Physical Nature of the Covalent Bond Appendix H + H > H 2 ( ) ( )
|
|
- Candace Greer
- 5 years ago
- Views:
Transcription
1 Physical Nature f the Cvalent Bn Appeni his stuy f the nature f the H cvalent bn frms a mlecular rbital as a linear cmbinatin f scale hyrgenic rbitals, LCAO-MO. he quantum mechanical integrals necessary t carry ut the require calculatins are prvie immeiately belw. Cnsult the first five sectins f Chapter 3 f ur tetbk fr an verview f the cvalent bn in the hyrgen mlecule in. he reactin fr its frmatin is, H H ----> H Fr the hyrgen atm: < E > -0.5; < > 0.5; < > -.0. he irial herem is epresse in a variety f ways: E E he evaluate integrals require fr this eercise are prvie belw: Overlap integral: Kinetic energy integrals: : ep( α) α S α, α aa α, α 3 α : ab α, : ep α α α 3 Ptential energy integrals: : α ep( α) aa α, α : α ab α, 5 3 α ep( α) Haa an Hab: tal energy integral: aa( α, ) aa( α, ) Haa α, : Hab α, Haa α, Hab( α, ) : E α, S α, : ab( α, ) ab( α, ) Bning mlecular rbital: Ψ bm α,, y, z, : ep α π y z ep S α, α y z Demnstrate wavefunctin is nrmalize: Ψ bm (,, y, z, ) y z.0000 Anti-bning mlecular rbital: Ψ am α,, y, z, : ep α π y z ep S α, α y z
2 Demnstrate wavefunctin is nrmalize: Ψ am (,, y, z, ) y z.0000 Nn-bning mlecular rbital: Ψ nm α,, y, z, : ep α π y z i ep α y z Demnstrate wavefunctin is nrmalize: ( Ψ nm (,, y, z, ) ) y z.0000 he Cvalent Bn in H ariatinal Calculatin f the Mlecular Grun State an Bn Energy he mlecular rbital fr the hyrgen mlecule in is frme as a linear cmibinatin f scale hyrgenic s rbitals centere n the nuclei, a an b. Ψ a b S Where a π ep α r α ( a) 3 b π ep α r ( b) S ab he energy peratr: H r r r r a r b he energy integral t be minimize by the variatin meth: E ( a b) H( a b) S Haa Hab S where Haa ( a a) a a a a a r a Hab ( a b) a b a b a r a r b r b a b an Haa aa aa an Hab ab ab an Hba Hab. hese integrals an the verlap integral S can be fun in the appeni abve.
3 . Plt E(α,) vs, fr α fr values f ranging frm 0. t 0 in increments f Yu can make space by pressing <enter>. Yu can eliminate space by pressing <elete>. Use the markers fr the - an y-ais t fin the ptimum internuclear separatin,, an the grun-state energy. α : :., E( α, ) Ntice hw shallw the energy minimum initially is. Yu can eagerate the minimum by pltting frm -0.6 t -0.4 n the y-ais.. Minimize the energy with respect t with α. his will require a Given/Fin slve blck an see values fr α an. eprt the ptimum value (equilibrium bn istance) an the grun-state energy. Cmpare these calculate values t the literature values f.00 a fr an E h fr the E. α : : Given E α, 0 : Fin.498 E α, % E( α, ) % E( α, ) % Demnstrate that the calculate hyrgen mlecule in energy es nt satisfy the irial herem. ab( α ) ab( α ) aa α,, : S( α, ) aa α,, : S( α, ) E( α, ).4759 E( α, ) Write the equatin fr breaking the H bn. hen use the theretical value f the grun state energy t calculate the bn energy f the hyrgen mlecule in an cmpare it t the eperimental value, 0.09 E h. Yu may recall that the hyrgen atm grun state energy is -0.5 hartree. HyrgenMleculeIn HyrgenAtm HyrgenIn BnEnergy % %.09
4 4. he first three eercises refer t a variatinal calculatin base n the hyrgen s rbital (α ). Nw treat bth α an as variatinal by minimizing the energy simultaneusly with respect t α an. Given E α, 0 α E α, 0 α : Fin( α, ) α.380 E α, Demnstrate that the calculate hyrgen mlecule in energy es satisfy the irial herem. ab( α ) ab( α ) aa α,, : S( α, ) aa α,, : S( α, ) E( α, ).0000 E( α, ) Cmpare E an with the literature values. ecalculate the H bn energy an cmpare it with the eperimental value. Cmment n the agreement between thery an eperiment as cmpare with that fun in part 3. HyrgenMleculeIn HyrgenAtm HyrgenIn BnEnergy % % E( α, ) % 6. he vibratinal frce cnstant is the secn erivative f the energy with respect t evaluate at the energy minimum. Calculate the frce cnstant an cmpare it t the eperimental value f.03 in atmic units. k : E( α, ) k k % 7. he appeni cntains the bning an antibning rbitals fr H. On ne graph plt Ψ fr the bning an antibning rbitals alng the bn ais (i.e. set y an z t zer). On anther graph plt Ψ fr the bning an antibning rbitals. Cmpare these rbitals. y : 0 z : 0 : 5, α : Ψ bm ( α,, y, z, ) Ψ am ( α,, y, z, ) 0 ( Ψ bm ( α,, y, z, ) ) ( Ψ am ( α,, y, z, ) )
5 hese figures shw that the electrn ensity is greatest at the nuclear centers, an that the bning mlecular rbital has significant electrn ensity in the internuclear regin. Just hw much charge is transfere t the bn regin will be calculate later. he antibning mlecular rbital has a ne eactly between the tw nuclei an thus remves charge frm the internuclear regin. his, f curse, is why it calle an anti-bning mlecular rbital. A Mechanism fr Cvalent Bn Frmatin in H he fllwing tw-step mechanism is prpse fr cvalent bn frmatin: he hyrgen atm an prtn frm an intermeiate, nnbning state at the equilibrium bn length (.0033) with the ptimum value f the ecay cnstant (α.38). he nn-bning state, N nm (a ib), mrphs int the final mlecular state, N bm (a b). Initial AtmicState H atm H in Intermeiate NnBningState a ib Ψ nm Final MlecularState a b Ψ bm S 8. We nw calculate the kinetic (), ptential () an ttal energy (E) fr each f the species invlve in the mechanism. In previus wrk we calculate the fllwing values fr the hyrgen atm. (he energy f the hyrgen in by cnventin is 0). E h : h : h : he energy f the nn-bning intermeiate state is calculate as fllws. E nb a a H aha bhb Haa aa aa because Hbb Haa tal: Haa α, Kinetic: aa α, Ptential: aa α,.58 Nuclear Ptential Energy: In eercise 4 we calculate the energy cntributins f the final mlecular state f H. E α, tal: Kinetic: Ptential: ab( α, ) aa α, S α, ab( α, ) aa α, S α,.730 Nuclear Ptential Energy: 0.499
