Class Note for CHM 218 at IPFW 3
Class Note for CHM 218 at IPFW 3
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31 Chapter 3 Covalent Bonding Lewis Formulas The interaction between two H atoms to form a covalent bond can be represented as shown below H39 H gt HH or H H The pair of electrons between the two atoms are said to be shared by the atoms and may be represented by a dash Here each h atom may be considered to be associated with two electrons giving each H atom a He electron con guration The interaction between H and Cl may be represented in a similar manner H gt H 1 or H 39C391 Here each atom again has a noble gas con guration H has a He con guration and Cl has an Ar con guration These representations of the H2 and HCl molecules are referred to as Lewis electron dot formulas or simply Lewis structures In Lewis structures electron pairs are represented by pairs of dots or dashes Bonding pairs shared pairs are those electrons that are shared by two atoms These are represented by a dash H Lone pairs unshared pairs are the electrons which are associated 4 H 39C HH with only one atom These are represented by a pair of dots FI Atoms of nonmetals tend to achieve a noble gas con guration by the sharing of electrons with each other Apart from hydrogen 3 H 39 T 39 39 H1l H and a few other exceptions we will mention later atoms will tend H to be associated with 8 valence electrons 2H O gt H O H This tendency for atoms other than H to acquire a total of eight quot valence electrons by the sharing of electrons is known as the Octet Rule H F gt H E O en the number of covalent bonds formed by an atom corresponds to the number of single electrons shown in its Lewis symbol 32 Coordinate Covalent Bonds In socalled normal covalent bonds each atom supplies one of the electrons being shared There is another type of covalent bond in which one atom provides both electrons that are share This is known as a coordinate covalent or dative bond H I H H lII H gt H llH H H Once formed the coordinate covalent bond is indistinguishable from other covalent bonds All of the bonds in the ammonium ion above for example are identical in all respects Multiple Bonds Sometimes atoms cannot achieve an octet by the sharing of one pair of electrons There are some instances in which two or even three pairs of electrons must be shared for two atoms to each achieve an octet RV N N N N gt NEN Double Bond A double bond is a covalent bond in which two electron pairs are shared by two atoms The atoms C N O and to a lesser extent S and P often have double bonds Triple Bond A triple bond is a covalent bond in which three electron pairs are shared Triple bonds are usually limited to C and N 33 Exceptions to the Octet Rule 1 Incomplete Octet An incomplete octet occurs when an atom has fewer than 8 valence electrons associated with it Incomplete octets are usually encountered in molecules with Be B or Al atoms For example 6valenoe ebctrors 0 139 61 4m 6160mm F mum B quot quot arourrlBe However these atoms can achieve an octet by the formation of a coordinate covalent bond As shown in the example below for B l l1 1 PE 1I H gt quot B 1I H H F 2 Expanded Octets An expanded octet involves more than 8 valence electrons being around an atom Expanded octets are not uncommon for atoms in the third period and beyond beginning with Si 516 F XeF4 1 PF5 15 SE 15Ci 4K 3915 In I I F quot F 34 Electronegativity and Bond Polality When electrons are shared between two identical atoms the electrons are shared equally For example when two H atoms are bonded together or two Cl HH 91 91 atoms are bonded together there is equal likelihood of L J nding the electrons near one nucleus or the other equal Sl aIing of electrons However when a bond is formed between atoms of two di erent elements the bonding electrons will not necessa1ily be shared equally A polar covalent bond is a covalent bond where the electrons are not shared equally but are more likely to be found nearer the nucleus of one atom than the other When a H atom bonds to either a F or Cl atom the bonding electrons will be more likely to be found near the F or Cl atom than near the H atom As a result the F or Cl atom acquires a partial negative charge while the H acquires a partial positive charge These partial charges are denoted by a lower case delta 6 6 F I l H F Na Eq39 nonpolar covalent polar covalent ionic A polar covalent bond is intermediate between a nonpolar covalent bond and an ionic bond This should also point out that covalent and ionic bonds are merely extreme idealizations on a continuum of bonding