Fundamental Chemistry With Matlab This pageintentionallyleftblank Fundamental Chemistry With Matlab Daniele Mazza Former Faculty, Politecnico di Torino, Turin, Italy e-mail: [email protected] Enrico Canuto Former Faculty, Politecnico di Torino, Turin, Italy e-mails: [email protected]; [email protected] Elsevier Radarweg29,POBox211,1000AEAmsterdam,Netherlands TheBoulevard,LangfordLane,Kidlington,OxfordOX51GB,UnitedKingdom 50HampshireStreet,5thFloor,Cambridge,MA02139,UnitedStates Copyright©2022ElsevierInc.Allrightsreserved. Nopartofthispublicationmaybereproducedortransmittedinanyformorbyanymeans,electronicor mechanical,includingphotocopying,recording,oranyinformationstorageandretrievalsystem,withoutpermission inwritingfromthepublisher.Detailsonhowtoseekpermission,furtherinformationaboutthePublisher’s permissionspoliciesandourarrangementswithorganizationssuchastheCopyrightClearanceCenterandthe CopyrightLicensingAgency,canbefoundatourwebsite:www.elsevier.com/permissions. ThisbookandtheindividualcontributionscontainedinitareprotectedundercopyrightbythePublisher(otherthan asmaybenotedherein). Notices Knowledgeandbestpracticeinthisfieldareconstantlychanging.Asnewresearchandexperiencebroadenour understanding,changesinresearchmethods,professionalpractices,ormedicaltreatmentmaybecomenecessary. Practitionersandresearchersmustalwaysrelyontheirownexperienceandknowledgeinevaluatingandusingany information,methods,compounds,orexperimentsdescribedherein.Inusingsuchinformationormethodsthey shouldbemindfuloftheirownsafetyandthesafetyofothers,includingpartiesforwhomtheyhaveaprofessional responsibility. Tothefullestextentofthelaw,neitherthePublishernortheauthors,contributors,oreditors,assumeanyliability foranyinjuryand/ordamagetopersonsorpropertyasamatterofproductsliability,negligenceorotherwise,or fromanyuseoroperationofanymethods,products,instructions,orideascontainedinthematerialherein. ISBN:978-0-323-91341-6 ForInformationonallElsevierpublications visitourwebsiteathttps://www.elsevier.com/books-and-journals Publisher:SusanDennis AcquisitionsEditor:KathrynEryilmaz EditorialProjectManager:FranchezcaCabural ProductionProjectManager:BharatwajVaratharajan CoverDesigner:MilesHitchen TypesetbyMPSLimited,Chennai,India Dedication To our families This page intentionallyleftblank Contents Introduction..........................................................................................................................................xv CHAPTER 1 Plotting atomic orbitals with Matlab...................................................1 1.1 Wave functionsand their factorization......................................................................1 1.1.1 Generalities......................................................................................................1 1.1.2 Angular wave functions...................................................................................3 1.1.3 Table ofthe radial functions............................................................................8 1.2 Graphical plot of the wave functions........................................................................9 1.3 Graphical algorithm..................................................................................................11 1.3.1 Description.....................................................................................................11 1.3.2 Matlab script..................................................................................................11 1.4 Graphical plot of the radial probability density for s-type orbitals........................14 1.4.1 Description.....................................................................................................14 1.4.2 Matlab script and graphical results................................................................15 1.5 Hybrid orbitals..........................................................................................................17 1.5.1 Hybridorbitals sp3.........................................................................................19 1.5.2 Hybridorbitals dsp3.......................................................................................20 1.5.3 Hybridorbitals d2sp3......................................................................................21 References.................................................................................................................21 CHAPTER 2 Balancing chemical reactions with Matlab.......................................23 2.1 Introduction..............................................................................................................23 2.2 Nonredox andredox reactions.................................................................................25 2.2.1 Nonredoxreactions(or metatheses)..............................................................25 2.2.2 Redoxreactions..............................................................................................25 2.2.3 Stoichiometryand nonredox reactions..........................................................26 2.2.4 Stoichiometryand redox reactions................................................................26 2.3 Generalmethod........................................................................................................26 2.3.1 Thebalance equation.....................................................................................26 2.3.2 Example..........................................................................................................28 2.4 Solutionof the homogeneous system of linear equations.......................................29 2.4.1 Thenullspacemethod....................................................................................29 2.4.2 Example..........................................................................................................30 2.4.3 Balancing algorithm fromchemical formulas...............................................30 2.5 Nullspace algorithm for balancing chemical reactions...........................................32 2.5.1 Nullspace function stoichiometry..................................................................33 2.5.2 Results ofthe plug-in code example.............................................................34 2.6 Catalog ofthe reactionsand oftheir plug-in codes................................................35 vii viii Contents 2.6.1 Oxidation ofhydrogenperoxide by potassiumpermanganate...................35 2.6.2 Oxidation ofsilver sulfideby aqua regia....................................................35 2.6.3 Oxidation ofbromidric acid bypotassium dichromate..............................36 2.6.4 Oxidation ofmercuryby nitric and chloridricacid....................................37 2.6.5 Oxidation ofchromium(II) bromideby sodium bromate...........................38 2.6.6 Zinc oxidationby silver arseniate...............................................................38 2.6.7 Precipitation ofan insoluble salt (AgCl).....................................................39 2.6.8 Neutralization ofcarbonic acid with sodiumhydroxide.............................40 2.6.9 Hydrolysis ofsodium carbonatewith nitric acid........................................40 2.6.10 Oxidation ofsodium sulfite to sulfate by potassium permanganate..........41 2.6.11 Oxidation ofiron(II) sulfate by hydrogen peroxide inacid solution.........42 2.6.12 Oxidation ofmanganese(II) chloride topotassiumpermanganate by sodium