6 We are nw in a psitin t cnstruct the fllwing quantitative summary f the mechanism. ne nn E Initial AtmicState H atm α H in Intermeiate NnBningState a ib Ψ nm α Final MlecularState a b Ψ bm S α Interpretatin f the Mechanism he first step is atmic an energic. It is atmic because there is n cnstructive interference between the atmic rbitals. It is energic because kinetic energy increases mre than ptential energy ecreases. he increase in kinetic energy an the ecrease in ptential energy are ue preminantly t atmic rbital cntractin frm α in the hyrgen atm t α.38 in the hyrgen mlecule in. he secn step is eergic an mlecular. he atmic rbitals frm a mlecular rbital leaing t charge reistributin relative t the nn-bning intermeiate state. his reistributin causes a ecrease in kinetic energy because the electrn is nw mre elcalize, an an increase in ptential energy because the electrn is rawn away frm the nuclear centers int the high-ptential energy internuclear regin. Overall the kinetic energy increases an ptential energy ecreases n bn frmatin, an the virial therem is satisfie. his is the surce f the cnclusin that cvalent bning is a ptential energy effect. Hwever, as this analysis shws, bth kinetic an ptential energy play imprtant rles in cvalent bn frmatin. his mechanism clarifies an imprtant issue. It is cmmnly thught, an frequently taught, that frm a ptential energy pint f view the internuclear regin is the mst favrable place fr electrn ensity because it is miway between t nuclei. Hwever, this mechanism clearly shws that the reistributin f charge int the internuclear regin ue t the interference term in the bning electrn ensity ccurs with an increase in ptential energy (0.058 E h ). Frm a purely electrstatic perspective the prefere lcatin fr an electrn is in the nucleus. he Bning Electrn Density 9. Hw much f the ttal electrn ensity, Ψ bm, actually cntributes t cvalent bning? his questin can be answere by cmparing the electrn ensity in the intermeiate nn-bning state with that f the final mlecular state. First we will emnstrate that Ψ nm (a b )/ an that this wave functin is nrmalize because a an b are nrmalize. a Ψ nm a a b a a a τ b Ψ nm shws the "atmic" electrn ensity - the electrn ensity that wul eist in the absence f cnstructive interference between the tw atmic rbitals, sa an sb.
7 he nn-bning wave functin is given in the appeni. Graph Ψ bm an Ψ nm alng the bn ais an cmpare them. ( Ψ bm ( α,, y, z, ) ) ( Ψ nm ( α,, y, z, ) ) he questin pse in sectin 9 can nw be answere. he bning electrn ensity can be efine as the charge reistributin that ccurs in step f the mechanism. Plt the ifference between the ttal electrn ensity an the nn-bning electrn ensity alng the bn ais. Interpret the plt. Fr eample, where es the electrn ensity in the internuclear regin cme frm? What is the sign n the ptential energy term fr this transfer f electrn ensity t the internuclear regin? If this is an energic prcess, hw is it fune? : Ψ bm ( α,, y, z, ) ρ b α,, y, z ( Ψ nm ( α,, y, z, ) ) ρ b ( α,, y, z) his graph shws that electrn ensity is being transferre frm the nuclear centers (lw ptential energy) t the internuclear regin (high ptential energy). his eplains why ptential energy increases uring step. he kinetic energy ecreases mre because this reistributin f charge als invlves charge elcalizatin, s it is the larger ecrease in kinetic energy that funs the transfer f charge t the internuclear regin.. he electrn ensity in the internuclear regin is equal t a plynmial in the verlap integral S an is given by 0.738S( - S)( S ). Use the value f S yu calculate earlier t evaluate the amunt f charge in the bning regin f H. Cmment n this value. Fr eample, hw es its value cmpare with a literal interpretatin f the Lewis electrn pair mel f chemical bning that says that chemical bns are frme by sharing electrns between tw nuclei. ( ) ( ) 0.738S α, S α, 0.577S α, 6. %
A Mechanistic Approach to Bond Formation in H 2
A Mechanistic Apprach t Bnd Frmatin in H Frank Riux Department f Chemistry Cllege f Saint Benedict Saint Jhnʹs University St. Jseph, MN 5674 Intrductin Ruedenbergʹs innvative analysis f the cvalent bnd
More informationChemistry 20 Lesson 11 Electronegativity, Polarity and Shapes
Chemistry 20 Lessn 11 Electrnegativity, Plarity and Shapes In ur previus wrk we learned why atms frm cvalent bnds and hw t draw the resulting rganizatin f atms. In this lessn we will learn (a) hw the cmbinatin
More informationThermodynamics and Equilibrium
Thermdynamics and Equilibrium Thermdynamics Thermdynamics is the study f the relatinship between heat and ther frms f energy in a chemical r physical prcess. We intrduced the thermdynamic prperty f enthalpy,
More informationChapters 29 and 35 Thermochemistry and Chemical Thermodynamics
Chapters 9 and 35 Thermchemistry and Chemical Thermdynamics 1 Cpyright (c) 011 by Michael A. Janusa, PhD. All rights reserved. Thermchemistry Thermchemistry is the study f the energy effects that accmpany
More informationInterference is when two (or more) sets of waves meet and combine to produce a new pattern.