How do we determine if a bond is polar and if so which atom will bear the pa1tial negative charge We need a measure of how strongly an atom attracts the electrons in a chemical bond The ELECTRONEGATIVITY of an atom is just such a measure Electronegativity X A measure of the ability of an atom in a molecule to attract bonding electrons to itself 35 Atoms that have a large negative electron attachment enthalpy readily accept electrons and a large positive ionization energy reluctant to give up electrons should be expected to strongly attract bonding electrons to themselves when they are bonded to other atoms Accordingly Mullilmn proposed that the electronegativity of an atom be given by 12 the diiTerence between its ionization energy and its electron attachment enthalpy In other words when the ionization energy and electron attachment enthalpies are expressed in appropriate units eV 13 AHI x 2 Linus Pauling proposed another more commonly used electronegativity scale shown below It should be kept in mind that electronegativity is a property of an atom in a molecule rather than of an isolated atom like ionization energy or electron af nity Therefore the values shown below cannot be taken too literally Nevertheless they are somewhat use ll Atoms of non metals tend to have higher electronegativities while metals tend to have smaller electronegativities They are said to be electropositive HA HA mA WA VA WA WA Li Be 10 15 8 3992 W B 39 39 H B WB VB W W B r quot 8 K Ca Sc TI V Cr Mn Fe Co NI Cu 08 10 13 15 16 16 15 18 18 18 19 Rb Sr Y Zr Nb Me To Ru Rh Pd A9 08 10 12 14 16 18 19 22 22 22 19 Cs Ba La Lu Hf Ta W Re Os Ir Pt Au 07 09 11 1213 15 17 19 22 22 22 24 Fr Ra Ac No 07 09 11 1 The greater the electronegativity difference between two bonded atoms the more polar the bond and the electrons will tend to be closer to the atom with the larger electronegativity As the diiTerence in electronegativity gets larger an ionic model of the bonding may become more useful 3 6 Formal Charge Suppose we have a compound whose molecules each contain one C atom one H atom and one N atom We can consider two possible H CEN and H NEC3 arrangements of the atoms Why are these the only two possibilities One of these is much more stable than the other Using the concept of formal charge allows us to select the more stable of two or more possible structures Formal charge the hypothetical charge that an atom in a molecule acquires when the bonding electrons are assumed to be shared equally between the atoms and lone pairs are assigned to a single atom Formal charge of valence electrons in the isolated atom 7 of non bonding electrons 7 12 of bonding electrons H CEN H NEC H1010 H1010 c4 0 40 c4 2 3 1 N5 2 30 N5041 When deciding on the relative stabilities of two or more possible structures 1 The Lewis structure which has the smallest magnitude of formal charges It is usually desirable to minimize the number of nonzero formal charges 2 When two or more Lewis structures have the same magnitude of formal charge the one that has the negative formal charges on the more electronegative atoms is preferred For a neutral molecule the sum of the formal charges of all the atoms equals 0 For an ion the sum of the formal charges of all the atoms equals the charge of the ion 37 Consider the structures shown below I 2 H 2 B IS o 0 0 s 6701282 s 670712120 O 676712271 70 676712271 0 67471240 The second Lewis structure implies that two of the Si 0 bonds should be diiTerent than the other two However experiment shows that all four 8 0 bonds are identical and are somewhat shorter than a typical 8 0 single bond but longer than a 80 double bond In reality the double bonds are not localized between the S atom and two of the O atoms as shown but rather are delocalized over all four 8 0 bonds Delocalized Bonding a type of bonding in which electrons are associated with several atoms rather than being localized between only two The bonding in metals metallic bonding can be viewed as an extreme case of delocalized bonding The valence electrons are delocalized over an entire crystal rather than being localized between pairs of atoms For instance in a crystal of sodium metal the 3s electrons one provided by each Na atom are free to move throughout the entire crystal of what can be regarded as Na ions occupying xed sites The mobility of the valence electrons accounts for the electrical conduction of Na metal For molecules in which delocalized bonding occurs a single Lewis structure cannot adequately describe the bonding in the molecule We use the concept of resonance to describe