In Figure 15.28, the logarithm of Er(t) versus the logarithm of time is plotted for PMMA at a variety of temperatures. Plot logEr(10) versus temperature and then estimate its Tg.
C117 Chapter 10 Notes- Chemical Bonding II: Molecular Shapes, Valence Bond Theory, and Molecular Orbital Theory 2-19-16 Molecular structure determines properties o Small structural changes cause large property changes o Structure includes: Skeletal atom arrangement Type of bonding between atoms Shape of molecule- described in terms of distances and angles in 3 dimensions o Lewis bonding theory predicts shapes of molecules Lewis Theory and Geometry o There regions of in molecules- electron groups − o Some regions result from shared bond pairs of valence between nuclei o Other regions from unshared lone pairs on single nucleus − o Lewis theory says these regions of groups should repel each other- negative charge groups around central atom most stable when they are as far apart as possible Basis for VSEPR theory- Valence Shell Electron Pair Repulsion Resulting geometric arrangement allows predictions of molecular shapes and bond angles The VSEPR Method o Draw Lewis structure o Determine number of groups around central atom − o Determine molecular geometry using VSEPR- find shape such that all pairs as spread out as possible Electron group geometry considers all domains- lone and bonding pairs; one single/double/triple bond makes one region Molecular geometry/shape considers only spatial arrangements of atoms Electron Geometry − o We will consider up to 6 regions around central atom (can have 2-6) o These arrangements result in different geometries o For molecules with resonance, does not matter which structure you use; geometry at central atom will be same o 2 groups- linear (180°) o 3 groups- trigonal planar (120°) o 4 groups- tetrahedral (109.5°) o 5 groups- trigonal bipyramidal (120° and 90°) Axial positions- above and below central atom Equatorial positions- same base plan as central atom Equatorial atoms less crowded Lone pairs occupy equatorial plane first (up to 3 pairs) o 6 groups- octahedral (90°) All positions equivalent − Molecular/ geometry can be different Molecular Geometry o Bond and lone pairs determine shape- where is central atom, is number of pendant atoms, is number of lone pairs on o First determine geometry; remove lone pairs to get molecular # Groups # Bonding # Lone # Pendant Approx. Bond Angles Molecular Shape = + Pairs Pairs Atoms 2 2 0 2 Linear 180 1 1 1 Linear 180 3 3 0 3 Trigonal Planar 120 2 1 2 Bent < 120 1 2 1 Linear 180 109.5 4 4 0 4 Tetrahedral 3 1 3 Trigonal Pyramidal 107.5 2 2 2 Bent 104.5 5 5 0 5 Trigonal Bipyramidal 90 and 120 4 1 4 Seesaw < 90 and < 120 3 2 3 T-shaped < 90 2 3 2 Linear 180 6 6 0 6 Octahedral 90 < 90 5 1 5 Square Pyramidal 4 2 4 Square Planar 90 3 3 3 T-shaped < 90 Bond Angles o If molecule contains bond pairs only, ideal bond angles correct o Angles change if any atom replaced by lone pair Lone pairs occupy more −pace on central atom; their electron density is only on central atom, rather than on 2 atoms like bonding groups- pull harder o Relative sizes of repulsive forces: Lone pair/lone pair strongest Lone pair/bond pair intermediate Bond/bond weakest o Bond pair angles smaller than expected o Ex. Tetrahedral geometry 4 Tetrahedral molecule, 109.5° between atoms 3 Trigonal pyramidal, 107.5° between atoms; − − angle reduced due to increased repulsion between lone pair and all 3 bonding pairs 2 Bent, 104.5° between atoms; two lone pairs increase repulsion more- − − angle reduced even more o Predicting exact values difficult despite general trends Ex. Bent Ex. Trigonal Planar 3D Shapes on Paper o Central atom put on plane of paper o Put as many other atoms as possible in same plane with straight line o For atoms in front of plane, use solid wedge o For atoms behind plane, use hashed/dashed wedge Multiple Central Atoms o Describe shape around each separately o Ex. Methanol Around - tetrahedral Around - bent o Ex. Alkanes- all carbons tetrahedral; do not lie in straight line Molecular Polarity o Ex. - is , has low density; is , has high density Bonding pulled towards end o Ex. 2 Each bond polar, but dipoles cancel; nonpolar molecule o Ex. 2 Each bond polar; both sets of bonding pulled towards end Net result is polar o Dipole moment - measure of molecular polarity Net dipole moment = sum of all dipoles Units- Coulomb meter = Debye ( ) Common values: To be polar: Must have polar