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Course: CHEM 211, Fall 2011
School: George Mason
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GeorgeMasonUniversity GeneralChemistry211 Chapter10 TheShapes(Geometry)ofMolecules Acknowledgements CourseText:Chemistry:theMolecularNatureofMatterand Change,6thedition,2011,MartinS.Silberberg,McGrawHill 04/22/12 TheChemistry211/212GeneralChemistrycoursestaughtat GeorgeMasonareintendedforthosestudentsenrolledinascience /engineeringorientedcurricula,withparticularemphasison...

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GeorgeMasonUniversity GeneralChemistry211 Chapter10 TheShapes(Geometry)ofMolecules Acknowledgements CourseText:Chemistry:theMolecularNatureofMatterand Change,6thedition,2011,MartinS.Silberberg,McGrawHill 04/22/12 TheChemistry211/212GeneralChemistrycoursestaughtat GeorgeMasonareintendedforthosestudentsenrolledinascience /engineeringorientedcurricula,withparticularemphasison chemistry,biochemistry,andbiologyThematerialontheseslidesis takenprimarilyfromthecoursetextbuttheinstructorhasmodified, condensed,orotherwisereorganizedselectedmaterial. Additionalmaterialfromothersourcesmayalsobeincluded. Interpretationofcoursematerialtoclarifyconceptsandsolutionsto problemsisthesoleresponsibilityofthisinstructor. 1 LewisElectronDotSymbols ALewiselectrondotsymbolisasymbolinwhichthe electronsinthevalenceshellofanatomorionare representedbydotsplacedaroundthelettersymbolof theelement Notethatthegroupnumberindicatesthenumberof valenceelectrons Group I Group II Group III Group IV Group V Group VI Group VII Group VIII :: : : : 2 2 1 04/22/12 2 2 1 2 2 2 3 2 4 : . . Na . Mg Al Si . P S . Cl . : Ar : ... : . .. . . : . . 3s 3s 3s 3p 3s 3p 3s 3p 3s 3p 3s 3p5 3s 3p6 2 LewisElectronDotFormulas ALewiselectrondotformulaisanillustrationusedto representthetransferofelectronsduringtheformation ofanionicbond TheMagnesiumhastwoelectronstogive,whereasthe Fluorineshaveonlyonevacancyeach 04/22/12 F :: ] 2+ Mg F . [ :: :: [ - :: :: : Mg . . F. : F :: ] - Consequently,Magnesiumcanaccommodatetwo 3 LewisStructures Thetendencyofatomsinamoleculetohaveeight electrons(ns2np6)intheiroutershell(twoforhydrogen) iscalledtheoctetrule Youcanrepresenttheformationofthecovalentbondin H2asfollows: H+H 04/22/12 HH ThisusestheLewisdotsymbolsforthehydrogen atomandrepresentsthecovalentbondbyapairof dots 4 TheElectronProbability DistributionfortheH2Molecule 04/22/12 5 LewisStructures ThesharedelectronsinH2spendpartofthetimeinthe regionaroundeachatom : HH 04/22/12 Inthissense,eachatominH2hasahelium(1s2) configuration 6 LewisStructures TheformationofabondbetweenHandClto giveanHClmoleculecanberepresentedina similarway . Cl : : 04/22/12 H : Cl : : + : : H. Thus,hydrogenhastwovalenceelectrons aboutit(asinHe)andClhaseightvalence electronsaboutit(asinAr) 7 LewisStructures FormulassuchasthesearereferredtoasLewis electrondotformulasorLewisstructures :: :: H Cl Anelectronpairiseithera: bondingpair(sharedbetweentwoatoms) lonepair(electronpairthatisnotshared) Hydrogenhasnounbondedpairs Chlorinehas3unbondedpairs 04/22/12 8 LewisStructures RulesforobtainingLewiselectrondotformulas Writetheskeletonstructureofthemoleculeorion Putatomwithlowestgroupnumberandlowest electronegativityasthecentralatom Distributeelectronstoatomssurroundingthecentral atomtosatisfytheoctetruleforeachatom Distributetheremainingelectronsaspairstothe centralatom(oratoms) 04/22/12 Calculatethenumberofvalenceelectronsforthe molecule(=group#foreachatom),addthecharge ofanionandsubtractthechargeofacation IftheCentralatomisdeficientinelectronsto completetheoctet;moveelectronpairsfrom surroundingatomstocompletecentralatomvalence 9 PracticeProblem WritealewisstructureforCCl2F2 Step1:ArrangeAtoms(CarbonisCentralAtom becauseishasthelowestgroupnumberandlowest electronegativity Step2:Determinetotalnumberofvalenceelectrons 1xC(4)+2xCl(7)+2xF(7)=32 Step3:Drawsinglebondstocentralatomandsubtract 2eforeachsinglebond(4x2=8) 328=24remaining Step4:Distributethe24remainingelectronsinpairs aroundsurroundingatoms(3electronpairs aroundeachFluorideatom) 04/22/12 10 WritingLewisDotFormulas TheLewiselectrondotformulaofacovalent compoundisasimpletwodimensional representationofthepositionsofelectronsina molecule 04/22/12 Bondingelectronpairsareindicatedby eithertwodotsoradash Inaddition,theseformulasshowthepositions oflonepairsofelectrons 11 WritingLewisDotFormulas Thefollowingrulesallowyoutowriteelectron dotformulasevenwhenthecentralatomdoes notfollowtheoctetrule Toillustrate,drawthestructureof: PhosphorusTrichloride PCl 3 Contonnextslide 