the bonding in such molecules 38 Consider another example SO3 Ifwe draw a single Lewis structure the implication is that two of the bonds are different than the third This is contrary to experimental data which indicate that all of the bonds are l exactly the same within experimental error Furthermore the bonds are 39 intermediate between a single bond and a double bond To indicate this O we draw a series of resonance structures also called contributing or canonical structures separated by double headed arrows 9 8 9 lt gt lt gt 0 O The actual structure of 03 is a weighted average of all the contributing structures It must be stressed that the molecule does not uctuate between these structures An analogy might clarify things A traveler to Africa described a rhinoceros as a cross between a unicom and a centaur That is he was describing something that was real as the hybrid of two imaginary creatures The resonance hybrid is similar It is something that actually exists described as the average of things that do not exist A Resonance structures diiTer only in the allocation of electrons not in the position of the atoms Molecular Geometry Lewis structures indicate how atoms are bonded to each other in molecules but they are not meant to represent the three dimensional structure of molecules Molecules have de nite shapes and these shapes in uence many of the chemical and physical properties of the molecules For example the structures of BF3 and NH3 are somewhat di erent The angle between F atoms in BF3 is 120 and the angle between H atoms in NH3 is about 107 5 3 quot mN f H le 120 H 107 Molecular geometry the general shape of a molecule as determined by the relative positions of the atomic nuclei 39 The Valence Shell Electron Pair Repulsion V SEPR Model is a relatively simple model that allows us to predict molecular geometry The basic premise of the VSEPR model is that electron pairs both bonding and nonbonding will be arranged around an atom in a molecule in such a way as to the electron electron repulsions We must rst consider the ELECTRONIC GEOMETREES about the central atom that the repulsions In this graphic we should replace the term Number of pairs with the term Steric Number or Regions of High Electron Density In this context a single unshared electron counts the same as an unshared pair of electrons and a multiple bond counts the same as a single bond This table gives us the arrangement of the regions of high electron density around the central atom which the electronelectron interactions for the given number of regions These are sometimes referred to as the electronic geometry The molecular geometry is partly determined by the electronic geometry 1 Start with the appropriate Lewis structure 2 Determine the appropriate electronic geometry 3 From the electronic geometry and the number of bonds no distinction between single and multiple bonds deduce the molecular geometry The following tables will be extremely helpful m5 2 3 4 Aggie Llneav Tngunal planar Teuahedml Number m pans 5 5 Arrangement octahedral m pans ELECTRoN RAIRs ARRANGEMENT Tulal Banding Lune 0F RAIRs 2 2 o Lmeav a o THgona 3 Mama 2 1 ELECTRON PAIRS ARRANGEM Tmnl Banding Lune 0F PAIRS A o 4 a 1 Teuahedva 310 MoLECuLAR GEoMETRv EXAMPLE Lmeav M Q Be2 F Ee F F Tngona I p anav 53 5 Axd F Eentov G7 angmay 502 AxZ gal 0 o ENT MOLECULAR GEOMEI RY EXAMPLE Tavahedval Ax CH Tngona D mmdax N Xi H H39 IN H H Baum angmay H20 AX ELECTRON PAIRS Tulal Banding Lune ARRANGEMENT OE PAIRS MOLECULAR GEOMETRV AX a xatom Tngona T bwpyvamwda Agtlt5 Seesaw ov dwstoned teuahedvon Ax 5 THgona mpyyarmdax Lmeav A X1 Lone paw ELECTRON PAIRS Tma Banding Lune ARRANGEMENT OF PAIRS MOLECULAR GEOMEl39PN Odehedva S ave Oaahedva q 397Lone paw 311 EXAMPLE ix 0 POWS C A C CT 5E C Fa gtlteE2 EXAMPLE T R E SE6 FfF E E IEs FgtltF E I E E T E XeF Steric Number 7 Pentagonal Bipyramidal Steric Number 8 Cubic B t Al l B B B I393 34 Capped Trigonal Prism Square Antiprism next three limited to actinides and lanthanides Hexagonal Bipyramidal Bicapped Trigonal Prism B B 3 39 39B B B a7quotquotB 5 l3 5 r A B39 B Bji B Steric Number 9 Tricapped Trigonal Prism Fairly common eg ReH9239 and MH209339 of lanthanides B 312 Capped Octahedron Triangualted Dodecahedron Bicapped Trigonal Antiprism 43 B tailnae Bquot 39793 B gt B BB 7 B i liB B B 313 We can attempt to show the three I I dimensional structure of molecules H bond gOIl g bel lIl Il bords wrthrntle on paper by usrng a combmatron tl B plare Oftl E page of lines wedges and cross plam Of f page hatched wedges to represent H quot39H H di erent bonds