Interference Interference is when tw (r mre) sets f waves meet and cmbine t prduce a new pattern. This pattern can vary depending n the riginal wave directin, wavelength, amplitude, etc. The tw mst extreme
More informationLecture 18 Title : Fine Structure : multi-electron atoms
Lecture 8 Title : Fine Structure : multi-electrn atms Page-0 In this lecture we will cncentrate n the fine structure f the multielectrn atms. As discussed in the previus lecture that the fine structure
More informationLecture 13: Electrochemical Equilibria
3.012 Fundamentals f Materials Science Fall 2005 Lecture 13: 10.21.05 Electrchemical Equilibria Tday: LAST TIME...2 An example calculatin...3 THE ELECTROCHEMICAL POTENTIAL...4 Electrstatic energy cntributins
More information1 The limitations of Hartree Fock approximation
Chapter: Pst-Hartree Fck Methds - I The limitatins f Hartree Fck apprximatin The n electrn single determinant Hartree Fck wave functin is the variatinal best amng all pssible n electrn single determinants
More information**DO NOT ONLY RELY ON THIS STUDY GUIDE!!!**
Tpics lists: UV-Vis Absrbance Spectrscpy Lab & ChemActivity 3-6 (nly thrugh 4) I. UV-Vis Absrbance Spectrscpy Lab Beer s law Relates cncentratin f a chemical species in a slutin and the absrbance f that
More informationLecture 17: Free Energy of Multi-phase Solutions at Equilibrium
Lecture 17: 11.07.05 Free Energy f Multi-phase Slutins at Equilibrium Tday: LAST TIME...2 FREE ENERGY DIAGRAMS OF MULTI-PHASE SOLUTIONS 1...3 The cmmn tangent cnstructin and the lever rule...3 Practical
More informationLCAO APPROXIMATIONS OF ORGANIC Pi MO SYSTEMS The allyl system (cation, anion or radical).
Principles f Organic Chemistry lecture 5, page LCAO APPROIMATIONS OF ORGANIC Pi MO SYSTEMS The allyl system (catin, anin r radical).. Draw mlecule and set up determinant. 2 3 0 3 C C 2 = 0 C 2 3 0 = -
More informationA Mechanistic Approach to Bond Formation in H 2
A Mechanistic Apprach t Bnd Frmatin in H Frank iux Prfessr Emeritus f Chemistry Saint Jhnʹs University The centrality f the cvalent bnd t chemistry is captured in a shrt and elquent statement by Peter
More informationChapter 5: Diffusion (2)
Chapter 5: Diffusin () ISSUES TO ADDRESS... Nn-steady state diffusin and Fick s nd Law Hw des diffusin depend n structure? Chapter 5-1 Class Eercise (1) Put a sugar cube inside a cup f pure water, rughly
More informationGeneral Chemistry II, Unit I: Study Guide (part I)
1 General Chemistry II, Unit I: Study Guide (part I) CDS Chapter 14: Physical Prperties f Gases Observatin 1: Pressure- Vlume Measurements n Gases The spring f air is measured as pressure, defined as the
More informationd sinθ = mλ Interference and diffraction double slit or diffraction grating d sinθ = mλ d sinθ is the path difference x (small angle approximation)
Wave Optics Wave prperties f light The clrs in a rainbw are ROY G. BIV (Red, range, yellw, green, blue, indig, vilet). White light is a cmbinatin f all clrs Black is the absence f light Wavelength determines
More informationTOPPER SAMPLE PAPER 2 Class XII- Physics
TOPPER SAMPLE PAPER 2 Class XII- Physics Time: Three Hurs Maximum Marks: 70 General Instructins (a) All questins are cmpulsry. (b) There are 30 questins in ttal. Questins 1 t 8 carry ne mark each, questins
More informationChem 111 Summer 2013 Key III Whelan
Chem 111 Summer 2013 Key III Whelan Questin 1 6 Pints Classify each f the fllwing mlecules as plar r nnplar? a) NO + : c) CH 2 Cl 2 : b) XeF 4 : Questin 2 The hypthetical mlecule PY 3 Z 2 has the general
More informationName: Period: Date: BONDING NOTES HONORS CHEMISTRY
Name: Perid: Date: BONDING NOTES HONORS CHEMISTRY Directins: This packet will serve as yur ntes fr this chapter. Fllw alng with the PwerPint presentatin and fill in the missing infrmatin. Imprtant terms
More informationAP CHEMISTRY CHAPTER 6 NOTES THERMOCHEMISTRY
AP CHEMISTRY CHAPTER 6 NOTES THERMOCHEMISTRY Energy- the capacity t d wrk r t prduce heat 1 st Law f Thermdynamics: Law f Cnservatin f Energy- energy can be cnverted frm ne frm t anther but it can be neither
More informationAccelerated Chemistry POGIL: Half-life
Name: Date: Perid: Accelerated Chemistry POGIL: Half-life Why? Every radiistpe has a characteristic rate f decay measured by its half-life. Half-lives can be as shrt as a fractin f a secnd r as lng as
More informationThermodynamics Partial Outline of Topics
Thermdynamics Partial Outline f Tpics I. The secnd law f thermdynamics addresses the issue f spntaneity and invlves a functin called entrpy (S): If a prcess is spntaneus, then Suniverse > 0 (2 nd Law!)