04/22/12 12 WritingLewisDotFormulas Step1:Totalallvalenceelectronsinthe molecularformula.Thatis,totalthegroup numbersofalltheatomsintheformula 5 e- P 3s23p3 PCl 3 (7 e ) x 3 - Cl 3s23p5 (2+3) + 3x(2+5) = 5+21 26 total electrons 04/22/12 Forapolyatomicanion,addthenumberof negativechargestothistotal Forapolyatomiccation,subtractthenumber Contonnextslide ofpositivechargesfromthistotal 13 WritingLewisDotFormulas Step2:Arrangetheatomsradially,withtheleast electronegativeatominthecenter.Placeone pairofelectronsbetweenthecentralatomand eachperipheralatom Cl Cl P 266=20remaining Cl Contonnextslide 04/22/12 14 WritingLewisDotFormulas : Cl Cl P : : : : Step3:Distributetheremainingelectronstothe peripheralatomstosatisfytheoctetrule : : : Cl : 26(3x6+6)=2remaining Contonnextslide 04/22/12 15 WritingLewisDotFormulas : : P Cl : : Cl : : : Step4:Distributeanyremainingelectrons(2)to thecentralatom.Ifthenumberofelectronson thecentralatomislessthanthenumberof electronsrequiredtocompletetheoctetforthat atom,useoneormoreelectronspairsfrom otheratomstoformdoubleortriplebonds Phosphorushasanoctetofelectrons Nodoublebondsrequired 04/22/12 : : Cl : 16 ExceptionstotheOctetRule Althoughmanymoleculesobeytheoctetrule, thereareexceptionswherethecentralatomhas morethaneightelectrons 04/22/12 Generally,ifanonmetalisinthethirdperiod orgreateritcanaccommodateasmanyas twelveelectrons,ifitisthecentralatom Theseelementshaveunfilleddsubshells thatcanbeusedforbonding 17 ExceptionstotheOctetRule Forexample,thebondinginphosphoruspentafluoride, PF5,showstenelectronssurroundingthephosphorus Totalvalenceelectrons : : DistributeelectronstoFatoms 5x6=30 Establishbondingpairs F: : : : F: P F : : F : : :F: : : 5x7+5=40 5x2=10 Remainingelectrons 403010=0 SincePhosphorusisinPeriod3,PF5isahypervalentmoleculeand Phosphorushas0nonbondingpairs thephosphorusutilizeselectronsfromothershells(vancantdorbitals) tocreateavalenceshellwithmorethan8electrons 04/22/12 18 ExceptionstotheOctetRule Inxenontetrafluoride,XeF4,thexenonatommust accommodatetwoextralonepairs Xe F: :: : :: : F: : : :F : : :F Totalvalenceelectrons 4x7+8=36 DistributeelectronstoFatoms 4x6=24 Establishbondingpairs 4x2=8 Remainingelectrons 36248=4 Add2nonbondingpairstoXe Xeviolatesoctetrule 04/22/12 XeF4isahypervalentmoleculeand utilizesvacantdorbitalstocreatea 19 DelocalizedBonding:Resonance Thestructureofozone,O3,canberepresentedbytwo differentLewiselectrondotformulas Ozone(O3) 04/22/12 O: :O O :: :: :: O or :: : : O O Experimentsshow,however,thatbothbondsare identical 20 DelocalizedBonding:Resonance AccordingtoResonanceTheory,thesetwoequalbonds arerepresentedasonepairofbondingelectronsspread overtheregionofallthreeatoms Ozone(O3) O O 04/22/12 O Thisiscalleddelocalizedbonding,inwhichabonding pairofelectronsisspreadoveranumberofatoms 21 Resonance&BondOrder Recall(Chap9)BondOrder Thenumberofelectronpairsbeingsharedbyanypair ofBondedAtomsor Thenumberofelectronpairsdividedbythenumberof bondedatompairs Bond Order = Ex.Ozone Bond Order = 04/22/12 Electron Pairs Bonded - Atom Pairs Electron Pairs 3 = = 1.5 Bonded - Atom Pairs 2 22 PracticeProblem Inthefollowingcompounds,theCarbonatomsformasinglering. DrawaLewisstructureforeachcompound,identifycasesforwhich resonanceexists,anddeterminetheCCbondorder(s). Electron Pairs Bonded - Atom Pairs 1 = =1 1 Bond Order = C3H4 Bond Order = C3H6 04/22/12 Electron Pairs 2 = =2 Bonded - Atom Pairs 1 Electron Pairs Bonded - Atom Pairs 1 = =1 1 Bond Order = 23 PracticeProblem C4H6 Bond Order = Bond Order = Electron Pairs 1 = =1 Bonded - Atom Pairs 1 Electron Pairs 2 = =2 Bonded - Atom Pairs 1 C4H4 Bond Order = 04/22/12 Electron Pairs 2 = =2 Bonded - Atom Pairs 1 Bond Order = Electron Pairs 1 = =1 Bonded - Atom Pairs 1 24 PracticeProblem C6H6 Electron Pairs 9 = = 1.5 Bonded - Atom Pairs 6 Note : There are 6 equivalent C - C bonds in the aromatic Benzene molecule Bond Order = 04/22/12 25 FormalCharge&LewisStructures Incertaininstances,morethanonefeasibleLewis structurecanbeillustratedforamolecule Forexample,H,CandN HC N: or H N C: Theconceptofformalchargecanhelpdiscernwhich structureisthemostlikely FormalCharge: Anatomsformalchargeis: 04/22/12 Minusallunsharedelectrons Totalnumberofvalenceelectrons Minusofitssharedelectrons FormalChargesmustsumtoactualchargeof species: 26 FormalCharge&LewisStructures WhenyoucanwriteseveralLewisstructures,choose theonehavingtheleastformalcharge FormI 1 e- 4 e- HC domain electrons I IV FormII 5 e- N: V 1 eor H I 5 e- 4e- V group number IV +1 N C: 1 FC:TotalValenceeunsharedeshared e FCH:[10(2)]=0 FCH:[10(2)]=0 FCC:[40(8)]=0 