A normal line indicates a bond that is in the plane of the page A wedge bOI Il out in ont indicates a bond that comes out in of E p1ane of B page front of the page while a cross hatched wedge indicates a bond that goes back behind the plane of the page The VSEPR model allows us to predict approximate bond angles in molecules 1 Lone pairs require more space than bonding pairs Take for example CH4 NH3 and H20 All of these structures are based on a tetrahedral electronic geometry in which the ideal bond angle is 10950 The speci c electronic structure of a molecule will alter these ideal angles somewhat In CH4 where there are no lone pairs the bond angles are all within experimental error 1095O actually 1090 28 the ideal angle for a tetrahedral geometry The angle between nonbonding electrons and bonding electrons will be somewhat larger than that between bonding electrons The angle between two sets of nonbonding electrons will be even larger The presence of one lone pair in NH3 causes the HNH angle to be smaller than the ideal The presence of two lone pairs in H20 causes an even lrther reduction in the HO H bond angle from the ideal H I Il l r 0 H 9in HQH HJ 1073quot 1045quot 10950 314 2 A single unshared electron will generally require less space than a bonding pair N02 N02 N0239 ONO 0N 0 oNo 1800 1340 1150 3 Multiple bonds require slightly more space than single bonds Take for example formaldehyde HZCO and ethylene C2H4 The ideal bond angles in each of these molecules are 1200 Steric number 3 no lone pairs The angle between the double and single bonds is somewhat larger than the ideal while the angle between the single bonds is somewhat smaller 0 H H 1220 l 117 C C 1160 1215quot Dipole Moment and Molecular Geometry We previously talked about the idea of the unequal sharing of electrons between two covalently bonded atoms This unequal sharing leads to a partial positive charge on one atom and a partial negative charge on the other The magnitude of this charge separation can be quanti ed A dipole moment is a quantitative 5 5 HF has anonzero dipole moment measure of the degree of charge Hi HF is a polar molecule separatlon in a bond or in a molecule F 391 F2 has no dipole moment quot F2 is a nonpolar molecule 5 5 E39 Even though it contaim polar bonds Be F Ber has no dipole moment Ber is a nonpolar molecule 3 l 5 The dipole moment is given by u 6d where u dipole moment 6 charge d distance of separation The unit of dipole moment is the Debye D l D 334 X 103930 C m Each polar bond in a molecule can be treated as a vector Two vectors of equal magnitude but opposite direction cancel each other OA lt39 H H We can also look at this from the standpoint of centers of positive and negative charge Ifthe centers of positive and negative charge are coincident the molecule will be nonpolar On the other hand if they do not coincide the molecule will be polar a 5 6 5 o QCQ H H 6 5 Formula AX6 Molecular Geometry Linear Linear Bent Trigonal Planar Trigonal Pyramidal Tshaped Tetrahedral Square Planar Seesaw Trigonal Bipyramidal Square Pyramidal Octahedral 316 Dipole Moment Nonzero Zero Nonzero Zero Nonzero Nonzero Zero Zero Nonzero Zero Nonzero Zero Assuming all X atoms are identical and A and X have di erent electronegatiVities 317 Models of Chemical Bonding I Valence Bond Theory According to Valence Bond Theory a bond form between two atoms when 1 An orbital of one atom occupies the same region of space as an orbital of another atom These orbitals are than said to overlap 2 A pair of electrons simultaneously occupies both orbitals Because of the overlap of the two orbitals the electrons are simultaneously attracted by both nuclei holding the atoms together The strength of the bond depends on the degree of overlap Orbitals other than s orbitals overlap only in particular directions These directions are such that maximum overlap is obtained Hybrid Orbitals Based on the bonding model we have considered so far it might seem as though an atom will form only as many covalent bonds as it has unpaired electrons in its valence shell F Li 1 HF ls 2s 2p L i i L L H20 ls 2s 2p L L L LL ls 2s 2p 318 However C which has only two unpaired electrons in its valence shell in its ground state almost always forms four covalent bonds 11H CH4 1s 2s 2p C We can rationalize this behavior by considering the process of promotion Keep in mind that in the n 2 shell the 2p subshell is higher in energy than the 2s subshell Moving an electron from the 2s to the 2p subshell requires the input of energy ZS promotion ZS ls ls We might now expect that three of the