09.26.2011 - Lecture 09 9/26/11 Today in Chemistry...

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Unformatted text preview: Lecture 09 9/26/11 Today in Chemistry 260/261 Lecture 9 9/26/2011 + •  Periodic trends: •  Atomic/ionic radii •  Ionization energy •  Electron affinity •  Electronegativity •  Valence bond model •  Hybrid atomic orbitals •  Resonance Later in Chemistry 260/261 •  Reading: 6.1, 6.4 •  Chemical bonding non-bonding atomic/ ionic radius Periodic Properties Atomic Size Atomic/Ionic Radius bonding atomic/ionic radius =1/2 bond length Ionization Energy Amount of energy required to remove an electron from a gaseous atom X( g ) !! X + ( g ) + e# " Electron Affinity Amount of energy released when a gaseous atom gains an electron X( g ) + e! "" X ! ( g ) # IN GENERAL Atomic radius increases with increasing principle quantum number Electronegativity Tendency of one atom to attract electrons from another atom to which it is bonded Atomic Size Deviations of contracting size within a row are due to shielding effect (filled subshells). 4f block 5d block Zn/Ga At Z= 30, 4s/4p electrons are well shielded by 3d electrons. Full 3d is shielding well – repelling more 5d elements not as big as expected f electrons are very inefficient shielders Zeff is thus larger than expected smaller atoms LANTHANIDE CONTRACTION Atomic radius decreases with increasing nuclear charge in any given shell/subshell. Ionic Size Cations shrink relative to the corresponding neutral atom Anions expand relative to the corresponding neutral atom Effective nuclear charge and e-–erepulsion explain both trends 1 Lecture 09 9/26/11 ConcepTest ConcepTest One of these spheres represents a K+ ion, the other a Cl- ion. True or False: The red sphere is the K+ ion. One of these spheres represents a K+ ion, the other a Cl- ion. True or False: The red sphere is the K+ ion. Of course True, same shielding (electron count) of a larger nuclei, will be more contracted! Ionization Energy Ionization Energy Outermost electron removed from atom to form cation X( g ) !! X + ( g ) + e# " Koopman s approximation I.E. " !En = [Z (n)] 2 ! eff n 2p orbital is higher in energy than the 2s orbital (2p is more shielded than 2s) Generally, ionization energy increases with nuclear charge… but there are some kinks. Explanations must balance effective nuclear charge, shielding/penetration, and e--e- repulsion. X( g ) !! X + ( g ) + e# " 2 electrons begin being paired in 2p ! more e--e- repulsion as Z eff !, I.E. ! Frozen orbital approximation: Assumes that the orbital energies are the same before and after ionization Relaxation effects (1-3 eV) included in Hartree-Fock method IP almost contant: increasing # of d electrons shields 4s from increasing Zeff (4S is ionized) Remember: Zeff for 2p < Zeff for 2s Second Ionization Energy Always takes a greater amount of energy to remove a 2nd electron relative to the first ConcepTest Where on the periodic chart are the elements with the smallest values of first ionization energy? A B C E D X + ( g ) !! X 2 + ( g ) + e# " X( g ) !! X + ( g ) + e# " I.E.1 < I.E.2 < I.E.3 < etc. LARGE jump when remove all electrons from upper most shell 2 Lecture 09 9/26/11 Electron Affinity ConcepTest Where on the periodic chart are the elements with the smallest values of first ionization energy? A B C E +/- Convention: In this class, + EA means a stable anion is formed Amount of energy released when a gaseous atom gains an electron For halogens, the additional electron experiences a strong Zeff, and has a half empty p orbital for an extra e- to enter X( g ) + e! "" X ! ( g ) # 5d block: 4f electrons don t shield very well, therefore, strong Zeff D Of course A, it is tempting to get rid from just one electron to get a noble gas configuration! Comparison of Trends All noble gases (Gr VIII) and most alkaline earth metals (Gr II) have EA < 0 (for noble gases e- enters n+1 shell, for alkaline earth metals e- enters p orbitals) Electronegativity LINUS PAULING Although Ionization Energy and Electron Affinity