Rate and Activation Energy of the Iodination of Acetone


 Rachel Short
 1 years ago
 Views:
Transcription
1 nd Activtion Energ of the Iodintion of Acetone rl N. eer Dte of Eperiment: //00 Florence F. Ls (prtner) Abstrct: The rte, rte lw nd ctivtion energ of the iodintion of cetone re detered b observing the disppernce of the chrcteristic color of iodine in wter. B sstemticll vring the concentrtion of rectnts, the rte lw is detered to be: 0 = [cetone] 0 [] 0. Once the rte lw epression is found, the ctivtion energ of the rection is found b mesuring the rte of the rection t multiple tempertures. The clculted ctivtion energ of 9 ± / mol is sufficientl lrge to me the rection slow enough to observe, but not so lrge s to me the rection eceedingl slow. Introduction: The ctivtion energ of chemicl rection is the energ required to initite collisions energetic enough to llow the trnsformtion of rectnts to products nd is described b the Arrhenius eqution. Ae where: = rte lw constnt A = frequenc fctor = universl gs constnt, 8.34 / mol K E = ctivtion energ of the rection Detertion of the rte lw constnt requires the rte of the rection to be eplored s the concentrtions of rectnts re sstemticll vried. This llows the orders of the rection with respect to ech regent to be detered, which is the foundtion of the rte lw epression. The iodintion of cetone is convenient rection to stud for number of resons: the color of the iodine rectnt is chrcteristic nd redil observble, so the chnge in [I ] cn be esil monitored; the rte of the rection is fst enough to llow multiple runs, but not so fst to be difficult to mesure; the rection is eroorder with respect to iodine so the chnge in concentrtion is liner with time. The fct tht the rection is ero order in cetone is especill importnt becuse it llows the rte of the rection to be clculted s n verge rte of the chnge in iodine concentrtion over (reltivel) long time periods. O O (q) + I (q) C + H + (q) (q) + I  (q) + H + (q) H C 3 C CH 3 H 3 C CH I Eperimentl Procedure: Detertion of the Lw Epression: A number of smples were prepred to eplore the dependence of the rte of rection upon the concentrtion of rectnts, summried in Tble. For ech smple, the listed volumes of 4.00 cetone solution, hdrochloric cid solution, nd wter were dded to one test tube (Tube A ), nd the listed volume of 5.00 iodine solution ws dded to second test tube (Tube B ). The tubes were plced in room temperture wter bth (0.8 C) nd the temperture ws llowed to equilibrte for t lest 5 utes. While the temperture of the smples ws stbiliing, the spectrophotometer ws clibrted nd SpectroPro ws set up to collect bsorbnce vs. time dt for 0 utes, smpling ever second. Once the spectrometer ws prepred nd the smples t temperture, the two tubes were removed from the wter bth nd dt collection ws strted in SpectroPro s the smples were combined. The miture ws poured bc nd forth between the two tubes number of times to mi thoroughl nd poured into smll test tube for use in the spectrophotometer. To imie temperture increses from inside the spectrophotometer, the tube ws not plced in the smple comprtment until most of the iodine color fded from the rection solution. The time ws recorded when the bsorbnce reding leveled off t or ner ero. Additionl eperiments were performed t room temperture, sstemticll doubling the concentrtion of rectnts while eeping the totl smple volume t. For ech condition, repet runs were performed until consistent rection times were observed. Detertion of the Activtion Energ: Clcultion of the ctivtion energ of this rection requires rection rte dt t dditionl tempertures. For this eperiment, two dditionl temperture conditions were used. The first ws cool bth. A 800mL beer ws filled E
2 with wter nd ice ws dded to bring the temperture of the bth down to pproimtel 0 C. The bth ws mgneticll stirred nd temperture ws monitored using LoggerPro. Smples were prepred s listed in Tble nd the tubes were plced in the cool bth to llow the temperture to equilibrte for 50 utes. During equilibrtion nd rection, the bth temperture ws mintined t 9.8±0. C. The smples were mied nd immeditel returned to the cool bth. This rection ws observed visull, recording the time required for ll visible color to fde from the solution. A third temperture condition, the cold bth, ws lso used. For the cold bth, beer ws filled with ice nd enough wter ws dded to fcilitte het trnsfer. Agin, tubes were prepred s described in Tble nd equilibrted to temperture for 0 utes before miing nd immeditel returned to the cold bth. The temperture of the cold bth ws checed periodicll nd mintined t 0 C b periodic removl of ecess wter nd ddition of ice. These smples were lso observed visull. Tble : Volumes of regents used nd rection times for ech eperiment. Tube A Tube B Ep t # Temp. ml Totl Solution n Time ml (q) ml H ( C) cetone(q) O(l) ml I (q) Volume, ml () Cool Cool Cold Cold Notes: All volumes were mesured with volumetric pipettes. esurements were ten t 0.7 C. The doublei run ws repeted fourth time becuse the first three times vried. esults nd Discussion: Initil concentrtions of ll regent were clculted bsed upon the stoc concentrtions nd the volumes listed in Tble. ection times nd concentrtions re summried in Tble. The rte of the rection is clculted s the chnge in concentrtion of iodine over rection time, lso summried in Tble. Tble : Initil concentrtions nd rections rtes for ll rections. Ep t # n Time ection [cetone] () 0 [] 0 [I ] 0 ( / ) Cool Cool Cold Cold
3 Smple Clcultions for Tble vlues: Initil concentrtion of cetone, run : cetone stocvolume of cetone stoc mL cetone.00 volume of solution totl Initil concentrtion of hdrochloric cid, run : stoc volume of stoc mL 0.48 volume of solution totl Initil concentrtion of iodine, run : I volume of I stoc stoc mL I.60 volume of solution totl of rection, run : 3 ΔI I I finl of rection Δt t t 3.7 finl For nlsis of the orders of rection in the rte lw epression, it is convenient to use verge rection rtes for ech set of conditions. The conditions re summried in Tble 3 s verges. Tble 3: Averge rection rtes for ech set of conditions. [cetone] 0 [] 0 [I ] 0 ection Error on the verge ( / ) rte Stndrd un ± (.5%) Double cetone ± (4.%) Double cid ± (.0%) Double iodine ± (4.5%) Cool uns ± (4.3%) Cold uns ± (0.6%) The consistentl sub5% errors on these verge rection rtes indicte tht the dt should be quite relible for detertion of the rte lw epression nd the ctivtion energ of the rection. Compring the stndrd run to the double cetone run, the rte of the rection pproimtel doubled when the concentrtion of cetone doubled; therefore, the rection is first order with respect to cetone. Compring the stndrd run to the double cid run, the rte of the rection pproimtel doubled when the concentrtion of cid doubled; therefore, the rection is first order with respect to cid. Compring the stndrd run to the double iodine run, the rte of the rection is unchnged when the concentrtion of iodine doubled; therefore, the rection is ero order with respect to iodine. