 of 81 VB theory of bonding in Formaldehyde (H2C=O) example of sp2 hybridization and a double bond • Lewis structure TMHsiung ©2016 Chapter 09 Slide 64 of 81 Continued lonelone σ π σ π σ σ • Valence bond model TMHsiung ©2016 Chapter 09 Slide 65 of 81 Resonance Structures, Delocalization, and π Bonding Localized or Delocalized Electrons • Localized electrons: Bonding electrons (σ or π) that are specifically shared between two atoms. • Delocalized electrons: Electrons that are spread over a number of atoms in a molecule or a crystal rather than localized on a single atom or a pair of atoms. TMHsiung ©2016 Chapter 09 Slide 66 of 81 Delocalized π bonds in benzene Benzene, total of 30 valence electrons, 24 valence form the σ bonds, 6 C(sp2)-C(sp2) and 6 C(sp2)H(1s) TMHsiung ©2016 Chapter 09 The remaining six valence electrons occupy these six pπ orbitals Slide 67 of 81 Continued benzene has a six-electron π system delocalized among the six carbon atoms. TMHsiung ©2016 Chapter 09 Slide 68 of 81 Delocalized π bonds in NO3- NO3-, total of 24 valence electrons, 12 as nonbonding pairs and 6 σ bonds (3 C(sp2)-N(sp2) bonds) TMHsiung ©2016 Chapter 09 Slide 69 of 81 Continued Delocalized the six-electron π system in NO3-. TMHsiung ©2016 Chapter 09 Slide 70 of 81 8. Molecular Orbital Theory: Electron Delocalization Chemical Bond Molecular Orbital (MO): A model of chemical bonding in which electrons reside in molecular orbitals delocalized over the entire molecule. • The molecular orbitals are linear combinations of atomic orbitals (LCAO). • Because the orbitals are wave functions, the waves can combine either constructively or destructively. TMHsiung ©2016 Chapter 09 Slide 71 of 81 MOs formed by combining two 1s AOs TMHsiung ©2016 Chapter 09 Slide 72 of 81 ***** LCAO–MO Theory: • The total number of MOs formed from a particular set of AOs always equals the number of AOs in the set. • When two AOs combine to form two MOs, one MO is lower in energy (the bonding MO) and the other is higher in energy (the antibonding MO). • When assigning the electrons of a molecule to MOs, fill the lowest energy MOs first with a maximum of two spin-paired electrons per orbital. • When assigning electrons to two MOs of the same energy, follow Hund’s rule—fill the orbitals singly first, with parallel spins, before pairing. TMHsiung ©2016 Chapter 09 Slide 73 of 81 Applications of MOs • Estimate the bond order: Bond Order (BO) = (Σ bonding e– - Σ antibonding e–)/2 • Predict the existence of molecule • Estimating bond length and bond energy • Predicting magnetic properties TMHsiung ©2016 Chapter 09 ***** Slide 74 of 81 ***** 1st Period Homonuclear Diatomic MOs H2 and He2 for example: σ1s* AOs of H (two 1s AOs) σ1s MOs of H2 BO = (2−0)/2 = 1 H2 molecule does exist Diamagnetic TMHsiung ©2016 Chapter 09 σ1s* AOs of He (two 1s AOs) σ1s MOs of He2 BO = (2−2)/2 = 0 He2 molecule does not exist Slide 75 of 81 8. Period 2 Diatomic Molecules MOs formed by combining two set 2p AOs σ2p and σ2p*: end-to-end overlap of AOs π2p and π2p*: side-by-side overlap of AOs TMHsiung ©2016 Chapter 09 Slide 76 of 81 2nd Period Homonuclear Diatomic MOs * Effects of 2s–2p Mixing: Increasing energy difference, decreasing the degree of mixing. TMHsiung ©2016 Chapter 09 Slide 77 of 81 ***** Continued TMHsiung ©2016 Chapter 09 Slide 78 of 81 Predicting magnetic properties by MOs Lewis structure Experiment For O2: showed O2 is .. .. paramagnetic .. O O .. MO prove O2 have unpaired electrons TMHsiung ©2016 Chapter 09 Slide 79 of 81 2nd Period Heteronuclear Diatomic MOs NO for example • Oxygen is more electronegative than nitrogen, so its atomic orbitals are lower in energy than nitrogen’s atomic orbitals. • The lower energy atomic orbital makes a greater contribution to the bonding molecular orbital and the higher energy atomic orbital makes a greater contribution to the antibonding molecular orbital. TMHsiung ©2016 Chapter 09 Slide 80 of 81 End of Chapter 09 TMHsiung ©2016 Chapter 09 Slide 81 of 81