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Chap 2

Course: CHE 534, Fall 2009
School: Maryville MO
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section,adetaileddescription CORROSIONFUNDAMENTALS Inthis oftheelectrochemical processesleading toand controllingcorrosionwillbeoutlined.Thefirstsectiondealswiththeelectrochemicalbasisfor corrosion,whichiscontrolledbythermodynamicprinciples,whiletheeffectofkinetic,orrate controlwillbeintroducedlaterinthesection.Itisimportanttounderstandtheroleofboth...

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section,adetaileddescription CORROSIONFUNDAMENTALS Inthis oftheelectrochemical processesleading toand controllingcorrosionwillbeoutlined.Thefirstsectiondealswiththeelectrochemicalbasisfor corrosion,whichiscontrolledbythermodynamicprinciples,whiletheeffectofkinetic,orrate controlwillbeintroducedlaterinthesection.Itisimportanttounderstandtheroleofboth thermodynamicandkineticprocessesininitiatingandcontrollingcorrosioninordertodetermine corrosionrates,orreducecorrosionbydifferentmethods,suchassacrificialanodesoralloy developmentsuchasstainlesssteels. MetalDissolution In most corrosion processes, with the exception of cathodically controlled processes, metalwilldissolve.Anunderstandingoftheprinciplesbehindhowmetaldissolvesinasolution isanecessarypartofunderstandingcorrosion.ConsiderapieceofpuremetalMinasolution whichcontainsitsownions,Mz+.Inthiscasethemetalhassolubilityinthesolutioninwhichit isplaced.Anexamplewouldbeapieceofpurecopperinasolutionofcoppersulfate. Thegeneralequilibriumreactionforametalelectrodeinasolutionofitsownionsis: M=Mz++ze whereMrepresentsametalatom,Mz+isthemetalion,Zisthepossiblevalencesande representsanelectron. Atequilibriumthereisnonetcurrentflowandtheabovereactioncanbeseparatedinto twodifferentreactions.Onereactionproducesmetalionsinsolutionfrommetalatomsinthe solidwiththereaction: M>Mz++ze Againatequilibriumthereisnonetcurrent,sotheelectronsproducedinthereaction aboveareconsumedinareactionwherealltheelectronscombinewithmetalionsinsolutionto depositasatomsonthesolidmetalsurfaceincontactwithsolutioninthereaction: Mz++ze>M Theseindividualreactions arecalledhalfcell reactions astheyanotherreaction to eitherconsumeorproduceelectrons forthemtoproceed.Thesehalfcellreactions arealso oxidationandreductionreactions. Oxidationisareactionthatproduceselectrons.Theionizationofmetalatomstoionsis thereforeanoxidationhalfcellreaction. Reductionisareactionthat consumes electrons.Deionizationtoformametalatomis thereforeareductionhalfcellreaction. M=Mz++ze TheabovereactioniscalledaREDOXreactionbecauseitcontainsbothanoxidationanda reductionhalfcellreaction. Bothoxidationandreductionareimportantreactions.Theoxidationreactionisthebasis of corrosionasmetalisdissolvedwhilsttransformingfromatomstoionsinasolution.The reductionreactionisalsoimportantasitisthebasisofelectroplatingwhereionsinsolutionare depositedasatomsonasurface,forexamplechromeorgoldplating. 1 Duringcorrosion,thehalfcellreactionsdonotusuallyinvolvethesameelementsand ions in both the oxidation and reduction reactions. The electrons produced in the oxidation reaction arenot available forthereverse reduction reaction, whichwouldreplace the metal atomsbackonthemetalsurface.Instead,theelectronsfromtheoxidationreactionareconsumed byadifferentreductionreactionresultinginanewreactionproduct.Thisleadstoasecondary reactionbetweentheproductsoftheoxidationandreductionhalfcellstoformastablematerial. Thesecanfurtherreactwiththeenvironmenttoformstablecompoundssuchasrust.Theseare thenverydifficultreactionstoreversebacktotheatomicformofthemetalwhichisoneofthe majorreasonswhycorrosionisanextremelydeleteriousprocess. BasicCorrosionProcesses. Fournecessaryprocessesarerequiredtohavecorrosiontakeplace.Alltheseprocesses