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Solution: In 11–18, find the indicial equation and the

Fundamentals of Differential Equations | 8th Edition | ISBN: 9780321747730 | Authors: R. Kent Nagle, Edward B. Saff, Arthur David Snider ISBN: 9780321747730 43

Solution for problem 17E Chapter 8.6

Fundamentals of Differential Equations | 8th Edition

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Fundamentals of Differential Equations | 8th Edition | ISBN: 9780321747730 | Authors: R. Kent Nagle, Edward B. Saff, Arthur David Snider

Fundamentals of Differential Equations | 8th Edition

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Problem 17E

Problem 17E

In Problems 11–18, find the indicial equation and the exponents for the specified singularity of the given differential equations.

Step-by-Step Solution:
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4/4/16 EXAMAPRIL14 th Ø 4/12NickTreichishostingareviewsession@415pminFulmer125 Ø 4/12Finneganishostingareviewsessioninthepit@7 Ø 4/11@515theChemclubishostingareviewsession AXE • • n=thenumberofbondinggroupsonthecentralatom • m=thenumberoflonepairsonthecentralatom • ANYtypeofbond(single,double,triple)isonebondinggroup • n+m=thenumberofelectrongroupsonthecentralatom ElectronGeometry • Thenumberofelectrongroupsdeterminesthis • Thereareonly5,seetable10.1 • Determinestheidealbondangles-elementstryandarrangethemselvesasfar awayfromeachotheraspossiblebecausetheelectronsrepulsethemselves MolecularGeometry(shape)-electrongeometryandthenumberoflonepairs determinethemoleculargeometry • Themolecularshape,thebonpolarities,andtheformalchargedistribution determinethemolecularpolarity 4/6/16 BondAngles • ElectronGeometrydeterminestheidealbondangles(theyareapproximate) Linear:180degreeangles Triganolplanar:120degreeangles Tetrahedral:109.5degreeangles Trigonalbipyramidal:90,120degreeangles Octahedral:90degreeangles • Lonepairstakeupmorespacethanbondingpairs • Doublebondstakeupmorespacethanasinglebonds • ImportantNote:Whendealingwithresonancestructures,theamountof spacethe“rotating”doublen=bondtakesupisnegligiblebecauseitis technicallyalldoublebonds ▯ • ElectronGeometry:TriganolBipyramidal • ℎ:Linearduetothe180degreeangle HowdowedothebondanglesforthismoleculeByusingtheideathatdouble bondstakeupmorespacethanasingle,andlonepairstakemorespacethanbonds • OctahedralElectronGeometry: ▯ ▯ • Molecularshape:squareplanar,duetothe90degreeangle • BondanglesforF-Xe-Fis90degrees • ElectronGeometry:Tetrahedral • MolecularShape:Triganolpyramidal • BondAnglesforH-N-Hislessthan109.5becausethelonepairwillmakethe anglesmallerthanthatofanormaltetrahedralmolecule NoticehowitisTetrahedralwiththelonepair,fortheshapethelonepairisnot drawn PolarandNon-PolarMolecules • Somethingispolarifithasanegativesideandanonpolarside • Inmoleculesthisisdeterminedbysymmetryaroundthecentralatom • If a molecule is symmetric (by polar bonds)around the central atom, the charges cancel eachother out • If the molecule is not semetric(by polar bonds) than the molecule is polar • A numeric measure of polarity is the Dipole moment(μ) • The more polar a molecule the larger the dipole moment • Is ▯ polar or non-polar Non-polar • Is ▯polar or non polar Non polar • Is ▯olar or non polar Polar • Look at the bonds and the way the bonds are arranged to see if they are polar or not! ValenceBondTheory • Acovalentbondisproducedbytheoverlapoforbitalsintheregion betweenthetwoatoms • Thegreatertheoverlap,thestrongerthebond. • But,theatomicorbitalsdonotalwayspointintherightdirectionsto producetheshapesthatthemoleculesaresupposedtohave Toexplainthis,itisassumedthattheatomicorbitalsaremixedtoproduce‘hybrid’ orbitalsthatpointinthecorrectdirection. • Hybridorbitalsarenamedfortheorbitalsthatcontributetothem.For Example isacombinationofonesorbitalandtwoporbitals • ImportantNote:Allorbitalsthataremixedmustcomefromthesame shell.ForExample3pand3scanbehybrids,but2pand4scannotbe combinedtogether. • The▯totalnumberoforbitalsisunchanged(Therewillbe2orbitals,three orbitalsandsoon) EachhybridhasitsownGeometryassociatedwithit,asshownbelow NoticehowforthegroundstateofCarbonthe2sorbitalisfull,butthe2porbitalis not▯evenhalffull,thismakescarbonunstablesothetwoorbitalscombinetoform ,makingcarbonstable • Singlebondsareformedbyoverlappingorbitalsinbetweenthe atoms.Thesebondsarecalledsigma(σ)bonds. • Doubleandtriplebondsalsocontainaσ-bondbutthesecond(andthird bond)cannotformdirectlybetweentheatoms(becausethereisalreadya pairofelectronsthere) • Theadditionalbondsareformedbyunhybridizedp-orbitalsthat overlapintheareastoeithersideofthesigmabond.Thesebondsare calledpi(π)bonds. • Adoublebondconsistsofaσ-bondandaπ-bond. • Atriplebondconsistsofaσ-bondandtwoπ-bonds. ThisDiagramshouldhelpyouvisualizetheprincipalofsigmaandpibonds

Step 2 of 3

Chapter 8.6, Problem 17E is Solved
Step 3 of 3

Textbook: Fundamentals of Differential Equations
Edition: 8
Author: R. Kent Nagle, Edward B. Saff, Arthur David Snider
ISBN: 9780321747730

Fundamentals of Differential Equations was written by and is associated to the ISBN: 9780321747730. The answer to “In 11–18, find the indicial equation and the exponents for the specified singularity of the given differential equations.” is broken down into a number of easy to follow steps, and 18 words. This full solution covers the following key subjects: Differential, equation, equations, exponents, Find. This expansive textbook survival guide covers 67 chapters, and 2118 solutions. The full step-by-step solution to problem: 17E from chapter: 8.6 was answered by , our top Calculus solution expert on 07/11/17, 04:37AM. Since the solution to 17E from 8.6 chapter was answered, more than 286 students have viewed the full step-by-step answer. This textbook survival guide was created for the textbook: Fundamentals of Differential Equations , edition: 8.

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Solution: In 11–18, find the indicial equation and the