More informationNUPOC STUDY GUIDE ANSWER KEY. Navy Recruiting Command
NUPOC SUDY GUIDE ANSWER KEY Navy Recruiting Cmmand CHEMISRY. ph represents the cncentratin f H ins in a slutin, [H ]. ph is a lg scale base and equal t lg[h ]. A ph f 7 is a neutral slutin. PH < 7 is acidic
More informationDr M. BROUARD. 5. Thermodynamic formulation of Transition State Theory Entropy of activation. Thermochemical kinetics. CHEMICAL REACTION RATES
CHEMICAL REACTION RATES Dr M. BROUARD Trinity Term 2003 A. Bimlecular Reactins 5 Lectures 1. Intrductin Simple cllisin thery. Ptential energy curves and surfaces. The reactin crdinate and barriers t reactin.
More informationALE 21. Gibbs Free Energy. At what temperature does the spontaneity of a reaction change?
Name Chem 163 Sectin: Team Number: ALE 21. Gibbs Free Energy (Reference: 20.3 Silberberg 5 th editin) At what temperature des the spntaneity f a reactin change? The Mdel: The Definitin f Free Energy S
More informationCHM112 Lab Graphing with Excel Grading Rubric
Name CHM112 Lab Graphing with Excel Grading Rubric Criteria Pints pssible Pints earned Graphs crrectly pltted and adhere t all guidelines (including descriptive title, prperly frmatted axes, trendline
More informationExperiment #3. Graphing with Excel
Experiment #3. Graphing with Excel Study the "Graphing with Excel" instructins that have been prvided. Additinal help with learning t use Excel can be fund n several web sites, including http://www.ncsu.edu/labwrite/res/gt/gt-
More informationChem 115 POGIL Worksheet - Week 8 Thermochemistry (Continued), Electromagnetic Radiation, and Line Spectra
Chem 115 POGIL Wrksheet - Week 8 Thermchemistry (Cntinued), Electrmagnetic Radiatin, and Line Spectra Why? As we saw last week, enthalpy and internal energy are state functins, which means that the sum
More informationSolution to HW14 Fall-2002
Slutin t HW14 Fall-2002 CJ5 10.CQ.003. REASONING AND SOLUTION Figures 10.11 and 10.14 shw the velcity and the acceleratin, respectively, the shadw a ball that underges unirm circular mtin. The shadw underges
More information11. DUAL NATURE OF RADIATION AND MATTER
11. DUAL NATURE OF RADIATION AND MATTER Very shrt answer and shrt answer questins 1. Define wrk functin f a metal? The minimum energy required fr an electrn t escape frm the metal surface is called the
More informationComplex Reactions and Mechanisms (continued)
5.60 Spring 2005 Lecture #29 page 1 Cmplex Reactins and Mechanisms (cntinued) Sme cmments abut analyzing kinetic data A) Reactins with ne reactant: A prducts a) Plt r analyze [A vs. t ln[a vs. t 1/[A vs.