mustbeavailableforcorrosiontooccur.Ifanyoftheseareunavailablethencorrosionwillnot occur.Thisprovidesthefirstmeasuresofcorrosionprotectionbydisablinganyoneofthefour necessaryprocesses,thencorrosionwillbeblocked. Thisverysimpleapproachtocorrosion protectionisoftenoverlookedbutcanbeaninvaluabletoolfortheengineertoavoidcostly corrosionproblems. OxidationHalfCellReaction. Thefirstprocessisanoxidation or anodic halfcell reaction.Theoxidationhalfcell reactionwasdescribedabove. Thecorrosionprocessisessentiallythisoxidationreactionas metalatomsaretransformedtotheirions.Solidmetalinasolutionistransformedintometalions insolution,resultinginweightlossorthinningofthesolidmaterial. M>Mz++ze ReductionHalfCellReaction. Thesecondprocessofacorrosioncellisareductionorcathodicreaction.Onereduction orcathodicreactionwasalsodescribedabovewhichistheplatingordepositionreaction. Mz++ze>M OthercathodicreactionsaredescribedbelowintermsoftheirREDOXreactions, althoughacathodicreactionwouldbeinthedirectionfromlefttoright: 2.Reductionofhydrogenionsinstrong,deaeratedacids: 2H++2e=H2 Forthecathodichalfcellreactionhydrogengasisproducedatthesametimeastheanodic reactionisprogressing.. 3.Reductionofoxygeninweakaeratedacidstoformwater. O2+4H++4e=2H2O 4.Changeinionicstate,e.g.,Cuprictocuprousion. 2 Cu2++e=Cu1+ 5.Reductionofoxygeninneutralorbasicsolutionstoformhydroxylions. O2+2H2O+4e=4(OH) For many practical service situations the last reaction is the most important. All the necessaryconstituentsforthereactiontoproceedarepresentinnormalenvironmentalexposure. Theoxygenispresentasdissolvedoxygeninwater.Alatersectionwilldiscussthereductionof oxygeninwateringreaterdetail.Theonlycomponentmissingarefourelectrons,whichduring corrosionwillbeproducedbytheoxidationoranodichalfcellreaction. CathodeSite. Animportantfeatureatthisstageistodistinguishthecathodichalfcellreactionfromthe physical cathode. The physical cathode is the location where the cathode half cell reaction occurs.Thecathodeonlyprovidestheelectricalconductivitynecessaryforelectrontransferfor thecathodehalfcellreaction.Anexamplecanbeobtainedfromthereductionofoxygeninwater reaction above,reaction5.Thisreactionwilloccuronasurfacewhichhasthecapabilityto conductelectrons.Thesurfaceonlyneedstobeaconductorofelectricity,itdoesnotneedtobe metallic, thereforenonmetallic materials thatareelectrically conductive canbecathodes. It should also be apparent that the cathode does not dissolve and can be termed as being cathodicallyprotected.Anothercathodereactionisreductionofhydrogenionstohydrogen, reaction 2. In this case hydrogen gas will be nucleated on a conducting surface as a correspondinganodicreactionproducestheelectronsforconsumption.Thisdistinctionbetween cathodereactionandthecathodematerialisimportantinlaterstageswhenlocalizedcorrosion formssuchaspittingandcrevicecorrosionarediscussedandlargeamountsofthemetalsurface exposedtoanenvironmentshownosignsofcorrosionwhileextensivecorrosionispresentin local regions on the surface. It is thought that the noncorroded regions are cathodically protected. IonTransport. The third process is ionic transport forwhich a conductive medium orelectrolyte is required.Inmanycasesofenvironmentalexposurethiscanbewater,seawater,acidicorbasic solutions.Thegreatertheionicflowcapabilityofthesolutionthegreaterthecorrosionrate whichcanbesupported.Thereforedistilledwaterwithahighresistanceandlowconductivity, usually supports a lower corrosion rate than seawater with a low resistance and high conductivity. ElectronTransport. Thefourthnecessaryprocessisamechanismforelectrontransportbetweentheanode andcathodesites. Aselectronsareproducedbytheoxidationanodichalfcellreactionsand consumed bythereduction cathodicreaction, electrons flow fromtheanodetothecathode. Withoutflowofelectronsbetweentheanodeandcathode,thesehalfcellreactionscannotoccur. 