bonds in CH4 might be at 900 to each other with the fourth bond being at any arbitrary angle corresponding to the p orbitals which are mutually perpendicular and an s orbital which has no directional character However we know that in CH4 all the bond angles are 10950 and all the bonds are equivalent The three 2p orbitals and the 2s orbital may mix resulting in four new hybrid orbitals which are equivalent to each other in all respects 2p hybridization L L L L sp3 2sl 3 2p orbitals 1 2s orbital 4 sp3 hybrid orbitals 319 In CH4 a H ls orbital overlaps with each of the four sp3 hybrid orbitals resulting in four equivalent covalent bonds Orbitals must be conserved in the hybridization process so of hybrid orbitals formed of atomic orbitals mixed An s orbital can mix with various numbers of p and d orbitals to give various hybrid orbital sets each with its own distinctive arrangement of lobes Atomic orbitals hybridization of hybrid orbitals arrangement 1 s l p sp hybrid 2 linear l s 2 p sp2 hybrid 3 trigonal planar l s 3 p sp3 hybrid 4 tetrahedral l s 3 p l d sp3d hybrid 5 trigonal bipyramidal l s 3 p 2 d sp3d2 hybrid 6 octahedral These arrangements should look familiar to you These correspond exactly to the electronic geometries used in the VSEPR model Therefore if we know the electronic geometry of an atom in a molecule or ion we can infer its hybridization 1 Write the Lewis structure 2 Use VSEPR to predict electronic geometry 3 From the electronic geometry deduce the hybridization 320 Multiple Bonding One hybrid orbital is required for each bond to another atom in a molecule and for each lone pair H H Consider ethylene C2H4 C H H Here each C atom is bonded to one C atom and two H atoms with no lone pairs Therefore 3 hybrid orbitals are required and sp2 hybridization is indicated Altematively we could rationalize that since the steric number for each C atom is 3 the electronic geometry is trigonal planar and the hybridization is therefore sp2 This leaves an unhybridized p orbital on each C atom perpendicular to the plane of the molecule We now need to consider two different types of bonds Sigma 0 bond A sigma bond has cylindrical symmetry about the bond axis and results from the headtohead overlap of two orbitals Q 0 9 a C O D C gt C 33 b 9 One component of the C C double bond is a sigma bond and each of the C H bonds is a sigma bond Pi 11 bond A pi bond has electron density above and below a plane that contains the bond axis and results from sidetoside overlap of parallel p or d orbitals H o unhybn39dized p orbitals 321 One component of the double bond is a pi bond The formation of the pi bond locls the molecule into this planar structure Molecules are free to rotate about single bonds but rotation about a double bond cannot occur We can compare the compounds l2dichloroethane and 12dichloroethene H7C Cia HK39EC Cec1 free C1 rotation C1 C1 H Free rotation about the single bond occurs in l2dichloroethane shown above There is only one compound with this name On the other hand 12dichloroethene has a double bond about which free rotation cannot occur H Cl H H CC C Cl H C1 C1 trans 12 dichloroethene cis l 2dichloroethene Two compounds with the name 12dichloroethene exist and they have diiTerent chemical and physical properties They are said to be isomers of each other The isomer in which the Cl atoms are on the same side of the C C bond is the cis isomer and the one in which they are on opposite sides is the trans isomer These isomers cannot be interconverted without breaking the pi bond Next we will consider acetylene C2H2 H C C H Each C atom is sp hybridized and each C H bond is a sigma bond The triple bond between the carbon atoms consists of one sigma bond and two pi bonds H370le 05 322 Molecular Orbital MO Theory Molecular orbital theory is a more sophisticated approach to chemical bonding than Lewis structures and valence bond theory MO theory may explain some properties of molecules that the other approaches cannot For instance experiment demonstrates that 02 is a paramagnetic molecule with two unpaired electrons The Lewis structure that is commonly drawn for O 02 does not demonstrate this fact Using molecular orbital theory it is very easy to rationalize the paramagnetic behavior of 02 In atoms atomic orbitals AO represent regions of space where there is a high probability of nding an electron Atomic orbitals have discrete energies as well In molecules molecular orbitals MO are regions of space where there is a high probability of nding an electron Unlike atomic orbitals however molecular orbitals are o en