1. Collision Theory 2. Activation Energy 3. Potential Energy Diagrams

Size: px
Start display at page:

Download "1. Collision Theory 2. Activation Energy 3. Potential Energy Diagrams"

Transcription

1 Chemistry 12 Reactio Kietics II Name: Date: Block: 1. Collisio Theory 2. Activatio Eergy 3. Potetial Eergy Diagrams Collisio Theory (Kietic Molecular Theory) I order for two molecules to react, they must with each other. Whe they collide they trasfer amog themselves. Cosider a hypothetical reactio betwee two gas particles, A ad B, to form AB accordig to the reactio: A (g) + B (g) à AB (g) Total possible collisios: The rate of reactio is directly proportioal to the product of the cocetratios of the reactats. Whe two variables are directly proportioal to oe aother, there is a costat that relates the two, called a proportioality costat, represeted by the letter k. Rate Law: Reactio rate = The proportioality costat is called a rate-costat. Each reactio has its ow uique rate law ad its ow uique rate costat. For may reactios, x ad y are equal to 1, ad are called reactat orders. We will oly be dealig with reactios with a order of Assume a reactio occurs by this rate law: rate = k[a]. How would the rate be affected by each of the followig chages i cocetratio? a) [A] is doubled. b) [A] is halved. 2. Assume a gaseous reactio occurs by this rate law: rate = k[a][b]. How would the rate be affected if the volume of the cotaier were halved?

2 3. We also kow that temperature chages the rate. a) Cosiderig the rate law, rate = k[a], how is the rate of a reactio affected by icreasig temperature? b) What part of the rate law must be affected by chagig temperature? Most collisios are ot successful ad do ot result i a reactio. A successful collisio requires the followig: Which of the followig reactio is fastest? a. H 2(g) + I 2(g) à 2HI (g) b. Ag + (aq) + I - (aq) à AgI (s) c. C 6H 12O 6 (s) + 6 O 2(g) à 6 CO 2(g) + 6 H 2O (g) d. 5C 2O 4 2- (aq) + 2MO 4 2- (aq) + 16H + (aq) à 10CO 2(g) + 2M 2+ (aq) + 8H 2O (l) Activatio Eergy (E a) Activatio Eergy: Must overcome: o Repulsive forces betwee electro clouds of the reactig molecules o Weake or break bods

3 Trasitio State Theory: Whe molecules have eough kietic eergy to react collide, their electro clouds iitially repel oe aother to form a ustable trasitory cofiguratio of atoms. Because they have sufficiet kietic eergy to overcome this, the ustable complex will form the desired products. Bod breakig requires eergy, while bod formig results i eergy. Example: H 2 (g) + I 2 (g) à 2 HI (g) Potetial Eergy Diagrams Potetial Eergy Diagrams: Graphical represetatio of the eergy chages that take place durig a chemical reactio. The activatio eergy, Ea, is the differece betwee the potetial eergy of the activated complex ad the potetial eergy of the reactat molecules. It represets the amout of eergy the reactat molecules must gai to form a activated complex. E a = The ethalpy chage (ΔH) is the differece betwee the total potetial eergy of the products ad the total potetial eergy of the reactats. ΔH = Calorimetry the sciece of measurig the chage i heat associated with a chemical reactio

4 1. Label each arrow i the followig diagram: Progress of Reactio 2. Cosider the followig graph o the right. a) What is the potetial eergy of the activated complex? b) What is the activatio eergy of the reactio? c) What is the ΔH for this reactio? d) Is the reactio edothermic or exothermic? POTENTIAL ENERGY Progress of Reactio ReactioReactio May chemical reactios are reversible uder certai coditios. The first potetial eergy diagram could be read i reverse to give the same measuremets provided by the secod diagram.

5 3. Aswer the followig questios about this potetial eergy diagram: a) Give ΔH for the forward reactio. Is this reactio exothermic or edothermic? b) Give ΔH for the reverse reactio. Is this reactio exothermic or edothermic? c) Give E a for the forward reactio. d) Give E a for the reverse reactio. e) Which is faster, the forward or reverse rate? f) Give the potetial eergy for the activated complex. How does this value compare for the forward ad reverse reactios? 4. Cosider the graph ad equatio o the right: a) What species represets the trasitio state? b) Which is faster, the forward or reverse rate? c) Circle the specie(s) that has the strogest bods: A 2 + B 2 OR AB d) Explai your aswer to the questio above. Hebde Workbook: Pg. 23 #34, 37 Pg. 25 #41-45

In order for two molecules to react, they must with each other. When they collide they transfer among themselves.

In order for two molecules to react, they must with each other. When they collide they transfer among themselves. Chemistry 12 Reaction Kinetics II Name: Date: Block: 1. Collision Theory 2. Activation Energy 3. Potential Energy Diagrams Collision Theory (Kinetic Molecular Theory) In order for two molecules to react,

More information

Chapter 14: Chemical Equilibrium

Chapter 14: Chemical Equilibrium hapter 14: hemical Equilibrium 46 hapter 14: hemical Equilibrium Sectio 14.1: Itroductio to hemical Equilibrium hemical equilibrium is the state where the cocetratios of all reactats ad products remai

More information

Chemical Kinetics CHAPTER 14. Chemistry: The Molecular Nature of Matter, 6 th edition By Jesperson, Brady, & Hyslop. CHAPTER 14 Chemical Kinetics