More informationI. Analytical Potential and Field of a Uniform Rod. V E d. The definition of electric potential difference is
Length L>>a,b,c Phys 232 Lab 4 Ch 17 Electric Ptential Difference Materials: whitebards & pens, cmputers with VPythn, pwer supply & cables, multimeter, crkbard, thumbtacks, individual prbes and jined prbes,
More informationEdexcel GCSE Physics
Edexcel GCSE Physics Tpic 10: Electricity and circuits Ntes (Cntent in bld is fr Higher Tier nly) www.pmt.educatin The Structure f the Atm Psitively charged nucleus surrunded by negatively charged electrns
More informationPart One: Heat Changes and Thermochemistry. This aspect of Thermodynamics was dealt with in Chapter 6. (Review)
CHAPTER 18: THERMODYNAMICS AND EQUILIBRIUM Part One: Heat Changes and Thermchemistry This aspect f Thermdynamics was dealt with in Chapter 6. (Review) A. Statement f First Law. (Sectin 18.1) 1. U ttal
More informationUnit 14 Thermochemistry Notes
Name KEY Perid CRHS Academic Chemistry Unit 14 Thermchemistry Ntes Quiz Date Exam Date Lab Dates Ntes, Hmewrk, Exam Reviews and Their KEYS lcated n CRHS Academic Chemistry Website: https://cincchem.pbwrks.cm
More informationPhysics 2010 Motion with Constant Acceleration Experiment 1
. Physics 00 Mtin with Cnstant Acceleratin Experiment In this lab, we will study the mtin f a glider as it accelerates dwnhill n a tilted air track. The glider is supprted ver the air track by a cushin
More informationA Few Basic Facts About Isothermal Mass Transfer in a Binary Mixture
Few asic Facts but Isthermal Mass Transfer in a inary Miture David Keffer Department f Chemical Engineering University f Tennessee first begun: pril 22, 2004 last updated: January 13, 2006 dkeffer@utk.edu
More informationPhysics 212. Lecture 12. Today's Concept: Magnetic Force on moving charges. Physics 212 Lecture 12, Slide 1
Physics 1 Lecture 1 Tday's Cncept: Magnetic Frce n mving charges F qv Physics 1 Lecture 1, Slide 1 Music Wh is the Artist? A) The Meters ) The Neville rthers C) Trmbne Shrty D) Michael Franti E) Radiatrs
More informationStudy Guide Physics Pre-Comp 2013
I. Scientific Measurement Metric Units S.I. English Length Meter (m) Feet (ft.) Mass Kilgram (kg) Pund (lb.) Weight Newtn (N) Ounce (z.) r pund (lb.) Time Secnds (s) Secnds (s) Vlume Liter (L) Galln (gal)
More informationThermochemistry. Thermochemistry
Thermchemistry Petrucci, Harwd and Herring: Chapter 7 CHEM 1000A 3.0 Thermchemistry 1 Thermchemistry The study energy in chemical reactins A sub-discipline thermdynamics Thermdynamics studies the bulk
More informationExperiment #4 Gauss s Law Prelab Hints
Eperiment #4 Gauss s Law Prela Hints This la an prela will make etensive use f Ptentials an Gauss s Law, an using calculus t recast the electric fiel in terms f ptential The intent f this is t prvie sme
More information5.60 Thermodynamics & Kinetics Spring 2008
MIT OpenCurseWare http://cw.mit.edu 5.60 Thermdynamics & Kinetics Spring 2008 Fr infrmatin abut citing these materials r ur Terms f Use, visit: http://cw.mit.edu/terms. 5.60 Spring 2008 Lecture #17 page
More informationRegents Chemistry Period Unit 3: Atomic Structure. Unit 3 Vocabulary..Due: Test Day
Name Skills: 1. Interpreting Mdels f the Atm 2. Determining the number f subatmic particles 3. Determine P, e-, n fr ins 4. Distinguish istpes frm ther atms/ins Regents Chemistry Perid Unit 3: Atmic Structure
More informationCHE 105 EXAMINATION III November 11, 2010
CHE 105 EXAMINATION III Nvember 11, 2010 University f Kentucky Department f Chemistry READ THESE DIRECTIONS CAREFULLY BEFORE STARTING THE EXAMINATION! It is extremely imprtant that yu fill in the answer
More informationSupporting information
Electrnic Supplementary Material (ESI) fr Physical Chemistry Chemical Physics This jurnal is The wner Scieties 01 ydrgen perxide electrchemistry n platinum: twards understanding the xygen reductin reactin
More informationMANIPAL INSTITUTE OF TECHNOLOGY
MANIPAL INSTITUTE OF TECHNOLOGY MANIPAL UNIVERSITY, MANIPAL SECOND SEMESTER B.Tech. END-SEMESTER EXAMINATION - MAY 013 SUBJECT: ENGINEERING PHYSICS (PHY101/10) Time: 3 Hrs. Max. Marks: 50 Nte: Answer any
More informationCapacitance. Applications of Electric Potential. Capacitors in Kodak Cameras 3/17/2014. AP Physics B
3/7/04 apacitance P Physics B pplicatins f Electric Ptential Is there any way we can use a set f plates with an electric fiel? YES! We can make what is calle a Parallel Plate apacitr an Stre harges between
More informationName: Period: Date: BONDING NOTES ADVANCED CHEMISTRY
Name: Perid: Date: BONDING NOTES ADVANCED CHEMISTRY Directins: This packet will serve as yur ntes fr this chapter. Fllw alng with the PwerPint presentatin and fill in the missing infrmatin. Imprtant terms
More informationSCIENCE 10: CHEMISTRY,
, 1 Atmic Thery and Bnding The Nucleus - The particles that make up an atm are called subatmic particles - The three subatmic particles are prtns, neutrns and electrns. - Prtns, which have a +1 (psitive)
More informationNUMBERS, MATHEMATICS AND EQUATIONS
AUSTRALIAN CURRICULUM PHYSICS GETTING STARTED WITH PHYSICS NUMBERS, MATHEMATICS AND EQUATIONS An integral part t the understanding f ur physical wrld is the use f mathematical mdels which can be used t
More informationEnergy considerations Energy considerations