delocalized over two or more atoms 1 Each MD has a de nite discrete energy 2 A maximum of two electrons may occupy any MO and then only if they have opposite spins 3 MOs are lled with electrons lowest energy to highest energy in accord with Hund s rule What do these MOs look like We can make an approximation that MOs are formed from a linear combination of AOs Orbitals are conserved so for every AO which combines one MO results 323 Linear Combination of Atomic Orbitals LCAO Approach 1 MOS are formed by combination of parent AOs on two or more atoms 2 Only valence orbitals and electrons are considered 3 Orbitals are conserved in chemical bonding 4 MOs follow the same rules as AOs Aufbau Principle Pauli Exclusion Principle Hund s Rules etc 5 Only AOs with identical symmetry properties can interact 6 Orbital mixing is most effective when there is a good energy match ElTectiveness of overlap decreases as energy mismatch increases Overlap of Atomic Orbitals AOs are said to overlap when they occupy the same region of space Overlap may be positive negative or zero Positive overlap signs of wavefunctions of overlapping orbitals are the same Negative overlap signs of wave lnctions of overlapping orbitals are diiTerent Zero overlap equal amounts of positive and negative overlap positive overlap negative overlap zero overlap 324 Consider HZ Each H atom contributes a Is atomic orbital As a result 2 MOs result from two di amt linear combinations of the atomic rbitals 15 ls giverisetoZMO 5 Addition of orbitals ouiios up eieotron de Slly in overlap region VJ Bonding orbital Subtraction of orbitals results in low eieotron de Slly in tne overlap region g j K a o g 3 7 r i L a Iaxn39r WV 51 Km 15 l Antibonding orbital The bonding MO designated a s is the lower in mergy of the two molecular orbitals while the antibonding MO designated 0 is higher in magy Molecular Orbital Energy Diagram We may write the electron con guration for a molecule just as we do for an atom For H2 the electron cm gjration is written as 052 since thae are two electrons in the 05 MO 3 25 Bond Order The bond order in a molecule may be determined from the MO diagram and it corresponds to 12 the di erence between the number of electrons in bonding MO s and the number in antibonding MOs Bond order 12 e39 in bonding MOs e39 in antibonding MOs A higher bond order indicates a shorter stronger bond If a bond order is calculated to be 0 or negative the species is not a stable molecule Integral and halfintegral bond orders are possible The bond order for H2 is 12 2 0 1 For He2 we can use the same diagram as for H2 The additional two electrons go into the 015 MO and the electron con guration is 015 2 0152 The bond order is given by 12 2 2 0 He2 is therefore not a stable molecule In order for two atomic orbitals to combine to form molecular orbitals two conditions must be met 1 There must be a reasonable energy match between the two atomic orbitals 2 The symmetry of the orbitals must be the same In the case of Liz the energy match between the ls atomic orbital and the 2s atomic orbital is not very good so the ls and 2s orbitals do not interact gtxlt 0 25 I z39 ll 25 l I l 25 x I l I x 7 0392S H as 0 15 r s H l r x I 0 Is Li Li2 Li 326 The electron con guration of LiZ may be written as Ols 2 0152 025 2 We can abbreviate the rst part Ols 2 0152 as K to indicate that the K shell of each atom is lled The con guration may therefore be written as K 025 A homonuclear diatomic molecule is a diatomic molecule which is composed of two like atoms for example H2 02 F2 etc A heteronuclear diatomic molecule is a diatomic molecule which is composed of two unlike atoms for example HF CO etc For the rest of the second period diatomics we must consider the MOs that can be formed by the overlap of the p atomic orbitals px py and p2 Two types of overlap are possible By convention the internuclear axis is taken as the Zaxis By this convention the pZ orbitals point at each other and can overlap in a headtohead or sigma fashion Additive overlap results in a sigma bonding MO 02p while subtractive overlap results in a sigma antibonding MO 0 2p These are shown in the gure below The px and py atomic orbitals line up in a sidetoside or pi fashion Additive overlap results in a pair of pi bonding MOs 1121 while subtractive overlap results in a pair of pi antibonding MOs 112p The two bonding MOs are at the same energy and the two antibonding MOs are at the same energy Orbitals of the same energy are said to be degenerate The ip and 112p MOs are shown in the gure below 327 Relative Energies of Molecular