Chemical Kinetics CHAPTER 14. Chemistry: The Molecular Nature of Matter, 6 th edition By Jesperson, Brady, & Hyslop. CHAPTER 14 Chemical Kinetics Chemical Kietics CHAPTER 14 Chemistry: The Molecular Nature of Matter, 6 th editio By Jesperso, Brady, & Hyslop CHAPTER 14 Chemical Kietics Learig Objectives: Factors Affectig Reactio Rate: o Cocetratio

More information

Announcements, Nov. 19 th

Announcements, Nov. 19 th Aoucemets, Nov. 9 th Lecture PRS Quiz topic: results Chemical through Kietics July 9 are posted o the course website. Chec agaist Kietics LabChec agaist Kietics Lab O Fial Exam, NOT 3 Review Exam 3 ad

More information

Unit 5. Gases (Answers)

Unit 5. Gases (Answers) Uit 5. Gases (Aswers) Upo successful completio of this uit, the studets should be able to: 5. Describe what is meat by gas pressure.. The ca had a small amout of water o the bottom to begi with. Upo heatig

More information

Answer Key. Chapter 1

Answer Key. Chapter 1 Aswer Key Chapter 1 Page 3, Quick Check a) Rate of decompositio of SO 2Cl 2. b) The slope becomes less ad less steep. c) The rate decreases as the reactio proceeds. d) -0.00023 mol/l/s (or +) e) Rate is

More information

Kinetics of Complex Reactions

Kinetics of Complex Reactions Kietics of Complex Reactios by Flick Colema Departmet of Chemistry Wellesley College Wellesley MA 28 wcolema@wellesley.edu Copyright Flick Colema 996. All rights reserved. You are welcome to use this documet

More information

Nernst Equation. Nernst Equation. Electric Work and Gibb's Free Energy. Skills to develop. Electric Work. Gibb's Free Energy

Nernst Equation. Nernst Equation. Electric Work and Gibb's Free Energy. Skills to develop. Electric Work. Gibb's Free Energy Nerst Equatio Skills to develop Eplai ad distiguish the cell potetial ad stadard cell potetial. Calculate cell potetials from kow coditios (Nerst Equatio). Calculate the equilibrium costat from cell potetials.

More information

Solutions to Equilibrium Practice Problems

Solutions to Equilibrium Practice Problems Solutios to Equilibrium Practice Problems Chem09 Fial Booklet Problem 1. Solutio: PO 4 10 eq The expressio for K 3 5 P O 4 eq eq PO 4 10 iit 1 M I (a) Q 1 3, the reactio proceeds to the right. 5 5 P O

More information

Physics Supplement to my class. Kinetic Theory

Physics Supplement to my class. Kinetic Theory Physics Supplemet to my class Leaers should ote that I have used symbols for geometrical figures ad abbreviatios through out the documet. Kietic Theory 1 Most Probable, Mea ad RMS Speed of Gas Molecules

More information

Answer Key, Problem Set 1, Written

Answer Key, Problem Set 1, Written Cheistry 1 Mies, Sprig, 018 Aswer Key, Proble Set 1, Writte 1. 14.3;. 14.34 (add part (e): Estiate / calculate the iitial rate of the reactio); 3. NT1; 4. NT; 5. 14.37; 6. 14.39; 7. 14.41; 8. NT3; 9. 14.46;

More information

Section 5.5. Infinite Series: The Ratio Test

Section 5.5. Infinite Series: The Ratio Test Differece Equatios to Differetial Equatios Sectio 5.5 Ifiite Series: The Ratio Test I the last sectio we saw that we could demostrate the covergece of a series a, where a 0 for all, by showig that a approaches

More information

Chem Discussion #13 Chapter 10. Correlation diagrams for diatomic molecules. Key

Chem Discussion #13 Chapter 10. Correlation diagrams for diatomic molecules. Key Chem 101 017 Discussio #13 Chapter 10. Correlatio diagrams for diatomic molecules. Key 1. Below is a plot of the first 10 ioizatio eergies for a sigle atom i 3 rd row of the periodic table. The x- axis

More information

What is the oxidation number of N in KNO3? Today. Review for our Quiz! K is +1, O is -2 molecule is no charge 1(+1) + 3(-2) = -5 N must be +5

What is the oxidation number of N in KNO3? Today. Review for our Quiz! K is +1, O is -2 molecule is no charge 1(+1) + 3(-2) = -5 N must be +5 Today What is the oxidatio umber of N i KNO3? Review for our Quiz! Thermo ad Electrochemistry What happes whe the coditios are ot stadard Nerst Equatio! A.!! 0! B.!! +1! C.!! -1! D.!! +3! E.!! +5 K is

More information

True Nature of Potential Energy of a Hydrogen Atom

True Nature of Potential Energy of a Hydrogen Atom True Nature of Potetial Eergy of a Hydroge Atom Koshu Suto Key words: Bohr Radius, Potetial Eergy, Rest Mass Eergy, Classical Electro Radius PACS codes: 365Sq, 365-w, 33+p Abstract I cosiderig the potetial

More information

Polymerization Lab p. 1 Polymerization Lab

Polymerization Lab p. 1 Polymerization Lab Polymerizatio Lab p. 1 Polymerizatio Lab Itroductio: Polymers (Greek-PLY...may ad MES...parts) have existed sice the begiig of life. Both "atural" ad "sythetic" polymers are a itegral part of our life.