Energy cnsieratins 99.0.8 DRFT. Energy cnsieratins The wrk reuire t assemble tw charges, an is fun by first bringing frm infinity t its esire psitin (which reuires n wrk) an then bringing frm infinity
More informationComputational modeling techniques
Cmputatinal mdeling techniques Lecture 4: Mdel checing fr ODE mdels In Petre Department f IT, Åb Aademi http://www.users.ab.fi/ipetre/cmpmd/ Cntent Stichimetric matrix Calculating the mass cnservatin relatins
More informationSurface and Contact Stress
Surface and Cntact Stress The cncept f the frce is fundamental t mechanics and many imprtant prblems can be cast in terms f frces nly, fr example the prblems cnsidered in Chapter. Hwever, mre sphisticated
More informationCHEMISTRY 1903 SHI-LING KOU 2011
CHEMISTRY 1903 SHI-LING KOU 2011 THE ORIGINS OF MODERN CHEMISTRY Evlutin f the atmic thery Daltn s Atmic Thery (1808) Matter cnsists f indivisible particles (atms) Atms f ne element can t be cnverted int
More informationStudy Group Report: Plate-fin Heat Exchangers: AEA Technology
Study Grup Reprt: Plate-fin Heat Exchangers: AEA Technlgy The prblem under study cncerned the apparent discrepancy between a series f experiments using a plate fin heat exchanger and the classical thery
More informationCHEM Thermodynamics. Change in Gibbs Free Energy, G. Review. Gibbs Free Energy, G. Review
Review Accrding t the nd law f Thermdynamics, a prcess is spntaneus if S universe = S system + S surrundings > 0 Even thugh S system
More informationCompressibility Effects
Definitin f Cmpressibility All real substances are cmpressible t sme greater r lesser extent; that is, when yu squeeze r press n them, their density will change The amunt by which a substance can be cmpressed
More informationPrinciples of Organic Chemistry lecture 5, page 1
Principles f Organic Chemistry lecture 5, page 1 Bnding Mdels Fact: electrns hld mlecules tgether. Theries: mre than ne way t cnceptualize bnding. Let s fllw Carrll in the cnsideratin f tw theries f bnding.
More informationVibrations. Matti Hotokka Department of Physical Chemistry Åbo Akademi University
Vibratins Matti Htkka Department f Physical Chemistry Åb Akademi University Harmnic scillatr V(r) Schrödinger s equatin Define q = r - r e V ( q) = 1 2 fq 2 α = f hν r e r 2 2 h d + V ( q) Ψ( q) = EΨ(
More informationBiplots in Practice MICHAEL GREENACRE. Professor of Statistics at the Pompeu Fabra University. Chapter 13 Offprint
Biplts in Practice MICHAEL GREENACRE Prfessr f Statistics at the Pmpeu Fabra University Chapter 13 Offprint CASE STUDY BIOMEDICINE Cmparing Cancer Types Accrding t Gene Epressin Arrays First published:
More informationLecture 23: Lattice Models of Materials; Modeling Polymer Solutions
Lecture 23: 12.05.05 Lattice Mdels f Materials; Mdeling Plymer Slutins Tday: LAST TIME...2 The Bltzmann Factr and Partitin Functin: systems at cnstant temperature...2 A better mdel: The Debye slid...3
More informationStudent Exploration: Cell Energy Cycle
Name: Date: Student Explratin: Cell Energy Cycle Vcabulary: aerbic respiratin, anaerbic respiratin, ATP, cellular respiratin, chemical energy, chlrphyll, chlrplast, cytplasm, glucse, glyclysis, mitchndria,
More informationELECTROSTATIC FIELDS IN MATERIAL MEDIA
MF LCTROSTATIC FILDS IN MATRIAL MDIA 3/4/07 LCTURS Materials media may be classified in terms f their cnductivity σ (S/m) as: Cnductrs The cnductivity usually depends n temperature and frequency A material
More informationQCE Chemistry. Year 2015 Mark 0.00 Pages 20 Published Jan 31, Chemistry: Revision Notes. By Sophie (1 ATAR)
QCE Chemistry Year 2015 Mark 0.00 Pages 20 Published Jan 31, 2017 11 Chemistry: Revisin Ntes By Sphie (1 ATAR) Pwered by TCPDF (www.tcpdf.rg) Yur ntes authr, Sphie. Sphie achieved an ATAR f 1 in 2016 while
More informationCS 477/677 Analysis of Algorithms Fall 2007 Dr. George Bebis Course Project Due Date: 11/29/2007
CS 477/677 Analysis f Algrithms Fall 2007 Dr. Gerge Bebis Curse Prject Due Date: 11/29/2007 Part1: Cmparisn f Srting Algrithms (70% f the prject grade) The bjective f the first part f the assignment is
More informationMATHEMATICS SYLLABUS SECONDARY 5th YEAR
Eurpean Schls Office f the Secretary-General Pedaggical Develpment Unit Ref. : 011-01-D-8-en- Orig. : EN MATHEMATICS SYLLABUS SECONDARY 5th YEAR 6 perid/week curse APPROVED BY THE JOINT TEACHING COMMITTEE
More informationEinstein's special relativity the essentials
VCE Physics Unit 3: Detailed study Einstein's special relativity the essentials Key knwledge and skills (frm Study Design) describe the predictin frm Maxwell equatins that the speed f light depends nly
More informationCONSTRUCTING STATECHART DIAGRAMS
CONSTRUCTING STATECHART DIAGRAMS The fllwing checklist shws the necessary steps fr cnstructing the statechart diagrams f a class. Subsequently, we will explain the individual steps further. Checklist 4.6
More informationMATHEMATICS Higher Grade - Paper I
Higher Mathematics - Practice Eaminatin B Please nte the frmat f this practice eaminatin is different frm the current frmat. The paper timings are different and calculatrs can be used thrughut. MATHEMATICS
More informationUnit 11 Solutions- Guided Notes. What are alloys? What is the difference between heterogeneous and homogeneous mixtures?