FCC:[42(6)]=1 PreferredFormFormI(LeastFormalCharge)(8)]=+1 FCN:[52(6)]=0 FCN:[50 Note:HCNisaneutralmolecule SumofFormalChargesinthepreferredform(0)equalsmolecularcharge(0) 04/22/12 27 FormalCharge&LewisStructures Ozone FCOA:[64(4)]=0 FCOA:[66(2)]=1 FCOB:[62(6)]=+1 FCOB:[62(6)]=+1 FCOC:[66(2)]=1 FCOC:[64(4)]=0 BothResonanceformshavethesameformalcharge andthus,areidentical Note:Ozone(O3)isaneutralmolecule SumofFormalCharges(0)equalsmolecularcharge(0) 04/22/12 28 B F F FCB=30(1/2*6) FCB=30(1/2*8) =1 FCF=74(1/2*4) =+1 O O S SulfurDioxide SO2 FCS=62(1/2*6)=1 04/22/12 O S =0 EventhoughBviolatesOctetRule, thisisthepreferredformbecauseit haslessformalcharge F O B F F F BoronTrifuoride BF3 FormalCharge&LewisStructures FCS=62(1/2*8)=0 PreferredForm(LessFormalCharge) 29 Resonance/FormalChargeNitrate Ion TotalValenceelectrons3x6(O)+1x5(N)+1(ioncharge)=24 Add1pairelectronsbetweencentralatomandeachotheratom3x2=6 Addelectronstooxygenatomstocompleteoctet Nitrogenstillmissing2electronstocompleteoctet Borrow2electronsfromoneoxygentoformdoublebond FormalChargeNitrogen:5(0+*8)=54=+1 FormalChargeSinglebondedOxygen:6(6+*2)=67=1x2=2 FormalChargeDoublebondedOxygen:6(4+*4)=66=0 NetChargeofionis:+1+(2)=1 04/22/12 30 Resonance/FormalChargeCyanateIon FCN=5(6+*2)=2 FCC=4(0+*8)=0 FCO=6(2+*6)=+1 FCN=5(4+*4)=1 FCC=4(0+*8)=0 FCO=6(4+*4)=0 FCN=5(2+*6)=0 FCC=4(0+*8)=0 FCO=6(6+*2)=1 PreferredForm: EliminateIHigherformalchargeonNitrogenthanCarbon&Oxygen PositiveformalchargeonOxygen,whichismore electronegativethanNitrogen EliminateIIFormsII&IIIhavethesamemagnitudeofformalcharges, butformIIIhasa1chargeonthemoreelectronegative Oxygenatom FormsII&IIIbothcontributetotheresonanthybridoftheCyanateIon, butformIIIisthemoreimportant 04/22/12 Note:NetformalchargeinformIIIissameasioniccharge(1) 31 FormalChargevsOxidationNo FormalChargeisusedtoexamineresonancehybridstructures, whereasOxidationNumberisusedtomonitorREDOXreactions FormalChargeBondingelectronsareassignedequallytothe atomsasifthebondingwereNonpolarcovalent,i.e.,eachatom hashalftheelectronsmakingupthebond FormalCharge=valencee(unbondede+bondinge) OxidationNumberBondingelectronsaretransferredcompletely tothemoreelectronegativeatom,asifthebondingwereIonic OxidationNo.=valencee(unbondede+bondinge) 04/22/12 32 FormalChargevsOxidationNo FC(2)(0)(+1)(1)(0)(0)(0)(0)(1) N5(6+(1))=2 C4(0+(8))=0 O6(2+(6))=+1 N5(4+(4))=1 C4(0+(8))=0 O6(4+(4))=0 N5(2+(6))=0 C4(0+(8))=0 O6(6+(2))=1 ON(3)(+4)(2)(3)(+4)(2)(3)(+4)(2) N5(6+2))=3 C4(0+0))=+4 O6(2+6))=2 N5(4+4))=3 C4(0+0))=+4 O6(4+4))=2 N5(2+6))=3 C4(0+0))=+4 O6(6+2))=2 Note:BothNitrogen(N)&Oxygen(O)aremoreelectronegativethan Carbon(C);thus,inthecomputationofOxidationNumberallthe electronsaretransferredtotheN&OleavingCwithnolonepairs andnobondedpairs Note:OxidationNosdonotchangefromoneresonanceformtoanother (electronegativitiesremainsame) 04/22/12 33 TheValenceShellElectronPair RepulsionModel(VSEPR) TheValenceShellElectronPairRepulsion(VSEPR) modelpredictstheshapesofmoleculesandionsby assumingthatthevalenceshellelectronpairsare arrangedasfarfromoneanotheraspossible MoleculargeometryTheshapeofamoleculeis determinedbythepositionsofatomicnucleirelativeto eachother,i.e.,angulararrangement CentralAtom 04/22/12 PlaceatomwithLowerGroupNumberincenter (NinNF3needsmoreelectronstocompleteoctet) Ifatomshavesamegroupnumber(SO3orClF3),place theatomwiththeHigherPeriodNumberinthe center(Sulfur&Chlorine) 34 VSEPRModelofMolecularShapes Thefollowingrulesandfigureswillhelpdiscern electronpairarrangements DrawtheLewisstructure Determinehowmanybondingelectronpairsare aroundthecentralatom. Determinethenumberofnonbondingelectron pairs Countamultiplebondasonepair 04/22/12 SelecttheCentralAtom(LeastElectronegative Atom) Arrangetheelectronpairsasfarapartas possibletominimizeelectronrepulsions 35 VSEPRModelofMolecularShapes Topredicttherelativepositionsofatomsarounda givenatomusingtheVSEPRmodel,youfirstnote thearrangementoftheelectronpairsaroundthat centralatom MolecularNotation: A TheCentralAtom(LeastElectronegative atom) X TheLigands(BondingPairs) a TheNumberofLigands AXaEb E NonBondingElectronPairs b TheNumberofNonBondingElectronPairs 04/22/12 Double&TripleBondscountasasingleelectron pair 36 VSEPRModelofMolecularShapes Molecule Lewis Structure ALxNy Notation BeH2 AX2E0 BH3 AX3E0 CH2Li2 AX4E0 or AX2X2E0 OH2 BiF5 04/22/12 Geometric ePair Arrangement a=2 b=0 a+b=2 a=3 b=0 a+b=3 a=4 b=0 a+b=4 3D Structure 3DView & Isomers Linear Trigonal Planar Tetrahedral AX2E2 a=2 b=2 a+b=4 Tetrahedral AX5E0 a=5 b=0 a+b=5 Trigonal Bipyramidal 37 VSEPRModelofMolecularShapes Molecule