More information

A. Much too slow. C. Basically about right. E. Much too fast

A. Much too slow. C. Basically about right. E. Much too fast Geeral Questio 1 t this poit, we have bee i this class for about a moth. It seems like this is a good time to take stock of how the class is goig. g I promise ot to look at idividual resposes, so be cadid!

More information

5.1 Energy Changes in Chemical and Nuclear Reactions

5.1 Energy Changes in Chemical and Nuclear Reactions Figure 1 Our use of fossil fuels is usustaiable. New sources of gree, sustaiable eergy are eeded to meet the world s growig demad. 5.1 Eergy Chages i Chemical ad Nuclear Reactios Our ability to haress

More information

AME 513. " Lecture 3 Chemical thermodynamics I 2 nd Law

AME 513.  Lecture 3 Chemical thermodynamics I 2 nd Law AME 513 Priciples of Combustio " Lecture 3 Chemical thermodyamics I 2 d Law Outlie" Why do we eed to ivoke chemical equilibrium? Degrees Of Reactio Freedom (DORFs) Coservatio of atoms Secod Law of Thermodyamics

More information

Atomic Physics 4. Name: Date: 1. The de Broglie wavelength associated with a car moving with a speed of 20 m s 1 is of the order of. A m.

Atomic Physics 4. Name: Date: 1. The de Broglie wavelength associated with a car moving with a speed of 20 m s 1 is of the order of. A m. Name: Date: Atomic Pysics 4 1. Te de Broglie wavelegt associated wit a car movig wit a speed of 0 m s 1 is of te order of A. 10 38 m. B. 10 4 m. C. 10 4 m. D. 10 38 m.. Te diagram below sows tree eergy

More information

Bohr s Atomic Model Quantum Mechanical Model

Bohr s Atomic Model Quantum Mechanical Model September 7, 0 - Summary - Itroductio to Atomic Theory Bohr s Atomic Model Quatum Mechaical Model 3- Some Defiitio 3- Projects Temperature Pressure Website Subject Areas Plasma is a Mixture of electros,

More information

Mathematics of the Variation and Mole Ratio Methods of Complex Determination

Mathematics of the Variation and Mole Ratio Methods of Complex Determination Joural of the Arkasas Academy of Sciece Volume 22 Article 18 1968 Mathematics of the Variatio ad Mole Ratio Methods of omplex Determiatio James O. Wear Souther Research Support eter Follow this ad additioal

More information

Chemical Engineering 160/260 Polymer Science and Engineering. Model for Polymer Solutions February 5, 2001

Chemical Engineering 160/260 Polymer Science and Engineering. Model for Polymer Solutions February 5, 2001 Chemical Egieerig 60/60 Polymer Sciece ad Egieerig Lecture 9 - Flory-Huggis Model for Polymer Solutios February 5, 00 Read Sperlig, Chapter 4 Objectives! To develop the classical Flory-Huggis theory for

More information

6.3 Testing Series With Positive Terms

6.3 Testing Series With Positive Terms 6.3. TESTING SERIES WITH POSITIVE TERMS 307 6.3 Testig Series With Positive Terms 6.3. Review of what is kow up to ow I theory, testig a series a i for covergece amouts to fidig the i= sequece of partial

More information

Chapter 4. Fourier Series

Chapter 4. Fourier Series Chapter 4. Fourier Series At this poit we are ready to ow cosider the caoical equatios. Cosider, for eample the heat equatio u t = u, < (4.) subject to u(, ) = si, u(, t) = u(, t) =. (4.) Here,

More information

MASSACHUSETTS INSTITUTE OF TECHNOLOGY Department of Electrical Engineering and Computer Science. BACKGROUND EXAM September 30, 2004.

MASSACHUSETTS INSTITUTE OF TECHNOLOGY Department of Electrical Engineering and Computer Science. BACKGROUND EXAM September 30, 2004. MASSACHUSETTS INSTITUTE OF TECHNOLOGY Departmet of Electrical Egieerig ad Computer Sciece 6.34 Discrete Time Sigal Processig Fall 24 BACKGROUND EXAM September 3, 24. Full Name: Note: This exam is closed

More information

x a x a Lecture 2 Series (See Chapter 1 in Boas)

x a x a Lecture 2 Series (See Chapter 1 in Boas) Lecture Series (See Chapter i Boas) A basic ad very powerful (if pedestria, recall we are lazy AD smart) way to solve ay differetial (or itegral) equatio is via a series expasio of the correspodig solutio

More information

Math 105: Review for Final Exam, Part II - SOLUTIONS

Math 105: Review for Final Exam, Part II - SOLUTIONS Math 5: Review for Fial Exam, Part II - SOLUTIONS. Cosider the fuctio f(x) = x 3 lx o the iterval [/e, e ]. (a) Fid the x- ad y-coordiates of ay ad all local extrema ad classify each as a local maximum

More information

Practice Questions for Exam 3 CH 1020 Spring 2017

Practice Questions for Exam 3 CH 1020 Spring 2017 Practice Questios for Exam 3 C 1020 Sprig 2017 1. Which of the followig ca be cosidered a Brøsted-Lowry base? 5. What is the p of a solutio for which [Ba(O) 2 ] = 0.015 M? 6. The figure below shows three

More information

Castiel, Supernatural, Season 6, Episode 18

Castiel, Supernatural, Season 6, Episode 18 13 Differetial Equatios the aswer to your questio ca best be epressed as a series of partial differetial equatios... Castiel, Superatural, Seaso 6, Episode 18 A differetial equatio is a mathematical equatio