3 Blocking this electron flow is therefore another method of corrosion protection. The anode thereforehasanexcessofelectronsandisthereforethenegativepole.Thecathodeisthepositive pole. The necessary electron flow can be achieved by several mechanisms. One is a wire conductorwhichconnectstheanodeandcathode.Electronsflowalongthewirefromtheanode tothecathode.Agoodexampleofthisprocessisaflashlight.Thebatteryintheflashlighthasa cathodeandananode.Thezinccasingistheanodeandusuallythenegativepole.Thecenter postofcarbonisthepositivepole.Whentheswitchisplacedintheonpositionacircuitis completerbetweenthepositiveandnegativepolethroughthelightbulbfilamentwhichglows whitehotduetoresistiveheatingfromtheelectronflowfromtheanodetothecathode.The electronflowisthereforeprovidingbothavoltageandacurrent. Asecondandmuchmoreimportantmethodofelectricalconnectionforanengineeris controlledbythe microstructure ofthematerials.Theintimatecontactofphasesinametallic alloy can providethe necessaryelectrical contact to establish anode andcathode regions. It shouldberememberedthateachphasehasitsowndistinctcompositionsoeachphasewillreact differentlytotheenvironment.Thesedifferenceswillcauseanodesandcathodestoformwhich areinphysicalcontact.Impuritiesinmetalscanalsoactasanodesorcathodesduetochemical differences. Insummary,thefournecessaryprocessesforacorrosioncellareanodereaction,cathode reaction,electrolyteandelectrontransport.Unfortunatelyformanyengineeringmaterialssuchas steelsinwater,allthesefourprocessesarepresentandcorrosionwilloccur.Forothermaterials inthesameenvironment,nocorrosionwilloccur.Anexamplewouldbegoldinwater.Ifthereis nocorrosion,thenoneofthesefourprocessesisnotoccurring,Forgolditsohappensthatno anodehalfcellreactionisavailablewhichmakesitimmunetocorrosion. ExchangeCurrentDensity. TheREDOXhalfcellreactionsofoxidationandreductionbothinvolveelectrons.The oxidation,anodicreactionproduceselectronswhilethereduction,cathodicreactionconsumes them. M=Mz++ze AtequilibriumforaREDOXreactionthereisnonetionicorelectronflow,sothereisno corrosionweightlostbythemetalordepositionorweightincreaseofthemetal.Theweightof themetalMwillbethesameattheendasatthebeginningandtheconcentrationofM z+ in solutionwillbethesameattheendasthestartingconcentration.However,foranoxidation reaction,thereisacurrentflownumberofelectronsperunittimeastheyareproducedinthe anodic half cell reaction. There is also current flow for the reduction half cell reaction as electronsareconsumed. M>Mz++ze Mz++ze>M 4 Atequilibriumthenumberofelectronsproducedbytheanodichalfcellreactionandthe number ofmeal ions transformedfrommetal atoms is thesameas thenumberofelectrons consumedbythecathodichalfcellreactionandalsothenumberofionstransformedbackto atoms,andsoboththehalfcellreactionsproceedatequalrates.Thecurrentflowsfortheanode and cathode half cell reactions are finite and identical, but in opposite directions. But the magnitudeofthecurrentflowsisidenticalforbothhalfcellreactions.Thismagnitudeofcurrent is called theExchange Current Density.The units usedare currentper unitarea ofsurface exposed, for example A/cm2, The reaction surface and ions involved controls the exchange current density. Some examples are given below for zinc when it is placed in a solution containingzincionsofthetypeindicatedinthetablebelow: Ion Perchlorate Sulfate Chloride ECD(A/cm) 2 3x108 3x105 3x104 The exchange current density or ECD represents an equilibrium point. The metal in solutionofitsowniontypecanonlycorrodeorhaveionsdepositwhenthecurrentdensityisnot attheexchangecurrentdensityvalue. Asdescribedabove,REDOXreactionsarebothanodicandcathodichalfcellreactions