SF5Cl PCL4Br TeCl3Br SF4Cl2 XeF2 04/22/12 Lewis Structure AX6E0 or AX5X1E0 Geometric ePair Arrangement a=6 b=0 a+b=6 AX5N0 or AX4X1E0 a=5 b=0 a+b=5 Trigonal Bipyramidal AX4E1 or AX3X1E1 b=4 a=1 a+b=5 Trigonal Bipyramidal AX6E0 or AX4X2E0 a=6 b=0 a+b=6 ALxNy Notation AX2E3 a=2 b=3 a+b=5 3D Structure 3DView & SelectedIsomers Octahedral Octahedral Trigonal Bipyramidal 38 ArrangementofElectronPairs AboutanAtom:BasicShapes CS2HCNBeF2NO2+ 04/22/12 39 ArrangementofElectronPairs AboutanAtom:BasicShapes SO3BF3NO3NO2CO32 SO2O3PbCl2SnBr2 04/22/12 40 ArrangementofElectronPairs AboutanAtom:BasicShapes CH4SiCl4 SO42ClO4 NH3PF3ClO3H3O+ 04/22/12 H2OOF2SCl2 41 ArrangementofElectronPairs AboutanAtom:BasicShapes PF5AsF5SOF4 ClF3BrF3 04/22/12 SF4,XeO2F2,IF4+,IO2F2 XeF2I3IF2 42 ArrangementofElectronPairs AboutanAtom:BasicShapes SF6 IOF5 BrF5TeF5XeOF4 04/22/12 XeF4ICl4 43 ElectronPairArrangement 04/22/12 44 ElectronPairArrangement 04/22/12 45 LinearGeometry Twoelectronpairs(lineararrangement) :: :: Carboniscentralatom becauseithaslower groupnumber Doublebondscountasasingleelectronpair 2bondingpairs 0nonbondingpairs AXaEb=a+b=2+0=2(Linear) 04/22/12 Thus,accordingtotheVSEPRmodel,thebondsare arrangedlinearly(bondangle=180o) 46 TrigonalPlanarGeometry ThreeelectronpairsonCentralatom CentralAtomCarbon :O: 3bondingelectronpairs (doublebondcountsas1pair) C 04/22/12 :: :: :Cl Cl : 0nonbondingelectronpairs a+b=3+0=3 TrigonalPlanar Thethreegroupsofelectronpairsarearrangedina trigonalplane.Thus,themolecularshapeofCOCl2is trigonalplanar.TheBondangleis120o 47 TrigonalPlanarGeometry EffectofDoubleBonds Bondanglesdeviatefromidealangleswhen surroundingatomsandelectrongroupsarenot identical Adoublebondhasgreaterelectrondensityand repelstwosinglebondsmorestronglythantheyrepel eachother H 120o H 120o = CO Ideal 04/22/12 H 116o H 122o = CO Actual 48 TrigonalPlanarGeometry EffectofLonePairs Themolecularshapeisdefinedonlybythepositions ofthenuclei Whenoneofthethreeelectronpairsinatrigonal planarmoleculeisalone(nonbonding)pair,itisheld byonlyonenucleus Itislessconfinedandexertsastrongerrepulsive forcethanabondingpair Thisresultsinadecreaseintheanglebetweenthe bondingpairs ThenormalTrigonal Planaranglebetween thebondingpairsis120o 04/22/12 49 TrigonalPlanarGeometry Threeelectronpairs(EffectofLonepairs) (trigonalplanararrangement) : O BF3 <120o : : O : : : O SO3 NO3 CO32 Ozonehastwobondingelectronpairsaboutthe centraloxygen(doublebondcountsas1pair) Thereisonenonbondinglonepair Thesegroupshavea: TrigonalPlanararrangement AXaEb(a+b=2+1=3) 04/22/12 Sinceoneofthegroupsisalonepair,themolecular 50 TetrahedralGeometry Fourelectronpairs (TetrahedralArrangement) : H :Cl: :: :: :N H H :O : : :Cl C Cl: :Cl: H H Fourelectronpairsaboutthecentralatomleadtothree differentmoleculargeometries a+b=4+0a+b=3+1a+b=2+2 =4=4=4 04/22/12 51 TetrahedralGeometry : MolecularGeometriesproducedbyvariablenon bondingelectronpairs H AX4 109o H CH4,SiCl4,SO42,ClO4 O : H H H AX4E 107o 107 o 04/22/12 : Cl: N : : Cl : :: :: :Cl C Noteimpactofnonbondingelectronpairsonbondangle : :Cl: AX2E2 105o 10 7o PF3,ClO3,H3O+ 105 o OF2,SCl2 52 TrigonalBipyramidal Fiveelectronpairs (trigonalbipyramidalarrangement) : : F: : :F: : P : : :F: : :F : 04/22/12 90oaxial 120oequatorial F: ASF5SOF4 Thisstructureresultsinboth90oand120o bondangles 53 TrigonalBipyramidal Othermoleculargeometriesarepossiblewhenoneor moreoftheelectronpairsisalonepair F F F S : F : Cl F : F F <90o(ax) <120o(eq) XeO2F2IF4+IOF2 04/22/12 <90 (ax) o ClF3BrF3 F : Xe : : F 180o XeF2I3IF2 54 OctahedralGeometry Sixelectronpairs (Octahedralarrangement) : :: S :: : :F: : : : :F: :F :F F: 90o F: : SF6IOF5 Thisoctahedralarrangementresultsin: 04/22/12 90obondangles 55 OtherGeometries Sixelectronpairs (octahedralarrangement) F I F F Xe F F : F F : F F : Iodineviolatesoctetrule Iodineissp3d2hybridized Iodineusesdorbitals Noblegasesnot alwaysinert Xenonforms 6electrondomains square pyramidal square planar <90o 90o BrF5TeF5XeOF4 04/22/12 XeF4ICl4 56 PracticeProblem IntheICl4ion,theelectronpairsarearrangedaroundthe centraliodineatomintheshapeof a.atetrahedron b.atrigonalbipyramid c.asquareplane d.anoctahedron e.atrigonalpyramid Ans:a Cl AX4 Cl I Cl Cl AXaEb a+b=4+0=4(AX4Tetrahedral) 04/22/12 57 DipoleMomentand MolecularGeometry Thedipolemomentisameasureofthedegree ofchargeseparationinamolecule Thepolarityofindividualbondswithina moleculecanbeviewedasvectorquantities Thus,moleculesthatareperfectlysymmetric haveazerodipolemoment.Thesemolecules areconsiderednonpolar + 04/22/12 58 DipoleMomentand MolecularGeometry