More information

Signals and Systems. Problem Set: From Continuous-Time to Discrete-Time

Signals and Systems. Problem Set: From Continuous-Time to Discrete-Time Sigals ad Systems Problem Set: From Cotiuous-Time to Discrete-Time Updated: October 5, 2017 Problem Set Problem 1 - Liearity ad Time-Ivariace Cosider the followig systems ad determie whether liearity ad

More information

Physics Oct Reading

Physics Oct Reading Physics 301 21-Oct-2002 17-1 Readig Fiish K&K chapter 7 ad start o chapter 8. Also, I m passig out several Physics Today articles. The first is by Graham P. Collis, August, 1995, vol. 48, o. 8, p. 17,

More information

Comparing your lab results with the others by one-way ANOVA

Comparing your lab results with the others by one-way ANOVA Comparig your lab results with the others by oe-way ANOVA You may have developed a ew test method ad i your method validatio process you would like to check the method s ruggedess by coductig a simple

More information

Zumdahl (pp [atomic properties] ), [ionic radii] )

Zumdahl (pp [atomic properties] ), [ionic radii] ) Chemistry 1B-AL Fall 2016 advetures lectures 7-8 Zumdahl (pp. 571-582 [atomic properties] ), 606-609 [ioic radii] ) 1 Chemistry 1B AL Electroic Structure ad Periodic Properties of Atoms 2 Zumdahl (pp.

More information

Lecture 9: Diffusion, Electrostatics review, and Capacitors. Context

Lecture 9: Diffusion, Electrostatics review, and Capacitors. Context EECS 5 Sprig 4, Lecture 9 Lecture 9: Diffusio, Electrostatics review, ad Capacitors EECS 5 Sprig 4, Lecture 9 Cotext I the last lecture, we looked at the carriers i a eutral semicoductor, ad drift currets

More information

First Year Quantitative Comp Exam Spring, Part I - 203A. f X (x) = 0 otherwise

First Year Quantitative Comp Exam Spring, Part I - 203A. f X (x) = 0 otherwise First Year Quatitative Comp Exam Sprig, 2012 Istructio: There are three parts. Aswer every questio i every part. Questio I-1 Part I - 203A A radom variable X is distributed with the margial desity: >

More information

9.4.3 Fundamental Parameters. Concentration Factor. Not recommended. See Extraction factor. Decontamination Factor

9.4.3 Fundamental Parameters. Concentration Factor. Not recommended. See Extraction factor. Decontamination Factor 9.4.3 Fudametal Parameters Cocetratio Factor Not recommeded. See Extractio factor. Decotamiatio Factor The ratio of the proportio of cotamiat to product before treatmet to the proportio after treatmet.

More information

For example suppose we divide the interval [0,2] into 5 equal subintervals of length

For example suppose we divide the interval [0,2] into 5 equal subintervals of length Math 1206 Calculus Sec 1: Estimatig with Fiite Sums Abbreviatios: wrt with respect to! for all! there exists! therefore Def defiitio Th m Theorem sol solutio! perpedicular iff or! if ad oly if pt poit

More information

Homework 7 Due 5 December 2017 The numbers following each question give the approximate percentage of marks allocated to that question.

Homework 7 Due 5 December 2017 The numbers following each question give the approximate percentage of marks allocated to that question. Name: Homework 7 Due 5 December 2017 The umbers followig each questio give the approximate percetage of marks allocated to that questio. 1. Use the reciprocal metric tesor agai to calculate the agle betwee

More information

CHEE 221: Chemical Processes and Systems

CHEE 221: Chemical Processes and Systems CHEE 221: Chemical Processes ad Systems Module 3. Material Balaces with Reactio Part a: Stoichiometry ad Methodologies (Felder & Rousseau Ch 4.6 4.8 ot 4.6c ) Material Balaces o Reactive Processes What

More information

Lab(8) controller design using root locus

Lab(8) controller design using root locus Lab(8) cotroller desig usig root locus I this lab we will lear how to desig a cotroller usig root locus but before this we eed to aswer the followig questios: What is root locus? What is the purpose of

More information

Measures of Spread: Standard Deviation

Measures of Spread: Standard Deviation Measures of Spread: Stadard Deviatio So far i our study of umerical measures used to describe data sets, we have focused o the mea ad the media. These measures of ceter tell us the most typical value of

More information

The Wave Function and Quantum Reality

The Wave Function and Quantum Reality The Wave Fuctio ad Quatum Reality Sha Gao Uit for History ad Philosophy of Sciece & Cetre for Time, SOPHI Uiversity of Sydey, Sydey, NSW 006, Australia Abstract. We ivestigate the meaig of the wave fuctio

More information

EXPERIMENT OF SIMPLE VIBRATION

EXPERIMENT OF SIMPLE VIBRATION EXPERIMENT OF SIMPLE VIBRATION. PURPOSE The purpose of the experimet is to show free vibratio ad damped vibratio o a system havig oe degree of freedom ad to ivestigate the relatioship betwee the basic

More information

Infinite Sequences and Series

Infinite Sequences and Series Chapter 6 Ifiite Sequeces ad Series 6.1 Ifiite Sequeces 6.1.1 Elemetary Cocepts Simply speakig, a sequece is a ordered list of umbers writte: {a 1, a 2, a 3,...a, a +1,...} where the elemets a i represet

More information

A sequence of numbers is a function whose domain is the positive integers. We can see that the sequence