Name: Perid: Unit 11 Slutins- Guided Ntes Mixtures: What is a mixture and give examples? What is a pure substance? What are allys? What is the difference between hetergeneus and hmgeneus mixtures? Slutins:
More information4 electron domains: 3 bonding and 1 non-bonding. 2 electron domains: 2 bonding and 0 non-bonding. 3 electron domains: 2 bonding and 1 non-bonding
[4.3D VSEPR] pg. 1 f 7 Curriculum The use f VSEPR thery t predict the electrn dmain gemetry and the mlecular gemetry fr species with tw, three and fur electrn dmains. Shapes f species are determined by
More informationLecture 24: Flory-Huggins Theory
Lecture 24: 12.07.05 Flry-Huggins Thery Tday: LAST TIME...2 Lattice Mdels f Slutins...2 ENTROPY OF MIXING IN THE FLORY-HUGGINS MODEL...3 CONFIGURATIONS OF A SINGLE CHAIN...3 COUNTING CONFIGURATIONS FOR
More informationDifferentiation Applications 1: Related Rates
Differentiatin Applicatins 1: Related Rates 151 Differentiatin Applicatins 1: Related Rates Mdel 1: Sliding Ladder 10 ladder y 10 ladder 10 ladder A 10 ft ladder is leaning against a wall when the bttm
More informationName: Period: Date: PERIODIC TABLE NOTES ADVANCED CHEMISTRY
Name: Perid: Date: PERIODIC TABLE NOTES ADVANCED CHEMISTRY Directins: This packet will serve as yur ntes fr this chapter. Fllw alng with the PwerPint presentatin and fill in the missing infrmatin. Imprtant
More informationCHEM 116 Electrochemistry at Non-Standard Conditions, and Intro to Thermodynamics
CHEM 116 Electrchemistry at Nn-Standard Cnditins, and Intr t Thermdynamics Imprtant annuncement: If yu brrwed a clicker frm me this semester, return it t me at the end f next lecture r at the final exam
More information( ) kt. Solution. From kinetic theory (visualized in Figure 1Q9-1), 1 2 rms = 2. = 1368 m/s
.9 Kinetic Mlecular Thery Calculate the effective (rms) speeds f the He and Ne atms in the He-Ne gas laser tube at rm temperature (300 K). Slutin T find the rt mean square velcity (v rms ) f He atms at
More informationv , Michael E. Hanyak, Jr., All Rights Reserved Page 7-18
v07.08.04 007, Michael E. Hanyak, Jr., All Rights Reserved age 7-8 Energy Balance Intrductin Functinal frm: Hw t evaluate hmix,,? [ X H 0.60* + 0.40* + Δ () mix Ĥ is mlar enthalpy (kj/gml) f mixture at
More informationAP Chemistry Assessment 2
AP Chemistry Assessment 2 DATE OF ADMINISTRATION: January 8 January 12 TOPICS COVERED: Fundatinal Tpics, Reactins, Gases, Thermchemistry, Atmic Structure, Peridicity, and Bnding. MULTIPLE CHOICE KEY AND
More informationCHAPTER 3 INEQUALITIES. Copyright -The Institute of Chartered Accountants of India
CHAPTER 3 INEQUALITIES Cpyright -The Institute f Chartered Accuntants f India INEQUALITIES LEARNING OBJECTIVES One f the widely used decisin making prblems, nwadays, is t decide n the ptimal mix f scarce
More informationComputational modeling techniques
Cmputatinal mdeling techniques Lecture 2: Mdeling change. In Petre Department f IT, Åb Akademi http://users.ab.fi/ipetre/cmpmd/ Cntent f the lecture Basic paradigm f mdeling change Examples Linear dynamical
More informationHigher Mathematics Booklet CONTENTS
Higher Mathematics Bklet CONTENTS Frmula List Item Pages The Straight Line Hmewrk The Straight Line Hmewrk Functins Hmewrk 3 Functins Hmewrk 4 Recurrence Relatins Hmewrk 5 Differentiatin Hmewrk 6 Differentiatin
More informationEE247B/ME218: Introduction to MEMS Design Lecture 7m1: Lithography, Etching, & Doping CTN 2/6/18
EE247B/ME218 Intrductin t MEMS Design Lecture 7m1 Lithgraphy, Etching, & Dping Dping f Semicnductrs Semicnductr Dping Semicnductrs are nt intrinsically cnductive T make them cnductive, replace silicn atms
More informationSynchronous Motor V-Curves
Synchrnus Mtr V-Curves 1 Synchrnus Mtr V-Curves Intrductin Synchrnus mtrs are used in applicatins such as textile mills where cnstant speed peratin is critical. Mst small synchrnus mtrs cntain squirrel
More informationName: Period: Date: PERIODIC TABLE NOTES HONORS CHEMISTRY
Name: Perid: Date: PERIODIC TABLE NOTES HONORS CHEMISTRY Directins: This packet will serve as yur ntes fr this chapter. Fllw alng with the PwerPint presentatin and fill in the missing infrmatin. Imprtant
More informationFebruary 28, 2013 COMMENTS ON DIFFUSION, DIFFUSIVITY AND DERIVATION OF HYPERBOLIC EQUATIONS DESCRIBING THE DIFFUSION PHENOMENA
February 28, 2013 COMMENTS ON DIFFUSION, DIFFUSIVITY AND DERIVATION OF HYPERBOLIC EQUATIONS DESCRIBING THE DIFFUSION PHENOMENA Mental Experiment regarding 1D randm walk Cnsider a cntainer f gas in thermal
More information2004 AP CHEMISTRY FREE-RESPONSE QUESTIONS
2004 AP CHEMISTRY FREE-RESPONSE QUESTIONS 6. An electrchemical cell is cnstructed with an pen switch, as shwn in the diagram abve. A strip f Sn and a strip f an unknwn metal, X, are used as electrdes.