However,moleculesthatexhibitanyasymmetryinthe arrangementofelectronpairswouldhaveanonzero dipolemoment.Thesemoleculesareconsideredpolar : H N H H + NH3PF3ClO3H3O+ 04/22/12 59 DipoleMomentand MolecularGeometry Formula DipoleMoment AX Linear CanBenonzero AX2E0 Linear Zero AX3E0 TrigonalPlanar Zero AX2E1 TrigonalPlanarBent CanBenonzero AX4E0 Tetrahedral Zero AX3E1 TetrahedralTrigonalPyramidal CanBenonzero AX2E2 TetrahedralBent CanBenonzero AX5E0 TrigonalBipyramidal Zero AX4E1 TrigonalBipyramidalSeeSaw CanBenonzero AX3E2 TrigonalBipyramidalTShaped CanBenonzero AX2E3 TrigonalBipyramidalLinear CanBenonzero AX6E0 Octahedral Zero AX5E1 OctahedralSquarePyramidal CanBenonzero AX4E2 04/22/12 MolecularGeometry OctahedralSquarePlanar Zero 60 PracticeProblem The Nitrogen atom would be expected to have the positive end of the dipole in the species + a. NH4 b. Ca3N2 c. HCN d. AlN N is more Electronegative than H N is more EN than Ca N is more EN than C N is more EN than Al O is more EN than Nitrogen e. NO+ Ans: e 04/22/12 61 PracticeProblem Whichofthefollowingmoleculesispolar? d.NO2 e.SF6 Ans:d O N O c.CO2 + O N= + O O = b.CBr4 a.BF3 N O TheLewisstructuresforBF3,CBr4,CO2,andSF6donothave anynonbondingelectronsonthecentralatom TheLewisstructureforNO2showsonedoublebondanda lonenonbondingelectronontheNitrogen TheVSEPRMolecularGeometryforNO2isAX2E1 (a+b=2+1=3)TrigonalPlanar FormalChargeonNis51(6)=+1 04/22/12 62 PracticeProblem Whichofthefollowingcompoundsisnonpolar? a.XeF2 b.HCl d.H2S c.SO2 e.N20 Ans:a 04/22/12 HCLisionicandverypolar SO2hasAX2E1TrigonalPlanarBentgeometrywitha dipolemoment(polar) H2ShasAX2E2TetrahedralBentgeometryandwitha dipolemoment(polar) N2OhasAX2E0linearwithasymmetricgeometry. SinceoxygenismoreENthanN,themoleculeispolar 63 EquationSummary Bond Order = Electron Pairs Bonded - Atom Pairs Formal Charge (FC) = Total Valence e - - (Non - Bonding e - + 1 / 2 Bonding e - ) Oxidation Number (ON) = Total Valence e- - (Non - Bonding e - + Bonding e - ) VSEPR Model - AXaEb Geometric Configuration Determined by the sum (a + b) 04/22/12 64
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George Mason - CHEM - 211
GeorgeMasonUniversityGeneralChemistry211Chapter11TheoriesofCovalentBondingAcknowledgementsCourseText:Chemistry:theMolecularNatureofMatterandChange,6thedition,2011,MartinS.Silberberg,McGrawHill04/22/12TheChemistry211/212GeneralChemistrycoursestaugh
George Mason - CHEM - 211
GeorgeMasonUniversityGeneralChemistry211Chapter12IntermolecularForces:Liquids,Solids,andPhaseChangesAcknowledgementsCourseText:Chemistry:theMolecularNatureofMatterandChange,6thedition,2011,MartinS.Silberberg,McGrawHillTheChemistry211/212GeneralChem
George Mason - CHEM - 211
GENERAL CHEMISTRY I (Chem 211)Lecture SyllabusInstructor: Dr. James C. SchornickCourse:Chemistry 211-004 T 4:30Office Hrs: M, T, W, F9:30 amR2:00 pmT2:00 amTelephone: 703-993-1091Email:jschorni@gmu.edu- 7:10 pm- 11:00 am- 4:00 pm- 4:00 pm
George Mason - CHEM - 211L
Absorption Spectroscopy Spectroscopy - Study of the Interaction ofElectromagnetic Radiation (Energy) andMatter When energy is applied to matter it can beabsorbed, emitted, cause a chemical change(reaction), or be transmitted. Electromagnetic Spectr
George Mason - CHEM - 211L
Anion Cation AnalysisBackgroundAnions- Elements or molecules that have gained electrons.They have negative charge and have been reduced.They can be oxidizing agents in a ReDox reactionCations - Elements or molecules that have lost electrons.They ha
George Mason - CHEM - 211L
Chem 211 laboratoryThis Week October 2, 2003 Synthesis of AspirinNext Week The Ideal Gas LawThis experiment is not in the Slayden lab manualThe instructions for this experiment can be found on theGenchem Website:http:/chem.gmu.edu/resultsUnder Chem
George Mason - CHEM - 211L
GenChem/Organic Chemistry LaboratoryDepartment OfficeRoom343 Science &amp; Technology IMSN3E2Phone703-993-1070FAX703-993-1055Dr. James C. SchornickOffice408A Science &amp; Technology IMailboxRoom 343 Science &amp; Technology IPhone703-993-1091E-Mail
George Mason - CHEM - 211L
Density of SolutionsNext Week Sept 25, 2003Experiment:Empirical Formula of Zinc IodideReferences:Slayden, S, Chem 211, 212, 251 LaboratoryExperiments, 2003, pp. 31 35http:/chem.gmu.edu/results Click on EmpiricalFormulahttp:/classweb.gmu.edu/jscho
George Mason - CHEM - 211L
Hesss Law Heat of Reaction Enthalpy A State of Matter Function Enthalpy Change ( H) in a chemical reaction is the difference between the Heat Contents of the products and the reactants. ( H)rxn = ( H)products - ( H)reactants ( H) associated with a chemica