bromate............................................................................................42 References.................................................................................................................43 CHAPTER 3 Chemical kinetics aided by Matlab/Simulink....................................45 3.1 Introduction..............................................................................................................45 3.2 First-order irreversiblekinetics................................................................................47 3.2.1 State equationconstruction............................................................................47 3.2.2 Simulink graphicalrepresentation.................................................................48 3.2.3 TheMatlab script...........................................................................................49 3.2.4 Asimpler alternative Matlab script...............................................................50 3.3 First-order reversiblereaction..................................................................................51 3.3.1 State equationconstruction............................................................................51 3.3.2 Simulink graphicalrepresentation and results..............................................52 3.3.3 AlternativeMatlab script...............................................................................53 3.4 Second-order reversible reaction.............................................................................54 3.4.1 State equations...............................................................................................54 3.4.2 Solutionof the Riccati equation....................................................................56 3.4.3 AlternativeMatlab script...............................................................................57 3.5 Consecutive irreversible reactions...........................................................................58 3.5.1 State equations...............................................................................................58 3.5.2 AlternativeMatlab script...............................................................................59 3.6 Two-stage NO to NO oxidation.............................................................................60 2 3.6.1 State equations...............................................................................................60 3.6.2 AlternativeMatlab script...............................................................................62 3.7 Ozonedecomposition into oxygen..........................................................................63 3.7.1 State equations...............................................................................................63 3.7.2 AlternativeMatlab script...............................................................................64 3.8 Irreversible A- B reaction with linear temperature increase..............................65 References.................................................................................................................66 Contents ix CHAPTER 4 More complex kinetics aided by Matlab/Simulink............................67 4.1 Introduction..............................................................................................................67 4.2 Michaelis(cid:1)Mentenkinetics.....................................................................................68 4.2.1 State equations,equilibrium, andstability....................................................68 4.2.2 TheMichaelis(cid:1)Menten equation of the productionrate..............................69 4.2.3 Script,block diagramand graphical results..................................................71 4.3 The iodine clockreaction.........................................................................................74 4.3.1 State equations...............................................................................................74 4.4 Oscillatingkinetics: introduction.............................................................................77 4.4.1 TheLotka(cid:1)Volterra model...........................................................................77 4.5 Oscillatingkinetics of Briggs(cid:1)Rauscher................................................................80 4.5.1 Simplified reaction scheme............................................................................80 4.5.2 State equationsand stability analysis............................................................81 4.5.3 Behavior of the state equations.....................................................................82 4.6 Introductionto Belousov(cid:1)Zhabotinsky kinetics.....................................................85 4.6.1 State equations...............................................................................................85 4.6.2 Equilibrium andstabilityanalysis.................................................................88 4.6.3 Simulated results............................................................................................90 4.6.4 Matlab script..................................................................................................92 References.................................................................................................................96 CHAPTER 5 Gaseous reactions and equilibria aided by Matlab..........................99 5.1 The second law ofthermodynamics........................................................................99 5.2 Applicationofthe Gibbs energycriterion tochemical reactions.........................100 5.3 Relationship ofΔGwith the equilibrium constant K .........................................103 P 5.4 The value ofΔS, ΔH, andΔGas afunction oftemperature..............................104 5.5 The table of the NASA CEA thermochemical coefficients..................................105 5.6 Introductionto Matlab scripts................................................................................106 5.6.1 Organization ofthe Matlab scripts..............................................................106 5.6.2 Thefunction NASAdata.................................................................................107 5.6.3 Thefunction ThermoCoef.............................................................................110 5.7 Hydrogen combustion............................................................................................110 5.7.1 Description...................................................................................................110 5.7.2 TheMatlab script.........................................................................................111 5.8 Ammonia synthesis (Haber process).....................................................................114 5.8.1 Description andgraphical plot.....................................................................114 5.8.2 TheMatlab script.........................................................................................115 5.9 Methane (CH ) combustion...................................................................................117 4 5.9.1 Description andgraphical plot.....................................................................117 5.9.2 Matlab script................................................................................................118 5.10 Hydrogen productionat high andlow temperature...............................................121