A sequence of numbers is a function whose domain is the positive integers. We can see that the sequence Sequeces A sequece of umbers is a fuctio whose domai is the positive itegers. We ca see that the sequece,, 2, 2, 3, 3,... is a fuctio from the positive itegers whe we write the first sequece elemet as

More information

PROBABILITY AMPLITUDE AND INTERFERENCE

PROBABILITY AMPLITUDE AND INTERFERENCE PROILITY MPLITUDE ND INTERFERENCE I. Probability amplitude Suppose that particle is placed i the ifiite square well potetial. Let the state of the particle be give by ϕ ad let the system s eergy eigestates

More information

1 Adiabatic and diabatic representations

1 Adiabatic and diabatic representations 1 Adiabatic ad diabatic represetatios 1.1 Bor-Oppeheimer approximatio The time-idepedet Schrödiger equatio for both electroic ad uclear degrees of freedom is Ĥ Ψ(r, R) = E Ψ(r, R), (1) where the full molecular

More information

Section 13.3 Area and the Definite Integral

Section 13.3 Area and the Definite Integral Sectio 3.3 Area ad the Defiite Itegral We ca easily fid areas of certai geometric figures usig well-kow formulas: However, it is t easy to fid the area of a regio with curved sides: METHOD: To evaluate

More information

Things you should know when you leave Discussion today for one-electron atoms:

Things you should know when you leave Discussion today for one-electron atoms: E = -R Thigs ou should kow whe ou leave Discussio toda for oe-electro atoms: = -.79 0-8 J = -.6eV ΔEmatter=E-Em ; Ioizatio Eerg=E E(iitial) ΔΕlight=hνlight= IE +KE. Cosider the followig eerg levels of

More information

SPEC/4/PHYSI/SPM/ENG/TZ0/XX PHYSICS PAPER 1 SPECIMEN PAPER. 45 minutes INSTRUCTIONS TO CANDIDATES

SPEC/4/PHYSI/SPM/ENG/TZ0/XX PHYSICS PAPER 1 SPECIMEN PAPER. 45 minutes INSTRUCTIONS TO CANDIDATES SPEC/4/PHYSI/SPM/ENG/TZ0/XX PHYSICS STANDARD LEVEL PAPER 1 SPECIMEN PAPER 45 miutes INSTRUCTIONS TO CANDIDATES Do ot ope this examiatio paper util istructed to do so. Aswer all the questios. For each questio,

More information

For example suppose we divide the interval [0,2] into 5 equal subintervals of length

For example suppose we divide the interval [0,2] into 5 equal subintervals of length Math 120c Calculus Sec 1: Estimatig with Fiite Sums I Area A Cosider the problem of fidig the area uder the curve o the fuctio y!x 2 + over the domai [0,2] We ca approximate this area by usig a familiar

More information

Section 5.2: Calorimetry and Enthalpy Tutorial 1 Practice, page 297

Section 5.2: Calorimetry and Enthalpy Tutorial 1 Practice, page 297 Sectio 52: Calorietry ad Ethalpy Tutorial 1 Practice, page 297 1 Give: V 60 L ; T iitial 25 C ; T fial 75 C; d H2O(l) H2O(l) 100 g/l Required: theral eergy required, q Aalysis: q cδt Solutio: Step 1: Deterie

More information

MATH 129 FINAL EXAM REVIEW PACKET (Revised Spring 2008)

MATH 129 FINAL EXAM REVIEW PACKET (Revised Spring 2008) MATH 9 FINAL EXAM REVIEW PACKET (Revised Sprig 8) The followig questios ca be used as a review for Math 9. These questios are ot actual samples of questios that will appear o the fial exam, but they will

More information

What Is Required? You need to determine the hydronium ion concentration in an aqueous solution. K w = [H 3 O + ][OH ] =

What Is Required? You need to determine the hydronium ion concentration in an aqueous solution. K w = [H 3 O + ][OH ] = Calculatig the [H3O + ] or [OH ] i Aqueous Solutio (Studet textbook page 500) 11. The cocetratio of hydroxide ios, OH (aq), i a solutio at 5C is 0.150 /. Determie the cocetratio of hydroium ios, H 3 O

More information

ChE 471 Lecture 10 Fall 2005 SAFE OPERATION OF TUBULAR (PFR) ADIABATIC REACTORS

ChE 471 Lecture 10 Fall 2005 SAFE OPERATION OF TUBULAR (PFR) ADIABATIC REACTORS SAFE OPERATION OF TUBULAR (PFR) ADIABATIC REACTORS I a exothermic reactio the temperature will cotiue to rise as oe moves alog a plug flow reactor util all of the limitig reactat is exhausted. Schematically

More information

Sequences A sequence of numbers is a function whose domain is the positive integers. We can see that the sequence

Sequences A sequence of numbers is a function whose domain is the positive integers. We can see that the sequence Sequeces A sequece of umbers is a fuctio whose domai is the positive itegers. We ca see that the sequece 1, 1, 2, 2, 3, 3,... is a fuctio from the positive itegers whe we write the first sequece elemet

More information

What Is Required? You need to find the ph at a certain point in the titration using hypobromous acid and potassium hydroxide solutions.

