Chemistry: The Central Science Chapter 9: Molecular Geometry and Bonding Theory The shape and size of a molecule of a particular substance, together with the strength and polarity of its bonds, largely determine the properties of that substance o Change in shape could result in different properties 9.1: Molecular Shapes Lewis structures do not indicate the shape of the molecule The overall shape of a molecule is determined by its bond angles Central atom A us bonded to n B atoms (AB n ) o Five basic geometric structures of the molecule Linear = 180 between two surrounding atoms Trigonal planar = 120 between three surrounding atoms Tetrahedral = 109.5 between four surrounding atoms Trigonal bypyramidal = 90 and 120 between five surrounding atoms Octahedral = 90 between six surrounding atoms o Can also have bent shape for AB 2 o Can have trigonal pyramidal and T-shape for AB 3 When A is a representative element (one of the elements from the s block or p block of the periodic table), the shape of the molecule can be predict by using the valenceshell electron-pair repulsion (VSEPR) model 9.2: The VSEPR Model Bonding pair a region in which the electrons are most likely be found Such region are referred to as electron domain Nonbonding pair (lone pair) an electron domain that is located principally on only one atom Each nonbonding pair, single bond, or multiple bond produces an electron domain around the central atom VSEPR model is base on the idea of electron-electron repulsion o The best arrangement of a given number of electron domains is the one that minimizes the repulsions among them o The shapes of different AB n molecules or ions depend on the number of electron domains surrounding the central atom The arrangement of electron domains about the central atom is called its electrondomain geometry
o The molecular geometry is the arrangement of only the atoms If all domain arise from bonds, the molecular geometry and electron-domain geometry are identical o If there s a lone pair, then the molecular would have the same shape of the electron-domain geometry but does not show the domain made by lone pair Steps in using VSEPR model o Draw the Lewis structure of the molecule or ion, and count the total number of electron domains around the central atom o Determine the electron-domain geometry by arranging the electron domains about the central atom so that the repulsions among them are minimized o Use the arrangement of the bonded atoms to determine the molecular geometry The Effect of Nonbonding Electrons and Multiple Bonds on Bond Angles o The bond angles decrease as the number of nonbonding electron pairs increases Bonding pair of electrons is attracted by both nucleus where as the nonbonding pair is attracted primarily by only one nucleus The nonbonding pair experiences less nuclear attraction thus causes its domain to be more spread out o The electron domains for nonbonding electron pairs exert greater repulsive forces on adjacent electron domains and tend to compress the bond angles o Multiple bonds contain a higher electronic-charge density than single bonds and represent larger domain In general, electron domains for multiple bonds exert a greater repulsive force on adjacent electron domains than do electron domains for single bonds Molecules with Expanded Valence Shells o Most stable electron-domain geometry for five electron domains is the trigonal pyramid Two contain axial positions while the remaining three contain the equatorial positions 90 between axial and equatorial while 120 between equatorial o Most stable electron-domain geometry for six electron domains is the octahedral 90 between bonds on all side Shapes of Larger Molecules o The VSEPR model can be extend to use on larger molecules
Find the shape of the molecule separately then join them together 9.3: Molecular Shape and Molecular Polarity The charge separation in molecules has a significant effect on physical and chemical properties For a molecule that consists of more than two atoms, the dipole moment depends on the polarities of the individual bonds and the geometry of the molecule o For each bond in the molecule, the bond can be considered bond dipole, which is the dipole moment of the two atom in that bond o E.g. CO 2 Each C=O bond is polar The geometry of the molecule is linear The direction of the polar are completely opposite Cancel each other out Dipole moment of CO 2 is zero The molecule is nonpolar o E.g. H 2 O Each O H bond is polar The geometry of the molecule is bent The direction of the bond dipoles do not directly oppose each other Do not cancel each other out Dipole moment of H 2 O is not zero The molecule is polar 9.4: Covalent Bonding and Orbital Overlap Combining the Lewis s notion of electron-pair bonds and the idea of atomic orbital leads to a model of chemical bonding called valence-bond theory Covalent bonding occurs when atoms share electrons which concentrates electron density between nuclei o In valence-bond theory, the concentrated electron density occurs when a valence orbital of one atom overlap with the other atom As the distance between atoms decrease, the overlap between the electron increase o Increase electron density causing the potential energy to decrease The internuclear distance, or bond length, is the distance that corresponds to the minimum of the potential-energy curve o Correspond to bond length