Potentials. but balanced under equilibrium conditions. Clearly, some standard has to be set for this equilibriumandsostandardconditionsaredefinedasoneatmosphereofgaspressure,puresolid present, normal ionic solution strengths at 25oC temperature. Normalcy is the number of equivalentsperliterofsolution.Normalionicstrengthiswhenonegramequivalentisdissolved perliterofwater.Forhydrochloricacid,aonenormalsolutionwouldbethegrammolecular weight, or gms per liter of solution. For one normal sulfuric acid, H 2SO4, half the gram molecularweightinaliterofwaterwouldberequiredasithastwohydrogenionspresentanda normalsolutionrequiresonlyoneelectrontobeavailable.Forbasicsolutionsthenumberof hydroxylionsisusedinsteadofhydrogenionsorthenumberofelectronstransferredinthe reaction. WhatisunavailableatthisstageisascaletodifferentiatebetweenthedifferentREDOX reactionslistedforbothmetalsandnonmetals.Areferencescaleisrequired.Thisissometimes calledtheElectroMotiveForce(EMF)seriesorREDOXpotentialseries. Tomeasurepotentials(orvoltages)forcomparisonofREDOXreactions,thereference used is a Standard Hydrogen Electrode (SHE). This electrode is a constructed by bubbling gaseoushydrogenat1atm.ofpressureoverapieceofpureplatinuminasolutionofonenormal H+ions.Theredoxreactionistherefore: 2H++2e=H2g 5 H 2g Pt foil Permeable membrane 1 N H ions StandardHydrogenElectrode. Thepotentialforthisreactionbydefinitionis0.0V.ItisacompleteREDOXreaction and will maintain a standard, constant voltage unless the conditions change away from the definedstandards.Theoxidation,anodicreactionandthereduction,cathodichalfcellreactions aregivenbelow: H2>2H++2e 2H++2e>H2 Noelectronremovalisallowedandthehydrogenionstrengthmustbemaintained. BycouplingdifferentmetalsMtotheSHEtheirpotentialscanbemeasuredin voltsonavoltmeter.ThisgivesrisetothedatabelowforEMForREDOXpotentials.Notethat issomeareas,thescaleisoppositewithgoldforexampleat1.48V.Mostengineeringpractices usethescalebelow,butbecareful. Reaction Au=Au3++3e O2+4H++4e=2H2O Pt=Pt2++2e O2+2H2O+4e=4(OH) 2H++2e=H2 Fe=Fe2++2e Cr=Cr3++3e Zn=Zn2++2e Al=Al3++3e 6 Potentialatequilibrium(volts). 1.498 1.229 1.2 +0.401 0.0 0.440 0.744 0.763 1.662 In the figure below showing how a SHE is coupled to the REDOX reaction being measured,ahighresistancevoltmeterisusedtomeasurethevoltageforthisseriestoensurethat nocurrentflowsfromtheREOXcellsandsonocorrosionordepositionisoccurringasallthe reactionsareequalandoppositeinrate.TheREDOXreactionbeingmeasuredmustalsobeat standardcondition.Thisseriesprovidesthethermodynamicprobabilitythatapuremetalunder standardconditionswilleitherionizebyananodicreactionorplateoutinacathodicreaction. V olts H 2g Pt foil Metal 1 N H ions 1 N M ions Permeable membrane CellfordeterminationofEMFseriesorRedoxpotentials. ThemorenegativethepotentialmeasuredintheEMForREDOXseries,themorelikely thematerialistooxidizeinananodichalfcellreaction.Therefore,gold,Auistermedverynoble asithasahighpositiveEMFvalue.ZincisveryanodicasithasalownegativevalueofEMF. Thereforeconnectingahalfcellofgoldtoahalfcellofzincwillinduceanodicreactionofthe zinctoproduceelectrons,i.e.: Zn>Zn2++2e Concurrently, the cathodic half cell reaction will be favored in the half cell with the more positivepotentialandgoldionswillbereducedtogoldby: Au3++3e>Au. Thezincwillhavecorrodedasweightlosswilloccur.Thisprocessisessentiallygalvanic corrosion.Aswillbediscussedlaterthisisausefulcorrosionprocessasprotectiontechniques 7 sometimesrelyondissolvingacheap,easilyreplacedmetalratherthantheexpensivestructural metals.Twoexamplesofthisaregalvanizingandsacrificialanodes. SomeimportantfeaturesfortheSHEandEMFseries. Thestandardhydrogenelectrodeisadifficultpieceofapparatustouse.Hydrogengasis required along with a reasonably strong acid