What Is Required? You need to find the ph at a certain point in the titration using hypobromous acid and potassium hydroxide solutions. 104. A chemist titrated 35.00 ml of a 0.150 mol/l solutio of hypobromous acid, HBrO(aq), K a = 2.8 10 9. Calculate the resultig ph after the additio of 15.00 ml of 0.1000 mol/l sodium hydroxide solutio,

More information

Lecture 3. Electron and Hole Transport in Semiconductors

Lecture 3. Electron and Hole Transport in Semiconductors Lecture 3 lectro ad Hole Trasort i Semicoductors I this lecture you will lear: How electros ad holes move i semicoductors Thermal motio of electros ad holes lectric curret via lectric curret via usio Semicoductor

More information

10-701/ Machine Learning Mid-term Exam Solution

10-701/ Machine Learning Mid-term Exam Solution 0-70/5-78 Machie Learig Mid-term Exam Solutio Your Name: Your Adrew ID: True or False (Give oe setece explaatio) (20%). (F) For a cotiuous radom variable x ad its probability distributio fuctio p(x), it

More information

Simple Linear Regression

Simple Linear Regression Chapter 2 Simple Liear Regressio 2.1 Simple liear model The simple liear regressio model shows how oe kow depedet variable is determied by a sigle explaatory variable (regressor). Is is writte as: Y i

More information

Controlo Em Espaço de Estados. First Test

Controlo Em Espaço de Estados. First Test Mestrado Itegrado em Egeharia Electrotécica e de Computadores Cotrolo Em Espaço de Estados 13/1 First Test April, 1, h. room C1 Duratio hours Its ot allowed either cosultatio of ay kid or programmable

More information

( ) ( ), (S3) ( ). (S4)

( ) ( ), (S3) ( ). (S4) Ultrasesitivity i phosphorylatio-dephosphorylatio cycles with little substrate: Supportig Iformatio Bruo M.C. Martis, eter S. Swai 1. Derivatio of the equatios associated with the mai model From the differetial

More information

THE KALMAN FILTER RAUL ROJAS

THE KALMAN FILTER RAUL ROJAS THE KALMAN FILTER RAUL ROJAS Abstract. This paper provides a getle itroductio to the Kalma filter, a umerical method that ca be used for sesor fusio or for calculatio of trajectories. First, we cosider

More information

Answer Key, Problem Set 7 Full

Answer Key, Problem Set 7 Full Chemistry Mies, Fall 07 Aswer Key, Problem Set 7 Full. NT;. 5.43; 3. 5.56; 4. 5.3; 5. 5.7; 6. 5.9; 7. NT; 8. 5.0; 9. 5.49; 0. 5.89 & 5.90;. NT3;. 5.70; 3. 5.9 & 5.9; 4. NT4 -----------------------------------------

More information

Phys 102 Lecture 25 The quantum mechanical model of light

Phys 102 Lecture 25 The quantum mechanical model of light Phys 102 Lecture 25 The quatum mechaical model of light 1 Recall last time Problems with classical physics Stability of atoms Atomic spectra Photoelectric effect Quatum model of the atom Bohr model oly

More information

All Excuses must be taken to 233 Loomis before 4:15, Monday, April 30.

All Excuses must be taken to 233 Loomis before 4:15, Monday, April 30. Miscellaeous Notes The ed is ear do t get behid. All Excuses must be take to 233 Loomis before 4:15, Moday, April 30. The PHYS 213 fial exam times are * 8-10 AM, Moday, May 7 * 8-10 AM, Tuesday, May 8

More information

Iterative Techniques for Solving Ax b -(3.8). Assume that the system has a unique solution. Let x be the solution. Then x A 1 b.

Iterative Techniques for Solving Ax b -(3.8). Assume that the system has a unique solution. Let x be the solution. Then x A 1 b. Iterative Techiques for Solvig Ax b -(8) Cosider solvig liear systems of them form: Ax b where A a ij, x x i, b b i Assume that the system has a uique solutio Let x be the solutio The x A b Jacobi ad Gauss-Seidel

More information

Principle Of Superposition

Principle Of Superposition ecture 5: PREIMINRY CONCEP O RUCUR NYI Priciple Of uperpositio Mathematically, the priciple of superpositio is stated as ( a ) G( a ) G( ) G a a or for a liear structural system, the respose at a give

More information

Free Radical Polymerization

Free Radical Polymerization Free Radical Polymerizatio Referece: Aspe Polymers: Uit Operatios ad Reactio Models, Aspe Techology, Ic., 2013. 1. Itroductio The free-radical bulk/solutio polymerizatio model is applicable to bulk ad

More information

( ) (( ) ) ANSWERS TO EXERCISES IN APPENDIX B. Section B.1 VECTORS AND SETS. Exercise B.1-1: Convex sets. are convex, , hence. and. (a) Let.

( ) (( ) ) ANSWERS TO EXERCISES IN APPENDIX B. Section B.1 VECTORS AND SETS. Exercise B.1-1: Convex sets. are convex, , hence. and. (a) Let. Joh Riley 8 Jue 03 ANSWERS TO EXERCISES IN APPENDIX B Sectio B VECTORS AND SETS Exercise B-: Covex sets (a) Let 0 x, x X, X, hece 0 x, x X ad 0 x, x X Sice X ad X are covex, x X ad x X The x X X, which

More information

Fermat s Little Theorem. mod 13 = 0, = }{{} mod 13 = 0. = a a a }{{} mod 13 = a 12 mod 13 = 1, mod 13 = a 13 mod 13 = a.