Orbitals The energies of molecular orbitals do not vary a great deal from the energies of the atomic orbitals from which they are formed There is some spreading of the bonding MO and anti bonding MO below and above the parent atomic orbitals though In general MOs formed from2p atomic orbitals will be higher in energy than those formed from 2s atomic orbitals A molecular orbital diagram appropriate to the second row homonuclear diatomics up to N2 is shown below The MOs arising from the ls atomic orbitals are omitted We can use this diagram to predict the bond order stability and magnetic properties of the homonuclear diatomics through N2 Molecule Stable Bond Order Paramagnetcdiamagnetic Liz Yes 1 Diamagnetic Bez No B2 Yes 1 Paramagnetic C2 Yes 2 Diamagnetic N2 Yes 3 Diamagnetic The diagram above does not rigorously apply to the rest of the homonuclear diatomics of the second period The reason concems the relative energies of the 2s and 2p orbitals in atoms of the 2quot 1 period elements 328 For auonue wlth a lugr 2 the 2s 210ml orbltal ls about 2 5 M moiquot lower u energy than the 2p level Thls allfereree results Sam the pereuauou of he s orbltal elose to are uueleus hence an demon lu an s orbltal ls more strongly ln uenced by are luereasug uuelear charge However atLhe beglnmng of are peuool the levels daffenn energy by only about 0 2M moiquot In these Circumstances the vvave funmons for the 2s and 2p orbltals beeorue mureol One result of are mlxmg ls an merease u erergy othe 07 moleeular orbltal to are pomt Where u has greats energy than the 17 orbltal Thls ordeung of orbltals applles o dmltxogen and are precedlng elements lu Penod 2 be M erossover occumng between dmltxogen and dloxygm 329 The appropriate MO diagram for the remaining homonuclear diatomisc of period 2 is 25 25 0 25 Molecule Stable Bond Order Paramagnetcdiamagnetic 02 Yes 2 Paramagnetic F2 Yes 1 Diamagnetic Nez No We can also use the MO energy diagram for cations and anions of the homonuclear diatomics For example each of the following ions is known 02 0239 and 02239 What are the bond orders and how many unpaired electrons does each contain Moleculeion bond order unpaired e39 of 25 l 02 2 2 0239 15 l 02239 l 0 Knowing the bond orders allows us to predict the relative bond lengths and strengths Bond length 02 lt 02 lt 0239 lt 02239 Bond strength 02 gt 02 gt 0239 gt 02239 330 Heceronuelear Dxatomms In due ease of hecermelear dwtomxcs me emerges of correspondmg acme orbxtals may differ appreerably The emerges of me eorresporrdmg acme orbrcals m N and o are rroc excremely far aparc and me M o dAagmm ofNO somewhac resembles mac of q wrch the o acme orbnals berng somewhac lower m Energy than me eorresporrdmg N acme orbxtzls Usrng arum Molecular Momc che q M o diagram for NO does noc on mm mcxoduee senous error However even Justtwo elemencs away 1 me acme orbnals ofC are sngn candy 39 hgher m Energy than the eorresporrdmg acme orbrca1s ofO As aresu1c che M 27 M o dAagram of co does rroc resemble are q diagmm ac au Inche ease ofHF are H 1s orbrcal rs sgm candy hghenn margy than even theF 2p orbnals As a result are H 1s orbxtal rmrres only wrch one of me F 2p orbrcals co grve abmdmg andan mnrbondmg M 0 quotRural 2s orbrca1 anache F 2px and 2py do rroc rmx wrch are H 1s orbxtal They are ra emedto as nonrbondmg Mo s L N L 2 c 2px Zny p my N 1 25 Noce mac che 0 bondmg M 0 rs mueh e1oser m 25 energy co LheF 2p orbrcals man co che H 1s orbrcal H H Whle the 0MO ls closa m Energy to the H15 orbrcal Ths rmplres chacche 0 bondmg M 0 has more F 2p eharaecer Th5 means mac che cwo e1eecrons whmh oeeupy Lhs M 0 have a greacer probabrlrcy ofbemg near co F char co H In otherwords che HeF bondrs polar wrch che F acorn havrng che pamal negacave eharge 3 3 1 Molecular Orbitals and Delomlized Bonding Another advantage of MO Theory over the valence bond approach lies in the way that it deals with molecules which involve delocalized bonding If you recall multiple resonance strurtures were required to describe the bonding in such molecules using the valence bond approach MO 39Iheory describes this bonding with a single electron con guration In the valmce bond approach the ozone molecule 03 is described by using two resonance structures r 0 T o o o The implication is that each 0 atom has three localized electron pairs associated with it and sp2 hybridization leaving one unhybridized p orbital on each 0 atom Since two of these localized pairs are diared two electron pairs may be thought of as delocalized In the picture above the delomlized electrons may be thought of as one