solution. It is not practical for everyday use. SecondlytheEMFseriesonlyappliestopuremetalsinhighlyspecifiedconditions,whichare notoftenseen,suchasonenormalionicsolutions.Itisagoodguideonlyfortheseconditions. Thirdly,someelementsareverylowintheseriessuchaschromium,yetthiselementisaddedto irontomakesteels"stainless". Atthispointthereissomediscrepancybetweentheoryandpractice,whichisansweredby thesofarundescribedroleofkineticsoncorrosion.Kineticsinvolvestherateofareaction; thermodynamicsconsiderswhethera reactionisfavorableornot.Forareactiontoproceedit mustbethermodynamicallyfavorable.Soreactionscanbethermodynamicallyfavorable,but kineticsdeterminestherateatwhichthereactionproceeds.Fortunatelyincorrosion,thekinetics ofareactionwilloftenaidinreducingtheexpectedrate.Exampleswouldbestainlesssteelsand titaniumanditsalloys. Reference Electrodes. The Standard Hydrogen reference electrode has already been described in earlier notes. It is an impractical electrode with a strong acid and highly flammable hydrogen gas required. A simpler reference electrode is required for practical measurements and several exist. The most common ones are the Calomel electrode, the copper/copper sulfate electrode and the silver/silver chloride electrode. The requirements of a reference electrode is that are a constant reference against the standard hydrogen electrode over a wide range of conditions. This usually means that a self contained half cell reaction occurs that cannot be change by the environment in which the reference electrode is placed. A good example is the Saturated Calomel Electrode or SCE. A diagram of the electrode is shown below. 8 To Voltmeter Platinum Wire Filling Hole Glass or Plasic Body Saturated KCl Porous Tip Saturated Calomel Reference Electrode. This is a very common electrode. It is based on the mercurous to mercury half cell reaction of:Hg2Cl2 = Hg2++ + 2ClHg2++ + 2e- = 2Hg Overall Reaction:Hg2Cl2 + 2e- = 2Hg + 2ClNernst Equation gives:ECal = Eo - (RT/zF) ln (aCl-)2 = Eo - (2.303RT/F) log aClECal = +0.2677 - 0.059 log aClEcal = +0.242 V against SHE for Hg/Hg2Cl2 in saturated KCL. 9 In the SCE the Calomel paste of mercurous chloride is mixed with mercury and and the filling solution is saturated potassium chloride. The saturated solution has a fixed chloride ion activity and the mercurous chloride is only slightly insoluble in water. A porous tip enables ionic transport to complete the necessary components for measuring voltage along with connection to a high resistance voltmeter.The electrode maintains its chemical conditions and provides a reference potential against the standard hydrogen electrode of +0.242 V. Other common reference electrodes are the Copper/Cupric Sulfate electrode where a copper bar is placed in a saturated cupric sulfate solution. E Cu/CuSO4 = +0.34 V(SHE) for saturated copper sulfate solution CorrosionRates,PolarizationandFaradaysLaw Sofar,muchhasbeenexaminedregardingequilibriumconditions.However,corrosion anddepositiondonotoccurunderequilibriumconditions.Themeasurementofthecorrosionrate ofmaterialintheenvironmentisvitaltothecorrectselectionofamaterial.Onemethodtoplace thematerialintheenvironmentandmonitoranyweightchange.Anotherisconductalaboratory studyandconductmeasurements.Theissueiswhatshouldbemeasured.Inthissection,the parameters which provide information on corrosion rates and which can be measured in a laboratorywillbedetermined. InconsideringthegeneralREDOXreactionatametalelectrodeM: M=Mz++ze AttheRedoxpotentialunderstandardconditionsusedtodeterminetheRedoxseries, thereisnonetcurrentflowastheanodereactionrateisthesameasthecathodereactionrate. ThisvoltagewillbecalledErforRedoxpotential.Whenthepotentialmovesawayfromthis