Fermat s Little Theorem. mod 13 = 0, = }{{} mod 13 = 0. = a a a }{{} mod 13 = a 12 mod 13 = 1, mod 13 = a 13 mod 13 = a. Departmet of Mathematical Scieces Istructor: Daiva Puciskaite Discrete Mathematics Fermat s Little Theorem 43.. For all a Z 3, calculate a 2 ad a 3. Case a = 0. 0 0 2-times Case a 0. 0 0 3-times a a 2-times

More information

4.3 Growth Rates of Solutions to Recurrences

4.3 Growth Rates of Solutions to Recurrences 4.3. GROWTH RATES OF SOLUTIONS TO RECURRENCES 81 4.3 Growth Rates of Solutios to Recurreces 4.3.1 Divide ad Coquer Algorithms Oe of the most basic ad powerful algorithmic techiques is divide ad coquer.

More information

MATH 129 FINAL EXAM REVIEW PACKET (Spring 2014)

MATH 129 FINAL EXAM REVIEW PACKET (Spring 2014) MATH 9 FINAL EXAM REVIEW PACKET (Sprig 4) The followig questios ca be used as a review for Math 9. These questios are ot actual samples of questios that will appear o the fial eam, but the will provide

More information

Notes on the GSW function gsw_geostrophic_velocity (geo_strf,long,lat,p)

Notes on the GSW function gsw_geostrophic_velocity (geo_strf,long,lat,p) Notes o gsw_geostrophic_velocity Notes o the GSW fuctio gsw_geostrophic_velocity (geo_strf,log,lat,p) Notes made 7 th October 2, ad updated 8 th April 2. This fuctio gsw_geostrophic_velocity(geo_strf,log,lat,p)

More information

Exercises and Problems

Exercises and Problems HW Chapter 4: Oe-Dimesioal Quatum Mechaics Coceptual Questios 4.. Five. 4.4.. is idepedet of. a b c mu ( E). a b m( ev 5 ev) c m(6 ev ev) Exercises ad Problems 4.. Model: Model the electro as a particle

More information

NATIONAL SENIOR CERTIFICATE GRADE 12

NATIONAL SENIOR CERTIFICATE GRADE 12 NATIONAL SENIOR CERTIFICATE GRADE 1 MATHEMATICS P1 NOVEMBER 016 MARKS: 150 TIME: 3 hours This questio paper cosists of 9 pages ad 1 iformatio sheet. Please tur over Mathematics/P1 DBE/November 016 INSTRUCTIONS

More information

Precalculus MATH Sections 3.1, 3.2, 3.3. Exponential, Logistic and Logarithmic Functions

Precalculus MATH Sections 3.1, 3.2, 3.3. Exponential, Logistic and Logarithmic Functions Precalculus MATH 2412 Sectios 3.1, 3.2, 3.3 Epoetial, Logistic ad Logarithmic Fuctios Epoetial fuctios are used i umerous applicatios coverig may fields of study. They are probably the most importat group

More information

5.61 Fall 2013 Problem Set #3

5.61 Fall 2013 Problem Set #3 5.61 Fall 013 Problem Set #3 1. A. McQuarrie, page 10, #3-3. B. McQuarrie, page 10, #3-4. C. McQuarrie, page 18, #4-11.. McQuarrie, pages 11-1, #3-11. 3. A. McQuarrie, page 13, #3-17. B. McQuarrie, page

More information

Kinetics of Dye Bleaching

Kinetics of Dye Bleaching /9/03 This exercise explores the time depedece of the reactio of the dye: Kietics of Dye Bleachig Objective: To examie the kietics of a reactio i which a dye is bleached Last Update: /9/03 8:5 AM Malachite

More information

OPTIMAL ALGORITHMS -- SUPPLEMENTAL NOTES

OPTIMAL ALGORITHMS -- SUPPLEMENTAL NOTES OPTIMAL ALGORITHMS -- SUPPLEMENTAL NOTES Peter M. Maurer Why Hashig is θ(). As i biary search, hashig assumes that keys are stored i a array which is idexed by a iteger. However, hashig attempts to bypass

More information

Math 176 Calculus Sec. 5.1: Areas and Distances (Using Finite Sums)

Math 176 Calculus Sec. 5.1: Areas and Distances (Using Finite Sums) Math 176 Calculus Sec. 5.1: Areas ad Distaces (Usig Fiite Sums) I. Area A. Cosider the problem of fidig the area uder the curve o the f y=-x 2 +5 over the domai [0, 2]. We ca approximate this area by usig

More information

Chemistry 104 Chapter 17 Summary and Review Answers

Chemistry 104 Chapter 17 Summary and Review Answers Chemistry 104 Chapter 17 Summary ad Review Aswers 1. You eed to make a buffer with a ph of 4.80. You have 0.150 M sodium hydroxide, 0.150 M acetic acid ad 0.150 M sodium bicarboate. What do you do? (Make

More information

How to Maximize a Function without Really Trying

How to Maximize a Function without Really Trying How to Maximize a Fuctio without Really Tryig MARK FLANAGAN School of Electrical, Electroic ad Commuicatios Egieerig Uiversity College Dubli We will prove a famous elemetary iequality called The Rearragemet

More information

COMP 2804 Solutions Assignment 1

COMP 2804 Solutions Assignment 1 COMP 2804 Solutios Assiget 1 Questio 1: O the first page of your assiget, write your ae ad studet uber Solutio: Nae: Jaes Bod Studet uber: 007 Questio 2: I Tic-Tac-Toe, we are give a 3 3 grid, cosistig

More information

CS537. Numerical Analysis and Computing

CS537. Numerical Analysis and Computing CS57 Numerical Aalysis ad Computig Lecture Locatig Roots o Equatios Proessor Ju Zhag Departmet o Computer Sciece Uiversity o Ketucky Leigto KY 456-6 Jauary 9 9 What is the Root May physical system ca be