both tend to increase across periods, the patterns are not exactly the same Tendency of one atom to attract electrons from another atom to which it is bonded ROBERT MULLIKEN !" Trends are shifted All noble gases (Gr VIII) and most alkaline earth metals (Gr II) have EA < 0 ( ! A " ! B = DAB " DA DB 2 2 ) 1/ 2 D is bond dissociation energy I .E. + E. A. 2 Electronegativity follows roughly the pattern : low in lower left hand corner, high in upper right hand corner This Week in Chemistry 260/261 Chapter 6: • Born-Oppenheimer Approximation •  Valence Bond Theory •  Adjustment of Valence Bond Theory to achieve better bonding description • VB based approach: bonding through overlap of orbitals ground state, structure properties intuitive + • MO based approach: ( ad hoc aufbau) , bonding, antibonding and non bonding energy level computational efficient Chemical bonding 3 Lecture 09 9/26/11 Quantum View of Chemical Bonds •  Quantum Mechanics successfully predicts atomic properties (sizes, energy levels, spectra, etc.) •  Want to extend it to molecules, intermolecular interactions, chemical reactivity, etc. •  Next logical step would be to solve the Schrödinger equation for a molecule of interest •  Even more difficult than for multi-electron atoms •  e--e- repulsion •  Dependence on nuclear coordinates •  Need to make further approximations Valence Bond Theory: Basics How to solve the Schrödinger equation beyond single atoms? •  Valence Bond Theory - Localized Orbitals •  Molecular Orbital Theory - Delocalized Orbitals •  As orbitals overlap  Electrons spend time around both nuclei  Electrons are attracted to both nuclei  Bond is formed •  Overlap  , bond strength  Valence Bond Theory Bond will occur between 2 atoms when: 1.  An orbital from one atom occupies the same space as an orbital from the other atom – overlap 2.  Total number of electrons in the overlapping orbitals is no more than two •  Both H and He have 1s orbital occupied H : 1s1 & He: 1s2 •  H2 :1s1+1s1 : 2e- in same space •  He2 :1s2+1s2 : 4e- in same space (no unpaired electrons in He) NOT bonded Yes bonded The Sigma (σ) Bond Simplest chemical bond: H-H Ψ built from the merging of H 1s orbitals, we can expect the overall distribution to be the mathematical sum of these shapes 1s(A) s(A) !1(1) ! 1s(B) (2) A B 1s(B) ! (1, 2) = ! A (1)! B ( 2) 1s(A) 1s(B) ! (1, 2) = ! A ( 2)! B (1) .. but we cannot keep track of either electron ! H-H (1, 2) = ! A (1)! B (2) + ! A (2)! B (1) good first approximation - though, it is not true that electrons do not interact Next, we apply the VB description to specific types of bonding: + A VB wave function with cylindrical symmetry around the internuclear axis is called a σ bond (imagine splitting the center of a sphere and extending the difference between the two points. " = !1A ( )!1B (2)+ !1A (2)!1B ( ) s1 s s s1 ! 1AS ! 1BS All VB wave functions are constructed in a similar way, by using atomic orbitals available on the participating atoms. In general for an A-B bond in VB theory: ! A-B (1, 2) = ! A (1)! B ( 2) + ! A ( 2)! B (1) 4 Lecture 09 9/26/11 σ vs. π bonds A VB Description of N2 σ bond Cylindrical symmetry about internuclear axis N N N " p z = !2p1z ( )!2p2z (2)+ !2p1z (2)!2p2z ( ) 1N 1 Descriptions similar to those used for H2 can be used for molecules built from atoms that contribute more than one electron to the bonding. For N2, consider the electron configuration of the N atoms: N z-axis [He]2s 22p1 2p1 2p1 x y z N [He]2s 22p1 2p1 2p1 x y z ! 2pz orbitals 2px and 2py orbitals π bond Nodal plane along the inter-nuclear axis (e- density above and below plane) Each N atom p orbital has one unpaired electron which can pair with a p electron from the other atom N1 2p z N N N " p x = !2p1x ( )!2p2x (2)+ !2p1x (2)!2p2x ( ) 1N 1 (1)! (2)+ ! (2)! (1) N2 2p z N1 2p z N2 2p z the merging of two orbitals that approach side-by-side (z is the bonding axis): N N N !2p1x ( )!2p2x (2)+ !2p1x (2)!2p2x ( ) 1N 1 N1 N2 N1 N2 ! 2 py (1) ! 2 py ( 2 ) + ! 2 py ( 2 ) ! 