equilibriumvaluesoitnolongerequalsEr,thenthereactionratesbecomesunbalancedandone orotherofthehalfcellreactiondominates,eithercathodicoranodic.Atthisnewpotentialeither anetfluxofelectronswillbeproduced,iftheanodichalfcelldominates,orelectronswillneed tobeprovidedtoallowthecathodichalfcellreactiontoproceed.Sobycontrollingthepotential thereactioncanbeeitheranodicorcathodic.ThisisalsocalledPolarization,themovement awayfromtheRedoxpotentialvalue. PolarizationofanElectrode. Polarizationofanelectrodeisthemovementawayfromtheequilibriumstatewherethe anodereactionrateisequalandoppositetothecathodicrateatstandardconditions.Asimplified modelofthesituationwillbepresentedinthissectiontodeterminewhathappenswhenthe conditions arealtered awayfromthestandardones.Theparticular casewillbewhen some electronsproducedbytheanodichalfcellreactionareremovedandnotavailableforusebythe cathodichalfcellreaction. Considerapuremetalatequilibriuminitsownions.Atomssitinlowenergypositionson thesurface.Anactivationenergybarrierexistsfortheseatomstobecomeionsandproduce electrons.Aschematicdiagramofthesituationisshowninthefirstfigurebelow. Atequilibriumtheionexchangecurrentdensityisavailableofatomstransformingtoions (anodereaction)andatanequalratetheionsfromsolutionaretransformingtoatoms(cathodic reaction)attheredoxpotentialofEr 10 AtequilibriumtheactivationenergybarrierisGe Ge=BF Theenergybarier,Ge,isthesameindependentofthereactiondirection,anodicorcathodic. Inthesecondfigurebelow,theenergyoftheatominthesurfacewasincreased,oritwas AnodicallyPolarisedtomakeitmorefavorablefortheatomstoformions. AssumeBE=FG LetBC/AC= ThenAB/AC=1 Ge Atom in Surface Ion in Solution G Ga F D Atom in Surface E Ion in Solution C B A Bysimilartriangles,CD/EB=AC/AB=1/(1) EB=CD(1) CD=Changeinanodicenergyappliedbyanexternalvoltage 11 CD=z aF whereznumberofelectronsinvolvedinthehalfcellreaction, aoverpotentialorvoltagemovementfromErvalue,FFaradaysconstant(96500coulombs). EB=(1a)z aF Thenthenewactivationenergybarrierforanatomtoiontransfer,releasingelectronsis: Ga= GeCD+FG Ga=GeCD+EB Ga=Gez aF+(1)z aF Ga=Gez aF Also,astheprocessisactivationcontrolleditfollowsanArheniusratelawof: Rate=Ke( G/RT) o RBoltzmannsconstantof1.96cal/oK,Ttemperaturein K Therateinthiscaseisproportionaltothecurrentflowing. Then: i=Ke( G/RT) i =Ke( Ga/RT) a i =Ke(( Gez aF)/RT) a AtequilibriumioistheExchangeCurrentDensityatRedoxpotential,Er i =Ke( Ge/RT) o Expandingtheequationforanodicdissolution: ia=Kexp(Ge/RT)exp(z aF/RT) ia=ioexp(z aF/RT) Takinglogs lnia=lnio+z aF/RT Rearranging: a=(lnialnio)(RT/zF) Forcathodicpolarization. c=(lniolnic)((RT/(1)zF) ThesearetheTafelequationsforpolarizationofanelectrode.Theyfollowthegeneralformofa straightlineifisplottedasafunctionoflogi. y=c+mx =a+/blogi TheequationaboveistheTAFELequationwhichrelatespotentialtocurrentdensityforan electrochemicalreaction. Theconstantsfortheequationarelistedbelow.Theconstant"b"iscalledtheTafelconstant. Anodic a=lnio(RT/zF) b=RT/zF 12 Cathodic a=lnio(RT/(1)zF) b=(RT/(1)zF) Overall,changingtheconditionsfromthe halfcellreactionsthereforeproducespolarization resultinginacurrent. 13
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Naval Academy - EE - 303
EE 303 Problem Set 19Complete the following problems from the textbook Principles of Electronic Communication Systems, 3rd ed. Chapter 11 Questions: 13, 23, 24 Additional Problems 1. An AM High Definition (HD) radio digital-only stream is broadcast
Naval Academy - EE - 303
EE 303 Problem Set 15Chapter 7 Questions 3. sampling 4. quantization Problems 1. Minimum sampling frequency (Nyquist) is 2 x 3.5 MHz = 7.0 MHz. 2. A 12-bit D-A converter can have up to 212 = 4096 discrete output levels. If the output voltage range i
Naval Academy - EE - 303