9.5: Hybrid Orbitals The observed bond length is the distance at which the attraction between unlike charges are balanced by the repulsion between like charges It is assumed that the atomic orbitals on an atom mix to form new orbitals called hybrid orbitals o The shape of any hybrid orbital is different from the shape of the original atomic orbitals The process of mixing atomic orbitals is called hybridization sp Hybrid Orbitals o E.g. BeF 2 molecule Be atom has two electron in the s orbital and none in the p orbital One of the electron is promoted to the p orbital Mix the 2s orbital with one of the 2p orbitals to generate 2 new orbital, sp sp hybrid orbitals have two lobe, one large and one small The two sp orbitals are identical in shape but opposite in direction The large lobe of sp bond to the F atom thus creating a linear geometry sp 2 and sp 3 Hybrid Orbitals o Whenever we mix a certain number of atomic orbitals, we get the same number of hybrid orbitals o All three sp 2 orbitals also have one big lobe and one small lobe The small lobe point to the center atom while the big lobe point to the surrounding atom This would lead to trigonal-planar geometry o sp 3 orbitals contain same shape as sp and sp 2 4 lobes are made with small lobe pointing to the vertex Creates similar shape to tetrahedral o The idea of hybridization is used in a similar way to describe the bonding in molecules containing nonbonding pairs of electron Hybridization Involving d Orbitals o There can be more than 4 hybrid orbitals by hybridizing with d orbitals o These hybrid orbitals are directed toward vertices of the geometry Hybrid Orbital Summary o Steps to predict the hybrid orbitals used by an atom in bonding:
9.6: Multiple Bonds Draw the Lewis structure for the molecule or ion Determine the electron-domain geometry using the VSEPR model Specify the hybrid orbitals needed to accommodate the electron pairs based on their geometric arrangement Sigma (σ) bond bond joining two nuclei passes through the middle of the overlap region Pi (π) bond bond produced by sideways overlap of p orbitals o Overlap sideway so the total overlap in a π bond tends to be less than that in a σ bond o π bond cannot be experimentally observe but the structure of ethylene (C 2 H 4 ) provides strong support for its presence The C C bond length in ethylene is shorter than in compounds with C C single bonds All six atoms in C 2 H 6 lies in the same plane Forms σ bond first before forming π bond If the π bond were absent, there would be no reason for the two CH 2 fragments of ethylene to lie in the same plane π bond can only be if unhybridized p orbitals are present on the bonded atoms o Therefore, only atoms having sp or sp 2 hybridization can be involved in such π bonding Resonance Structures, Delocalization, and π Bonding o The molecules that are localized, means that the σ or π electrons are associated totally with the two atoms that form the bond o Molecules with resonance structure can have bonds that cannot be adequately describe as localized E.g. Benzene (C 6 H 6 ) A representation that reflects both resonance structures has the six π electrons smeared out among all six carbon atoms Cannot describe the π bonds as individual electron-pair bonds o Said to be delocalized Give benzene special stability Responsible for the color of many organic molecules Cause all atoms to lie on the same plane General Conclusions o Every pair of bonded atoms shares one or more pairs of electrons
In every bond at least one pair of electrons is localized in the space between the atoms in a σ bond o The electrons in σ bonds are localized in the region between two bonded atoms and do not make a significant contribution to the bonding between any other two atoms o When atoms are share more than one pair of electrons, one pair is used to form a σ bond; the addition pairs form π bonds The centers of the charge density in a π bond lie above and below the internuclear axis o Molecules with two or more resonance structures can have π bonds that extend over more than two bonded atoms 9.7: Molecular Orbitals Valence-bond theory and hybrid orbitals do not explain all aspects Some aspects of bonding are better explained by a more sophisticated model called molecular orbital theory o Describe electrons in molecules by using specific wave function called molecular orbitals (MO) Similar to atomic orbitals but MOs are associated with the entire molecule, not with a single atom The Hydrogen Molecule o Whenever two atomic orbitals overlap, two molecular orbitals form o One of the molecular orbitals lies lower in energy from the two atomic orbitals from which it was made; the other molecular orbital lies higher in energy The lower-energy MO of H 2 concentrates electron density between the two hydrogen nuclei and is called the bonding molecular orbital More stable An electron in this MO is attracted to both nuclei The higher-energy MO has very little electron density between the nuclei and is called antibonding molecular orbital Less stable The atomic orbital wave functions cancel each other in this region, leaving the greatest electron density on opposite sides of the nuclei o The MOs with electron density that is centered about the internuclear axis are called sigma (σ) molecular orbitals Bonding sigma MO of H 2 is labeled σ 1s ; the subscript indicates that the MO is formed from two 1s orbitals