of the pair in the double bond and one of the unshared pairs on the O atoms which are being shuf ed by the arrows These three unhybridized p orbitals contribute to three molecular orbitals one bonding one antibonding and one non bonding as shown below l re A aa oo l l Anilbondlng 1r orblial Nonbondlng 1r orblial l r Bondlng 1r orbllal Two of the electrons occupy the bonding MO which is the lowest of the three in energy and two electrons occupy the nonbonding MO whid1 is intermediate in energy The antibonding orbital whid1 is highea in energy is unoccupied 332 Intermolecular Forces IMF Intermolecular forces are relatively weak forces of interaction between molecules They are typically much weaker than ionic or covalent bonds In the gas phase we normally neglect the intermolecular forces however they are quite important in the condensed phases and may be used to explain some of the physical properties of liquids and solids Intermolecular forces are responsible for keeping the molecules in the liquid phase The strength of the intermolecular forces affects the ability of the molecules to escape into the vapor phase The strength of the intermolecular forces therefore has a profound effect on the boiling point heat of vaporization and vapor pressure of a liquid Stronger llVJFs result in higher boiling points greater AH3p lower vapor pressure at a giver temperature Van der Waals force is a general term for two types of Ms dipoledipole forces and London forces These forces are described below 1 Dipoledipole Forces Dipoledipole forces are attractive forces between the positive end of one polar molecule and the negative end of another polar molecule Polar molecules ten to align themselves in a to 7 fashion The molecules of HCl in the solid phase are wellordered in this alignment In the liquid phase these interactions are only partially disrupted In general the more polar the molecules are the stronger the dipoledipole forces will be 333 2 London Dispersion Forces Consider a normally nonpolar substance such as neon or argon 712 7 On average the electrons are distributed in a symmetric fashion around the nucleus At some instant in time this distribution may not be perfectly symmetric and an instantaneous dipole moment 5 57 5 57 5 57 710 7 i 0 Ne Ne Ne 237 5 57 5 results This temporary dipole moment can affect the distribution 710 7 710 7 of electrons in a neighboring atom or molecules as shown Thus an instantaneous dipole is induced in a neighboring atom Ne Ne C London or dispersion forces are the weak attractive forces which result from these small instantaneous dipole moments which arise due to uctuations in electron distributions London forces increase with increasing molecular weight Gas BPK AW Hydrogen Bonding Ne Ar Kr Xe 27 87 120 166 2018 3995 8380 1313 A third type of IMF commonly encountered is the hydrogen bond Hydrogen bonds vary widely in strength They are responsible for some of the properties of liquid and solid water as well as the secondary structure of many proteins Hydrogen Bond A weak to moderately strong attractive o 5395 force between a hydrogen atom covalently trquot bonded to a highly electronegative atom 39Hydmgen bonds H such as F O or N and a lone pair of r T electrons on another highly electronegative 38 mg a H O atom h H HOH To appreciate the effect of hydrogen bonding consider the A 8 compounds uoromethane CH3F and methanol CH3OH Both of these have about the same molecular weight and CH3 CHBOH dipole moment We might expect the magnitude of the lMFs in each of these compounds to be roughly the same and molecular We gll mm 3403 3204 therefore might expect their boiling points to be comparable dipole momem D 181 170 However as you can see there is a large difference in their boiling points so there must be some type of IMF present in boiling point C 78 65 methanol which is not present in uoromethane 334 Let s consider valiations in boiling points of some hydrogen containing compounds of groups IV to VII There is a trend observed where as the atomic weight of the nonhydrogen atom decreases the boiling point decreases This trend does not hold for the compounds containing F O and N These are the atoms which allow for hydrogen bonding Hydrogen bonds are substantially stronger than van der Waals forces but in most cases considerably weaker than covalent or ionic bonds 12D in mu m an am an mu 4n EIBEI 2D EIED aamng pmth a C aamng pmth a C HTE 2 mm EIZEI mm EMU DMD EIBEI man H25 2D 4D EEI ED mu 1m 2D 4D EEI ED mu 12D Mulecularwelght Mulecularwelght A E
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