bonds; electronegativity difference and bond dipole moments Must have non-symmetrical shape; vector addition Polarity affects intermolecular forces- boiling points, solubilities To be nonpolar: Must be and all must be identical 0 o 2 2 0 Linear o 3 3 0 Trigonal planar o 4 4 0 Tetrahedral o 5 5 0 Triangular bipyramidal o 6 6 0 Octahedral OR must be “divisible” into nonpolar 0 shapes olecules polar if don’t divide into nonpolar shapes, and: > 0 when s equivalent: o Ex. 2 2 2 bent, polar o Ex. 3 3 1 trigonal pyramidal, polar s differ: o Ex. 2 2 4 0 tetrahedral, polar o Ex. 4 5 0 triangular bipyramidal, polar Polarities of Molecular Shapes Assume identical s and identical polar bonds Linear- nonpolar Bent- polar Trigonal planar- nonpolar Tetrahedral- nonpolar Trigonal pyramidal- polar Molecular Polarity and Solubility Recall like dissolves like Recall polar and nonpolar ends of soaps/detergents Problems with Lewis Theory o Generally predicts trends in properties, but does not give good numerical predictions (ie. bond strength/length) o Gives good first approximations for bond angles, but cannot be used to get actual angle o Cannot write one correct structure when resonance structures present o Often does not predict correct magnetic behavior of molecules (2e. paramagnetic, but Lewis structure predicts diamagnetic) o Valence bond theory and molecular orbital theory more sophisticated models − − Valence bond theory- we know occupy atomic orbitals; atoms share when atomic orbitals overlap o Bond forms when singly-occupied atomic orbitals on two atoms overlap − o 2 shared in region of overlap must be opposite spin o Formation of bond results in lower PE for system o Ex. Overlap of orbitals in 2 o o Main Ideas Atomic orbitals (AOs) can be hybridized- form hybrid AOs that can overlap with neighboring atom’s orbitals Types of hybrid orbitals formed postulated based on observations Number of hybrids formed = number of AOs mixed Hybrid orbitals used for either making single bonds or to hold lone pairs All have somewhat similar shape Sets of identical hybrid orbitals form similar bonds Hybrid orbitals follow VSEPR rules; get as far away as possible Can understand bond angles and molecular shapes Hybridization- mixing different types of orbitals in valence shell to make new set of equal-energy (degenerate) orbitals o Prepares AOs to maximize bonding; more bonds = more full orbitals = more stability 2 3 3 3 2 o Ex. , , , , o Same type of atom can have different hybrid types in different molecules Particular kind that occurs is one that yields lowest energy for molecule Number and type of AOs combined determines shape/orientation of hybrid orbitals o Electron Geometry Remaining Orbitals Mixed # and Hybrid Type Unhybridized Geometry + 2 + Linear 2 + + 3 Trigonal Planar 4 3 None Tetrahedral + + + + + + + 5 + + + Trigonal Bipyramidal 3 2 + + + + + 6 + + Octahedral Expanded-octet molecules hypervalent- hybridization includes orbitals 3 o Orbitals One + ,,= four 3 Intuitively gives tetrahedral shape Ex. forms 4 orbitals − Each orbital, 109.5° apart, holds 1 4 equivalent covalent bonds form, ie. 4 Ex. 3 Recall hybrid orbitals can hold lone pairs Ex. 2 o Orbitals 2 One + three remains unused Each hybrid 120° apart; trigonal planar shape Ex. Boron compounds (ie. ,3 , 3tc.) 3 equivalent covalent bonds o Orbitals One + two along -axis and not used Each 180° apart; linear shape Ex. Beryllium compounds (ie. , , etc.) 2 2 2 equivalent covalent bonds 3 o Orbitals Atom with 5 groups Uses empty orbitals from valence shell − Trigonal bipyramidal geometry; 120° and 90° bond angles Ex. 5 o Orbitals − Atom with 6 groups Octahedral geometry Ex. 6 Predicting Hybridization and Bonding Scheme o Draw Lewis structure − o Use VSEPR to predict geometry of central atom o Select hybridization that matches geometry Sigma Bonds and Pi Bonds o Different ways for orbitals to overlap o Sigma () bond- 2 half-filled orbitals combine end-to-end horizontally; found only in single bonds Can be standard or hybrid orbitals to , to , hybrid to hybrid, to hybrid, etc. Overlap of orbitals along internuclear axis Always first to form Have free rotation o Pi () bond- 2 half-filled orbitals combine end-to-end vertically; found in double and triple bonds Must be parallel to each other and perpendicular to axis connecting two bonding nuclei Between unhybridized orbitals Forms second and third in multiple bonds Weaker than bonds Prevent rotation about bond axes: Molecule C/C