2 py (1) N N N " p y = !2p1y ( )!2p2y (2)+ !2p1y (2)!2p2y ( ) 1N 1 NN The VB model of N2 consists of one σ and two π bonds Bond strength is related to the orbital overlap: Overlap  , bond strength  Each bond involves 2p orbitals on the two atoms Overlap for σ bond > π bond ∴ σ bond stronger than π bond Two adjustments of VB theory solve these problems. Promotion and Hybridization of Atomic orbitals 1. Promotion Inability of plain VB theory to account for the number of bonds that atoms can form e.g. tetravalence of carbon C : [He] s 2 2p1 2p1 2 x y According to VB theory, C is only capable of making two bonds, since it has only 2 unpaired electrons 1. Promote a valence electron to an empty atomic orbital  more unpaired electrons that can form bonds 2p    ΔE is small: relieves e--e- repulsions in 2s Energy required by promotion is more than recovered by the atom s ability to form four bonds 2s   the four C unpaired electrons can then pair with 4 H 1s electrons to form CH4 Promotion implies the presence of three σ bonds of one type (C2p-H1s overlap) and a fourth, distinctly different type (C2s-H1s overlap). It is well-known, however, that the four C-H bonds in methane are equivalent in terms of both their chemical and physical properties… The four C-H bonds in methane are equivalent in terms of both their chemical and physical properties and Two adjustments of VB theory improve agreement with experimental observations: tetrahedral coordination. 2. Hybridization Second adjustment of VB theory addresses this problem Quantum mechanics allows the same electron distribution to be described in different ways… We can describe electron distribution in CH4 as arising from four different mixtures of s and p orbitals. These mixtures (more formally, linear combinations) are called hybrid orbitals Hybrid Orbitals 2. Hybridization sp3 Linear combinations Linear combinations that give rise to four equivalent hybrid orbitals 1 h1 = 2s + 2p x + 2p y + 2p z 2 1 h2 = 2s ! 2p x ! 2p y + 2p z 2 1 h3 = 2s + 2p x ! 2p y ! 2p z 2 1 h4 = 2s ! 2p x + 2p y ! 2p z 2 A linear combination of N functions result in N hybrid functions. The LCs are of functions on the same atom. [ [ [ A linear combination of two functions f and g is given by c1f + c2g , where c1 and c2 are numerical coefficients. [ Each hybrid orbital has a lobe pointing toward the corner of a tetrahedron Note there are four coefficients in h1-h4 which are either +1/2 or -1/2. Equal contribution from each orbital involved s p3 5 Lecture 09 9/26/11 The sp3 Hybrid Orbitals Hybridization in Alkenes H H CC H 120° H C : [He] s12p1 2p1 2p1 2 x y z p z Linear combinations that give rise to three equivalent hybrid orbitals # , 1) 1& '2p y ! h1 = $2s + * * ' 3$ ! + 2( % " h2 = ed in π bo nd # , 3) , 1) 1& ' * ' $2s + * * 2 '2p x - * 2 '2p y ! 3$ ! + ( + ( % " h3 = us # , 3) , 1) 1& * ' * ' $2s - * '2p x - * 2 '2p y ! 3$ ! + 2( + ( % " Normalization factor Hybridization in Alkynes H Linear combinations that give rise to two equivalent hybrid orbitals 1 [2s + 2pz ] h1 = 2 CC H2O with VB theory H 180° 1 [2s ! 2pz ] h2 = 2 C : [He] s12p1 2p1 2p1 2 x y z The hybridization of N atomic orbitals always results in the formation of N hybrid orbitals used in π bond O-H ! bond is sp3 + s character H O 104° H the bonding in H2O with VB theory Other Hybridizations sp3d The hybridization of N atomic orbitals always results in the formation of N hybrid orbitals We can use VB theory to explain VSEPR theory number shape hybridization 2 linear sp 3 trigonal planar sp2 4 tetrahedral sp3 5 trigonal bipryramidal sp3d 6 octahedral sp3d2 These pure schemes with equal contribution from each orbital are not the only possibilities: it is possible to form hybrid orbitals with optimized proportions of atomic orbitals. increase p sp decrease s 180° sp2 120° 6 ...
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This note was uploaded on 01/19/2012 for the course CHEM 260 taught by Professor Staff during the Fall '08 term at University of Michigan.

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