The antibonding sigma MO of H 2 is labeled σ * 1s; the asterisk indicate that the MO is antibonding o The interaction between two 1s atomic orbitals and the molecular orbitals that result can be represented by an energy-level diagram a.k.a. molecular orbital diagram Show interacting atomic orbitals in the left and right columns and the MOs in the middle column o Electrons occupying a bonding molecular orbital are called bonding electrons Bond Order o The stability of a covalent bond is related to its bond order, defined as half the difference between the number of bonding electrons and the number of antibonding electrons Bond order = ½(no. of bonding electrons no. of antibonding electrons) Take half the difference becase we are used to think of bonds as pairs of electrons A bond order of 1 represents a single bond, a bond order of 2 represents a double bond, and a bond order of 3 represents a triple bond 9.8: Second-Row Diatomic Molecules Rules summarizing the guiding principles for the formation of MOs and for how they are populated by electrons o The number of MOs formed equals the number of atomic orbitals combined o Atomic orbitals combine most effectively with other atomic orbitals of similar energy o The effectiveness with which two atomic orbitals combine is proportional to their overlap As the overlap increases, the energy of the bonding MO is lowered and the energy of the antibonding MO is raised o Each MO can accommodate, at most, two electrons, with their spins paired o When MOs of the same energy are populated, one electron enters each orbital (with the same spin) before spin pairing occurs (Hund s rule) Molecular Orbitals for Li 2 and Be 2 o Li 2 has four MOs o 1s interact with 1s while 2s interact with 2s o Each Li has three electrons so six electrons must be placed in the MOs of Li These electrons occupy the σ 1s, σ * 1s, and σ 2s
4 electrons in the bonding MO and 2 in the nonbonding MO Bond order = 1 Single bond o Both the σ 1s and σ * 1s are completely filled so contribute almost nothing to bonding Core electrons usually do not contribute significantly to bonding in molecule formation o Be 2 has 4 electrons in the bonding MO and 4 in the nonbonding MO Bond order = 0 Does not exist Molecular Orbitals from 2p Atomic Orbitals o The 2p z orbitals face each other directly Form the σ 2p and σ * 2p o The other 2p orbitals overlap sideways MOs of this type are called pi (π) molecular orbitals Form the π 2p and π * 2p o The σ 2p MO is expected to be more stable than the π 2p MOs Similarly, the σ * 2p MO should be less stable than the π * 2p Electron Configurations of B 2 Through Ne 2 o The notable features of the energy-level diagram for homonuclear diatomic molecules from boron through neon The 2s atomic orbitals are lower in energy than the 2p atomic orbitals The overlap of the two 2p z orbitals is greater than that of the two 2p x or 2p y orbitals Both the π 2p and π * 2p molecular orbitals are doubly degenerate; that is, there are two degenerate MOs of each type o The interactions between 2p orbital and 2s orbital can take place o The 2s-2p interactions are strong enough that the energetic ordering of the MOs can be altered: For B 2, C 2, and N 2, the σ 2p MO is above the π 2p MOs in energy For O 2, F 2, and Ne 2, the σ 2p MO is below the π 2p MOs Electron Configurations and Molecular Properties o Molecules with one or more unpaired electrons have the magnetic behavior of being attracted to magnetic field called paramagnetism o Molecules with no unpaired electrons are weakly repelled from a magnetic field, the property called diamagnetism o As bond orders increase, bond distances decrease and bond enthalpies increase
The molecules with the same bond orders do not have the same bond distances and bond enthalpies Other factors also include the nuclear charges and the extent of orbital overlap Heteronuclear Diatomic Molecules o The same principles used in developing an MO description of homonuclear diatomic molecules can be extended to heteronuclear diatomic molecules o If the atoms in a heteronuclear diatomic molecule do not differ too greatly in their electronegativities, the description of their MOs will be similar A major difference is that the atomic energies of the more electronegative atom will be slightly lower than those of the less electronegative element Another important change is that in general, an MO will have greater contribution from the atomic orbital to which it is closer in energy o The bond order of NO is 2½ which agrees better with experiment than the Lewis structures do