Bonding C/C Rotation Ethane ( − ) Yes 3 3 Ethene ( 2 ) 2 , No Ethyne ( = ) ,, No Non-rotating double bonds allow cis-trans isomerism to occur o In double bond: one bond, one bond o In triple bond: one bond, two bonds o Ex. Carbon molecules with multiple bonds Tetrahedral centers- 4 ,3 2,6etc. 2 Trigonal planar centers- 2, 2,4etc. Linear centers- 2 2, etc. o Ex. Ethene 2 Each C atom has head-to-head overlap of orbitals; bond Each C also has sideways overlap of orbitals; bond − Unhybridized orbitals each have 1 Each C has 2 orbitals that bond to H atoms o Molecules with Triple Bonds Ex. 22(acetylene); hybridized One bond, two bonds Leaves two unhybridized orbitals on each ; each contains single to make bonds and overlap to make bond between carbons and between C and H Problems with Valence Bond (VB) Theory o Predicts many properties better than Lewis theory (ie. bonding schemes, bond strengths, bond lengths, bond rigidity) Predicts many properties incorrectly (ie. magnetism o2 ) o Presumes electrons are localized in orbitals on atoms in molecule; does not account for delocalization Molecular Orbital Theory o Valence atomic orbitals (AOs) combine to form molecular orbitals (MOs)- called linear combination of atomic orbitals (LCAO) # AOs mixed = # MOs formed − Valence fill MOs in molecules Ex. atom has 1 valence orbital;2 has 2 MOs Ex. has 4 valence orbitals (2 and 22; has 8 MOs o MOs can extend over entire molecules; not confined to pairs of atoms o Filling Molecular Orbitals Arrange MOs in order of increasing energy; relative energies of MOs deduced from experiments Each MO can hold up to 2 ; in filled MO, have opposite spins by Pauli Exclusion − Electrons occupy lowest-energy orbitals first; use all valence to fill from “the bottom up” by Aufbau principle − If there are equal-energy orbitals, 1 goes in each orbital with same spin before pairing any due to Hund’s rule o Bonding MOs- constructive interference; more stable/lower energy than original AOs − o Antibonding (*) MOs- destructive interference; less stable; have a node between atoms (area of 0 density) o Properties Bond order related to difference between # electrons in bonding/antibonding orbitals Only need to consider valence May be a fraction Higher bond order = stronger/shorter bonds If bond order = 0, bond is unstable compared to individual atoms, no bond forms # − # Bond order = 2 − Substance is paramagnetic if its MO diagram has unpaired ; if all paired, diamagnetic o Ex. Consider 2 2 molecular orbitals produced by combining 1 atomic orbitals from each 2−0 Bond order = 2 = 1 o Ex. Find the bond order of 2. 2 + 2 = 4 − 2−2 Bond order = 2 = 0; as noble gas, does not bond o Interaction of Orbitals o Molecular Orbital Diagrams Ordered by increasing energy; 2 and 2can change for different systems For convenience, only use left one Ex. 2, 2, 2 , 2 All but 2 paramagnetic 2−0 2bond order = 2 = 1 6−2 2bond order = 2 = 2 6−4 2bond order = = 1 26−6 2bond order = = 0 2 o Paramagnetic behavior of 2 Predicted diamagnetic by Lewis and Valence Bond models Unpaired in 2molecular orbital predict paramagnetism, which is correct according to experiments o Heteronuclear diatomic molecules- simple model Same MO energy ordering as diatomic molecules Ex. vs. − − has 9 valence , one unpaired in 2 5−0 Bond order = 2 = 2.5 has 10, all paired 6−0 Bond order = = 3 2 When combining AOs are identical and of equal energy, contribution of each AO to MO is equal When combining different types and different energies, AO closest in energy to MO contributes more to MO The more electronegative an atom, the lower in energy its orbitals Lower energy AOs contribute more to bonding MOs; higher energy to antibonding o Polyatomic molecules- when many atoms combined, AOs of all atoms combine to make set of MOs, which are delocalized over entire molecule Gives results that better match real molecule properties better than Lewis and VB theories Ex. Ozone o Resonance structures explain properties o Geometry of each structure asymmetric o Multiple structures needed to get symmetric bonding picture as seen in experiments There is delocalized MO over whole molecule o Holds 2 ; picture consistent with experiment −2 Ex. 3 Has 3 resonance structures; all bonds experimentally shown to be equal There is delocalized MO with 2 Ex. Benzene MOs spread around entire ring Total of 6 in 3 different orbitals (each shown in picture) MO theory consistent with symmetric structure/equal bonds found in benzene