George Mason - CHEM - 211L
The Ideal Gas lawThe Ideal Gas LawThis experiment is not in the Slayden lab manualThe instructions for this experiment can be found on theGenchem Website:http:/chem.gmu.edu/resultsUnder Chem 211 Handouts click on:Gas Law HandoutGas Law Lab Instruc
George Mason - CHEM - 211L
Chem 211 Laboratory Next Week Oct 2, 2003 Experiment: Synthesis of Aspirin References: Slayden, S, Chem 211, 212, 251 Laboratory Experiments, 2003, pp. 57 - 66 http:/chem.gmu.edu/results Click on Synthesis of Aspirin http:/classweb.gmu.edu/jschorni/chem21
George Mason - CHEM - 211L
VSEPR Theory &amp; Molecular ModelingPurpose- To understand, visualize, and predict the spatialarrangement of molecular shapes.Approach - Use Lewis Dot diagrams, Ball &amp; Stick models, and theValence Shell Electron-Pair Repulsion (VSEPR) theory toconstruc
George Mason - CHEM - 211L
General Chemistry 211 LaboratoryNext WeekExperiment - Density of SolutionsLab Manual - p. 23-29Quiz- Material in Lab Manual and Web SitePrelab- Density ExperimentLab Report- Measurements (Pennies) Experiment is dueMeasurements The Penny Experime
George Mason - CHEM - 211L
Volumetric Analysis - Titration of VinegarVolumetric AnalysisThe quantitative determination of the concentration of one substanceby titration against a substance of known concentration.TitrationA solution of known concentration (the standard) is adde
George Mason - CHEM - 315
IsolationofCaffeineOverviewExtractionofCaffeinefromVivarin,anoverthecountercaffeinetabletAnaqueousVivarin/SodiumCarbonatemixtureisextractedwithDichloromethane(MethyleneChloride)AfterevaporationtodrynesstheproductisrecrystallizedfromAcetone/Petroleu
George Mason - CHEM - 315
SynthesisofCyclohexeneSynthesisofanAlkenebyDehydrationofanAlcoholviaE1(Elimination)MechanismSolomans&amp;Fryle: pp29730204/22/121E1SynthesisofCyclohexeneBackgroundAnEliminationreactionisatypeoforganicreactioninwhichtwosubstituentsareremovedfromamole
George Mason - CHEM - 315
GasChromatographyAcetates04/22/12GasChromatography,RefractiveIndex&amp;Distillation Thenexttwo(2)experimentsintroduceGasChromatographyandSimple&amp;FractionalDistillation. TheyarethentiedtogetheralongwiththeRefractiveIndextechniqueinathirdexperiment.ThisWe
George Mason - CHEM - 315
SpectroscopyBuildingAToolsetForTheIdentificationofOrganicCompoundsPhysicalChemical TestsPropertiesHydrocarbonsMelting PointAlkanesBoiling PointAlkenesDensityAlkynesSolubilityHalidesRefractive IndexAlcoholsAldehydesKetones04/22/12Spect
George Mason - CHEM - 315
InfraredSpectroscopy(IR)LabInfraredSpectroscopyIdentificationofUnknownTheuseofselectedphysicalpropertiesandInfraredSpectroscopytodeterminetheidentityofanunknowncompound.TextMaterialsSlayden pp.3344Pavia pp.851885`(InfraredSpectroscopy)pp.941959(
George Mason - CHEM - 315
GenChem/Organic Chemistry LaboratoryDepartment OfficeRoom343 Science &amp; Technology IMSN3E2Phone703-993-1070FAX703-993-1055Dr. James C. SchornickOfficeRoom 318 Science &amp; Technology IMailboxRoom 343 Science &amp; Technology IPhone703-993-1091E-M
George Mason - CHEM - 315
OrganicQualitativeAnalysisPhysicalProperties,ChemicaltestsandInfraredSpectroscopytoIdentify:UnknownHalide (primary,secondary,tertiary)HydrocarbonAlcohol(alkane,alkene,aromatic)(primary,secondary,tertiary)References:Slayden,S.,Stalick,W.;2010,Cata
George Mason - CHEM - 315
Experiment:Date:Grignard ReagentNamePartnersCourseSectionDrawer No.Laboratory Report Template InstructionsThe first 7 pages of this document contain hints &amp; instructions for using thetemplate and formatting the report. Delete these pages and any
George Mason - CHEM - 315
Recrystallization/FiltrationecrystallizationPurificationofanorganiccompoundbydissolvingasolidinahotsolventandrecrystallizingthecompoundbyslowcoolingacuumFiltrationSeparationofthesolidsolutefromaliquidsolventReferences:Slayden,et.al.,pp.2931PaviaT
George Mason - CHEM - 315
Simple&amp;FractionalDistillationExperimentSimple&amp;FractionalDistillationEvaluationoftherelativeeffectivenessofSimple&amp;FractionalDistillationtoseparatemixturesoforganiccompoundsbasedondifferencesinBoilingPointDeterminationofMole0romDistillateVolumeData,Gas
George Mason - CHEM - 315
TButyl(tPentyl)ChlorideSynthesisSynthesizetButyl(ortPentyl)ChlorideNote:ThisexperimentmayutilizeeithertButylAlcohol(m.p.25.7oC)ortPentylAlcohol(m.p.9.5oC)asoneofthestartingreactants.TextReferencesSlayden PaviaExp#21PaviaTech1204/22/12pp.4950p
George Mason - CHEM - 318
SynthesisofAcetanilideSynthesisofAcetanilideNucleophilicAcylSubstitution(addition/elimination)reactionbetweenAnilineandAceticAnhydrideReferencesPaviaSchornick http:/classweb.gmu.edu/jschorni/chem31804/22/12 p.65681SynthesisofAcetanilideOvervie