EE 303 Problem Set 21 SolutionsChapter 11, Questions: 53, 54, 57, 58, 59, 60, 62, 64, 65, 68 53. Spread spectrum is a modulation technique in which the modulated signal is spread over a wide bandwidth. 54. The two types of spread spectrum are freque
Saint Louis - MATH - 403
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Saint Louis - MTA - 142
Math 142Bryan ClairRead Chapter 1.2,1.4,1.5.Ch. 1.2#13b,25 Ch. 1.4#1,3,11,23,25,35,36 Ch. 1.5#5,13,15,17,37,41Homework 2Problems from Hughes-Hallett:Calculator problem:Graph f(x) = 100x4 and g(x) = 1.1x . Which one starts out growing fast
Saint Louis - MATH - 403
Math 403Fall 2008Homework 14Due Friday, Dec. 5 WMMY: Problem A: Ch 11 # 3, 7, 13, 31, 49, 63a, 68 Show that these two expressions for the Pearson correlation coefficient are the same:S xy = 1 x- x y- y s s n-1 x y S xx S yyProblem B:
Saint Louis - MATH - 403
Math 403Fall 2008Homework 10Due Monday, November 3 WMMY: Ch 8 # 46, 47, 49 Ch 9 # 1*, 5*, 7, 9, 11, 13, 15 * Hints: You can follow Example 9.1, or more directly use E X 2 = 2 X E X 2 , which comes from Thm 4.2. * See Problem A. For Exercise 9
Saint Louis - MATH - 403
Math 403 Due Monday, September 29 WMMY: Ch 4 # 33, 35, 43*, 45 * Just find the mean and covariance for X, not for Y.Fall 2008Homework 5Problem D: Suppose X has the uniform distribution on the interval [a,b]. That is, the PDF for X is f(x) = 1/(
Saint Louis - CS - 220
CS 220Bryan ClairHomework 1 - Due Wednesday, Jan. 21Skim Appendix B, C. Read Chapter 1. wordlength.C: Chapter 1 Programming Project #1.3multquiz.C: The program should quiz the user on their multiplication table (use random numbers from 0 to 12
Saint Louis - CS - 220
CS 220Bryan ClairHomework 5 - Due Friday, March 5 (at 5:00pm)War.C: War is a classic childrens card game. In War, each player gets half the deck of cards. The two players then battle until one player runs out of cards. Each battle has both playe
Saint Louis - CS - 220
CS 220Bryan ClairHomework 4 - Due Wednesday, Feb. 25ApptBook.C: Revise your appointment book program so that the user can save all appointments to a file, and read appointments from a file. The user should have a chance to specify the name of th
Saint Louis - CS - 220
CS 220Bryan ClairHomework 6 - Due Monday, March 22Revsort.C: Write a program that reads lines from cin (with no prompting) until it reaches end-of-file, and then prints the lines back sorted in reverse alphabetical order. Your program can assume
Saint Louis - CS - 220
CS 220Bryan ClairHomework 7 - Due Wednesday, March 31Edit.C: Write a line text editor. Line text editors date back to the days before video terminals, when all of a computers output was via a printer. Unix comes standard with a line text editor
Saint Louis - CS - 220
CS 220Bryan ClairHomework 3 - Due Friday, Feb. 13Blackjack.C: Write a program to allow the user to play one hand of blackjack, with the computer as dealer. The program should "deal" two cards to the player and two to the dealer. One of the deale
Stanford - CS - 193
CS193i, Stanford University Spring, 2004Handout #9 Ron B. YehNAT ExampleNAT ClientThe local machine using the Network Address Translation (NAT) router has a nonroutable IP address, such as 192.168.1.2 The local machine can do normal TCP connect
Maryville MO - CHE - 332
2-13Bonding Forces and Energies2.13 The attractive force between two ions FA is just the derivative with respect to the interatomic separation of the attractive energy expression, Equation 2.8, which is just A d- A r = = dr r2FA =dE A drT
Maryville MO - CHE - 332
2-142.14 (a) Differentiation of Equation 2.11 yieldsB A d d- r rn = + dr drdE N dr=nB A - = 0 r (1 + 1) r ( n + 1)(b) Now, solving for r (= r0)A2 r0=nB r0( n + 1)or A 1/(1 - n) r0 = nB (c) Substitution for r0 into Equati
Maryville MO - CHE - 332