More informationAP Statistics Notes Unit Two: The Normal Distributions
AP Statistics Ntes Unit Tw: The Nrmal Distributins Syllabus Objectives: 1.5 The student will summarize distributins f data measuring the psitin using quartiles, percentiles, and standardized scres (z-scres).
More informationThe special theory of relativity
The special thery f relatiity The preliminaries f special thery f relatiity The Galilean thery f relatiity states that it is impssible t find the abslute reference system with mechanical eperiments. In
More informationChapter 17: Thermodynamics: Spontaneous and Nonspontaneous Reactions and Processes
Chapter 17: hermdynamics: Spntaneus and Nnspntaneus Reactins and Prcesses Learning Objectives 17.1: Spntaneus Prcesses Cmparing and Cntrasting the hree Laws f hermdynamics (1 st Law: Chap. 5; 2 nd & 3
More informationChemistry 1A Fall 2000
Chemistry 1A Fall 2000 Midterm Exam III, versin B Nvember 14, 2000 (Clsed bk, 90 minutes, 155 pints) Name: SID: Sectin Number: T.A. Name: Exam infrmatin, extra directins, and useful hints t maximize yur
More informationUNIT 5: ATOMIC THEORY & THE PERIODIC TABLE CHEMISTRY 215, DUFFEY, CHAPTER 4 & SECTION 6.1
UNIT 5: ATOMIC THEORY & THE PERIODIC TABLE CHEMISTRY 215, DUFFEY, CHAPTER 4 & SECTION 6.1 BIG IDEAS (we will tuch n small parts f Chp.5 as well) 4.1 Early Ideas Abut Matter 4.2 Defining the Atm 4.3 Hw
More informationFall 2013 Physics 172 Recitation 3 Momentum and Springs
Fall 03 Physics 7 Recitatin 3 Mmentum and Springs Purpse: The purpse f this recitatin is t give yu experience wrking with mmentum and the mmentum update frmula. Readings: Chapter.3-.5 Learning Objectives:.3.
More informationQ1. In figure 1, Q = 60 µc, q = 20 µc, a = 3.0 m, and b = 4.0 m. Calculate the total electric force on q due to the other 2 charges.
Phys10 Secnd Majr-08 Zer Versin Crdinatr: Dr. I. M. Nasser Saturday, May 3, 009 Page: 1 Q1. In figure 1, Q = 60 µc, q = 0 µc, a = 3.0 m, and b = 4.0 m. Calculate the ttal electric frce n q due t the ther
More informationmaking triangle (ie same reference angle) ). This is a standard form that will allow us all to have the X= y=
Intrductin t Vectrs I 21 Intrductin t Vectrs I 22 I. Determine the hrizntal and vertical cmpnents f the resultant vectr by cunting n the grid. X= y= J. Draw a mangle with hrizntal and vertical cmpnents
More informationMidterm Review Notes - Unit 1 Intro
Midterm Review Ntes - Unit 1 Intr 3 States f Matter Slid definite shape, definite vlume, very little mlecular mvement Liquid definite vlume, takes shape f cntainer, mlecules mve faster Gas des nt have
More informationMore Tutorial at
Answer each questin in the space prvided; use back f page if extra space is needed. Answer questins s the grader can READILY understand yur wrk; nly wrk n the exam sheet will be cnsidered. Write answers,
More informationhttps://goo.gl/eaqvfo SUMMER REV: Half-Life DUE DATE: JULY 2 nd
NAME: DUE DATE: JULY 2 nd AP Chemistry SUMMER REV: Half-Life Why? Every radiistpe has a characteristic rate f decay measured by its half-life. Half-lives can be as shrt as a fractin f a secnd r as lng
More information, which yields. where z1. and z2
The Gaussian r Nrmal PDF, Page 1 The Gaussian r Nrmal Prbability Density Functin Authr: Jhn M Cimbala, Penn State University Latest revisin: 11 September 13 The Gaussian r Nrmal Prbability Density Functin
More informationModule 4: General Formulation of Electric Circuit Theory
Mdule 4: General Frmulatin f Electric Circuit Thery 4. General Frmulatin f Electric Circuit Thery All electrmagnetic phenmena are described at a fundamental level by Maxwell's equatins and the assciated
More informationLecture 5: Equilibrium and Oscillations
Lecture 5: Equilibrium and Oscillatins Energy and Mtin Last time, we fund that fr a system with energy cnserved, v = ± E U m ( ) ( ) One result we see immediately is that there is n slutin fr velcity if
More informationSession #22: Homework Solutions
Sessin #22: Hmewrk Slutins Prblem #1 (a) In the cntext f amrphus inrganic cmpunds, name tw netwrk frmers, tw netwrk mdifiers, and ne intermediate. (b) Sketch the variatin f mlar vlume with temperature
More information