George Mason - CHEM - 318
Aldehydes&amp;KetonesClassificationTestsTheuseofChemicalClassificationTests,SelectedPhysicalProperties,NMR,andIRtoIdentifyanUnknownAldehydeorKetoneReferences:Pavia04/22/12Slayden p.7376WebNoteshttp:/classweb.gmu.edu/jschorni/chem318p.4914961Aldehy
George Mason - CHEM - 318
ElectrophilicAromaticSubstitution(BrominationofToluene)Demonstrationoftheeffectofamonosubstitutedelectrondonargroup(ringactivator)onsubsequentsubstitutionofothergroupsontheBenzeneringReferences04/22/12SlaydenLabManual p.7576Website:http:/classweb
George Mason - CHEM - 318
SynthesisofDibenzalacetoneSynthesisofDibenzalacetoneMixedAldolCondensation(ClaisenSchmidt)reactionbetweenAcetoneandBenzaldehydeinthepresenceof95%Ethanoland20%SodiumHydroxideReferences:Pavia04/22/12Slayden p.77Schornick http:/classweb.gmu.edu/jsch
George Mason - CHEM - 318
FriedelCraftsAlkylationPurposePreparationof4,4ditertbutylbiphenylusingtheFriedelCraftsalkylationofBiphenylthroughElectrophilicsubstitutionofaLewisBase(tButylChloride(Haloalkane)inthepresenceofFerricChlorideactingasaLewisAcidReferences:Website:http
George Mason - CHEM - 318
GrignardReagent/ReactionsPreparationofaGrignardReagent(Phenylmagnesiumbromide)andreactionwithCarbonDioxidetoformBenzoicAcidthroughanElectrophilicAdditionreactionReferences:Pavia - p. 303 309; 313 314Schornickhttp:/classweb.gmu.edu/jschorni/chem318
George Mason - CHEM - 318
SynthesisofIsopentyl(Amyl)AcetateEster(BananaOil)OverviewSynthesisAcid(H2SO4)catalyzedFischerEsterificationreactionofaCarboxylicAcid(AceticAcid)withtheHydroxylgroupofanAlcohol(Isopentyl[amyl]Alcohol).ThisisaCondensationreactionwherethemoleculesbecom
George Mason - CHEM - 318
NitrationofMethylBenzoateDemonstrationoftheeffectofanelectronwithdrawinggrouponamonosubstitutedbenzeneringonsubsequentsubstitutionofothergroupsontheBenzeneringReferences:04/22/12Pavia,etal. pp352357Slayden,etal. pp67691NitrationofMethylBenzoate
George Mason - CHEM - 318
Organic Chemistry LaboratoryBuildingAToolsetForTheIdentificationofOrganicCompoundsPhysicalPropertiesMeltingPointBoilingPointDensitySolubilityRefractiveIndex04/22/12ChemicalTestsHydrocarbonsAlkanesAlkenesAlkynesHalidesAlcoholsAldehydesKe
George Mason - CHEM - 318
SpectroscopyExperiment(NMR)DeterminationoftheIdentityofanunknownorganiccompoundusingselectedphysicalproperties,InfraredSpectroscopy,andNMRSpectroscopyUnknownList:pp.126127inSlaydenLabManualReferences Slayden,etal.pp.5960 Pavia,etal. Schornick04/
George Mason - SYST - 220
George Mason - SYST - 220
Log to base 10 usedpage 26xyXlogx12345.119.5467800.301030.4771210.60206Ylog yXYX^2y hat(y-yhat)^2 (y-ybar)^20.70757005.0231.290035 0.388339 0.090619 19.815391.662758 0.793337 0.227645 44.224531.892095 1.139154 0.362476 78.170
George Mason - SYST - 220
SYST 220 Class NotesLecture 1: Discrete Dynamical Models Introduction to ModelingMain point: Similar set of mathematical equations can be used to solve diverse range of real-worldproblemsDiscrete Dynamical Systems ModelingDiscrete: Time is measured i
George Mason - SYST - 220
SYST 220Class NotesLecture 2: Discrete DynamicalReviewword problemdynamical system: a (n + 1) = f (a (n )solve using spreadsheetcobweb analysisfind equilibrium a = f (a )Terminologya (n + 1) = f (a (n ) , First order dynamic systema (0 ) = a 0
George Mason - SYST - 220
SYST 220 Class NotesLecture 3: Discrete Dynamical ModelsReviewAffine system: a (n + 1) = ra (n ) + bSolution isa (n ) = Cr n +b1 requilibrium rn blows up if rn goes to 0 ifr &lt; 1 (stable) rn oscillates ifSolution isr &gt; 1 (unstable)r = 1 (mar
George Mason - SYST - 220
SYST 201 Class NotesLecture 4: Discrete Dynamical ModelsNon-homogeneous Dynamic Systems: Exponential Driving TermsNon-homogeneous Dynamic SystemsSystems so far: a (n +1) = ra (n) + bThis chapter: a (n +1) = ra (n) + g ( n)g(n) can be thought of as a
George Mason - SYST - 220
SYST 220 Class NotesLecture 5: Discrete Dynamical ModelsNon-homogeneous Dynamic Systems: Exponential Driving TermsSection 4.1 (p.160)1 1. Problem Statement:Given: a) a(n +1) = 2a(n) +3nd) a(n+1) = 2a(n) + 3n + 4nf) a(n+1) = 3a(n) +2 * 4n- 6General
George Mason - SYST - 220
Lecture 6: Discrete Dynamical ModelsSecond-order systemsA second-order system is a system in which the present state of the system depends uponthe previous two system states.Example: a (n) = - 3.5a (n - 1) + 2a (n - 2)Note: This system is also equiva
George Mason - SYST - 220
1.26 1.12 (new book)1.33 1.19 (new book)1.42 1.25 (new book)1.43 1.26 (new book)