5-29= 3.8 x 10-12 m2/sNote: this problem may also be solved using the Diffusion module in the VMSE software. Open the Diffusion module, click on the D0 and Qd from Experimental Data submodule, and then do the following: 1. In the left-hand window
Maryville MO - CHE - 332
9-3Microstructure9.3 Three variables that determine the microstructure of an alloy are (1) the alloying elements present, (2) the concentrations of these alloying elements, and (3) the heat treatment of the alloy.Excerpts from this work may be r
Maryville MO - CHE - 332
9-69.6 The melting and boiling temperatures for ice at a pressure of 0.1 atm may be determined by moving horizontally across the pressure-temperature diagram of Figure 9.2 at this pressure. The temperature corresponding to the intersection of the I
Maryville MO - CHE - 332
9-119.9 It is possible to have a Cu-Ag alloy, which at equilibrium consists of a phase of composition 92 wt% Ag-8 wt% Cu and a liquid phase of composition 77 wt% Ag-23 wt% Cu. From Figure 9.7 a horizontal tie line can be constructed across the +
Maryville MO - CHE - 332
9-139.11 Upon heating a lead-tin alloy of composition 30 wt% Sn-70 wt% Pb from 150C and utilizing Figure 9.8: (a) The first liquid forms at the temperature at which a vertical line at this composition intersects the eutectic isotherm-i.e., at 183C.
Maryville MO - CHE - 332
9-159.13This problem asks us to determine the phases present and their concentrations at severaltemperatures, as an alloy of composition 52 wt% Zn-48 wt% Cu is cooled. From Figure 9.19: At 1000C, a liquid phase is present; WL = 1.0 At 800C, the
Maryville MO - CHE - 332
9-239.20 For this problem, we are asked to determine the composition of the phase given that C0 = 40 (or 40 wt% B-60 wt% A) C = 13 (or 13 wt% B-87 wt% A) W = 0.66 W = 0.34 If we set up the lever rule for W C C 0 C 40 = C C C 13W = 0.66 =An
Maryville MO - CHE - 332
9-269.23 This portion of the problem asks that we derive Equation 9.6a, which is used to convert from phase weight fraction to phase volume fraction. Volume fraction of phase , V, is defined by Equation 9.5 asvV =v + v(9.S1)where v and v a
Maryville MO - CHE - 332
9-27Incorporation of these relationships into Equation 9.S3 leads toW (m + m ) V = W (m + m ) + W (m + m ) W V = + W W (9.S6)which is the desired equation.For this portion of the problem we are asked to derive Equation 9.7a, which is
Maryville MO - CHE - 332
9-35Development of Microstructure in Eutectic Alloys9.28 Upon solidification, an alloy of eutectic composition forms a microstructure consisting of alternating layers of the two solid phases because during the solidification atomic diffusion must
Maryville MO - CHE - 332
9-399.32 (a) This portion of the problem asks that we determine the mass fractions of and phases for an 80 wt% Sn-20 wt% Pb alloy (at 180C). In order to do this it is necessary to employ the lever rule using a tie line that extends entirely acros
Maryville MO - CHE - 332
9-429.35 Schematic sketches of the microstructures that would be observed for an 64 wt% Zn-36 wt% Cu alloy at temperatures of 900C, 820C, 750C, and 600C are shown below. The phase compositions are also indicated. (Note: it was necessary to use the
Maryville MO - CHE - 332
12-1CHAPTER 12STRUCTURES AND PROPERTIES OF CERAMICS PROBLEM SOLUTIONSCrystal Structures12.1 The two characteristics of component ions that determine the crystal structure of a ceramic compound are: 1) the magnitude of the electrical charge on
Maryville MO - CHE - 332
12-212.2In this problem we are asked to show that the minimum cation-to-anion radius ratio for acoordination number of four is 0.225. If lines are drawn from the centers of the anions, then a tetrahedron is formed. The tetrahedron may be inscri