More information

The Advanced Placement Examination in Chemistry. Part II - Free Response Questions & Answers 1970 to Electrochemistry

The Advanced Placement Examination in Chemistry. Part II - Free Response Questions & Answers 1970 to Electrochemistry The Advaced Placemet Examiatio i Chemistry Part II - Free Respose Questios & Aswers 970 to 005 Electrochemistry Teachers may reproduce this publicatio, i whole or i part, i limited prit quatities for o-commercial,

More information

Response Variable denoted by y it is the variable that is to be predicted measure of the outcome of an experiment also called the dependent variable

Response Variable denoted by y it is the variable that is to be predicted measure of the outcome of an experiment also called the dependent variable Statistics Chapter 4 Correlatio ad Regressio If we have two (or more) variables we are usually iterested i the relatioship betwee the variables. Associatio betwee Variables Two variables are associated

More information

ECE 8527: Introduction to Machine Learning and Pattern Recognition Midterm # 1. Vaishali Amin Fall, 2015

ECE 8527: Introduction to Machine Learning and Pattern Recognition Midterm # 1. Vaishali Amin Fall, 2015 ECE 8527: Itroductio to Machie Learig ad Patter Recogitio Midterm # 1 Vaishali Ami Fall, 2015 tue39624@temple.edu Problem No. 1: Cosider a two-class discrete distributio problem: ω 1 :{[0,0], [2,0], [2,2],

More information

1.3 Convergence Theorems of Fourier Series. k k k k. N N k 1. With this in mind, we state (without proof) the convergence of Fourier series.

1.3 Convergence Theorems of Fourier Series. k k k k. N N k 1. With this in mind, we state (without proof) the convergence of Fourier series. .3 Covergece Theorems of Fourier Series I this sectio, we preset the covergece of Fourier series. A ifiite sum is, by defiitio, a limit of partial sums, that is, a cos( kx) b si( kx) lim a cos( kx) b si(

More information

FINALTERM EXAMINATION Fall 9 Calculus & Aalytical Geometry-I Questio No: ( Mars: ) - Please choose oe Let f ( x) is a fuctio such that as x approaches a real umber a, either from left or right-had-side,

More information

AP CALCULUS - AB LECTURE NOTES MS. RUSSELL

AP CALCULUS - AB LECTURE NOTES MS. RUSSELL AP CALCULUS - AB LECTURE NOTES MS. RUSSELL Sectio Number: 4. Topics: Area -Sigma Notatio Part: of Sigma Notatio Upper boud Recall ai = a+ a + a3 + L + a idex i= Lower boud Example : Evaluate each summatio.

More information

Material Balances on Reactive Processes F&R

Material Balances on Reactive Processes F&R Material Balaces o Reactive Processes F&R 4.6-4.8 What does a reactio do to the geeral balace equatio? Accumulatio = I Out + Geeratio Cosumptio For a reactive process at steady-state, the geeral balace

More information

MOTION. The easy stuff; The gaseous state - Translational motion. The crystalline state - Oscillations about a Mean position.

MOTION. The easy stuff; The gaseous state - Translational motion. The crystalline state - Oscillations about a Mean position. The easy stuff; MOTION The gaseous state - Traslatioal motio The crystallie state - Oscillatios about a Mea positio The hard stuff; The liquid state - Coupled motios MOTION IN POLYMERS LARGE SCALE MOTION

More information

Analytic Theory of Probabilities

Analytic Theory of Probabilities Aalytic Theory of Probabilities PS Laplace Book II Chapter II, 4 pp 94 03 4 A lottery beig composed of umbered tickets of which r exit at each drawig, oe requires the probability that after i drawigs all

More information

All Excuses must be taken to 233 Loomis before 4:15, Monday, April 30.

All Excuses must be taken to 233 Loomis before 4:15, Monday, April 30. Miscellaeous Notes The ed is ear do t get behid. All Excuses must be take to 233 Loomis before 4:15, Moday, April 30. The PYS 213 fial exam times are * 8-10 AM, Moday, May 7 * 8-10 AM, Tuesday, May 8 ad

More information

Review Sheet for Final Exam

Review Sheet for Final Exam Sheet for ial To study for the exam, we suggest you look through the past review sheets, exams ad homework assigmets, ad idetify the topics that you most eed to work o. To help with this, the table give

More information

CS321. Numerical Analysis and Computing

CS321. Numerical Analysis and Computing CS Numerical Aalysis ad Computig Lecture Locatig Roots o Equatios Proessor Ju Zhag Departmet o Computer Sciece Uiversity o Ketucky Leigto KY 456-6 September 8 5 What is the Root May physical system ca

More information

MCT242: Electronic Instrumentation Lecture 2: Instrumentation Definitions

MCT242: Electronic Instrumentation Lecture 2: Instrumentation Definitions Faculty of Egieerig MCT242: Electroic Istrumetatio Lecture 2: Istrumetatio Defiitios Overview Measuremet Error Accuracy Precisio ad Mea Resolutio Mea Variace ad Stadard deviatio Fiesse Sesitivity Rage

More information

11 Hidden Markov Models

11 Hidden Markov Models Hidde Markov Models Hidde Markov Models are a popular machie learig approach i bioiformatics. Machie learig algorithms are preseted with traiig data, which are used to derive importat isights about the

More information