George Mason - SYST - 220
3.2 a3.4 b Roots are -5 and -5 Steady part is 3 There are 2 exponential terms for the transient part 3.5 c Complex roots with positive real part. UNSTABLE 3.6 b or 3.9 b (new book)
George Mason - SYST - 220
SYST 220: Dynamical Modeling ISpring 2012Systems Engineering and Operations ResearchGeorge Mason UniversityCourse Overview: An important problem in engineering is to predict the behavior of systems thatchange in time. Such systems are called dynamica
George Mason - OR - 649
Meta heuristics Final exam: Due May 9th1) Solve the TSP with GA. Distance in hundreds of miles. Generate an initial population ofsize 3. Use one point cross over and 1 mutation per iteration. Perform at least 5 iterationsNYMiami DallasChicagoNew Yor
George Mason - OR - 649
Metaheuristics Meta Greekwordforupperlevelmethods Heuristics Greekwordheuriskein artofdiscoveringnewstrategiestosolveproblems. ExactandApproximatemethods Exact MathprogrammingLP,IP,NLP,DP Approximate Heuristics Metaheuristicsusedfor Combinatoria
George Mason - OR - 649
MetaheuristicsMeta- Greek word for upper level methodsHeuristics Greek word heuriskein art of discoveringnew strategies to solve problems.Exact and Approximate methodsExactApproximateMath programming LP, IP, NLP, DPHeuristicsMetaheuristics used f
George Mason - OR - 649
MetaheuristicsThe idea: search the solution space directly. No mathmodels, only a set of algorithmic steps, iterative method.Find a feasible solution and improve it. A greedy solutionmay be a good starting point.Goal: Find a near optimal solution in
George Mason - OR - 649
NeighborhoodRepresentation of solutionsVector of Binary values 0/1 Knapsack, 0/1 IP problemsVector of discrete values- Location , and assignment problemsVector of continuous values on a real line continuous,parameter optimizationPermutation sequenci
George Mason - OR - 649
Escaping local optimasAccept nonimproving neighborsIterating with different initial solutionsMultistart local search, greedy randomized adaptive searchprocedure (GRASP), iterative local searchChanging the neighborhoodTabu search and simulated anneal
UC Davis - CHI - 10
Welcome /BienvenidosDr. Lorena V. MarquezIm sitting in My HistoryClass,Im Olivas,Richardsitting in my1989history class,The instructorcommencesrapping,Im in my U.S.History class,And Im on theverge of napping.The MayflowerThe History of Chica
George Mason - OR - 649
Escaping local optimasAccept nonimproving neighborsIterating with different initial solutionsMultistart local search, greedy randomized adaptive searchprocedure (GRASP), iterative local searchChanging the neighborhoodTabu search and simulated anneal
UC Davis - CHI - 10
TheSpanishConquest,1500sBirthofMestizoNation?Conquest:Istheacquisitionofaterritoryanditsinhabitantsthroughwar.Itisaninstitutionthatrequiresenforcinglabor/economicsystems;usurpingoflocalpoliticsandgovernments;andimposingpowerthroughreligion,culture
George Mason - OR - 649
Escaping local optimasAccept nonimproving neighborsIterating with different initial solutionsMultistart local search, greedy randomized adaptive searchprocedure (GRASP), iterative local searchChanging the neighborhoodTabu search and simulated anneal
UC Davis - CHI - 10
Pre-Columbian CivilizationsPopular Image of AztecsIztacchuatl (female) and Popocatptl (male)Bering Strait Ice Bridge Melted, 9000BCIndigenous Diet: Corn, Beans, Chili, andSquashCivilizationIs where people live in large complexagricultural groups w
George Mason - OR - 649
Escaping local optimasAccept nonimproving neighborsIterating with different initial solutionsMultistart local search, greedy randomized adaptive searchprocedure (GRASP), iterative local searchChanging the neighborhoodTabu search and simulated anneal
UC Davis - CHI - 10
American Conquest:A Quest for Manifest DestinyMiguel Hidalgo y CostillaMexican War of Independence,1810-1821What to do with MexicosNorthern Frontier? Increase Population Increase Trade Increase ProductionThe Alamo, 1836Richard Henry Dana, Jr.
George Mason - OR - 649
Population-based metaheuristicsNature-inspiredInitialize a populationA new population of solutions is generatedIntegrate the new population into the current one usingone these methods by replacement which is aselection process from the new and curre
UC Davis - CHI - 10
New Spain, 1500s-1800sNorthern FrontiersRomanticismRealistic Padre JaimeSeven Cities of CibolaAn 1898 painting by Frederic Remington portrays Spanishexplorer Francisco Vazquez de Coronado on his ill-fatedquest in 1541 to find the fabled Seven Citi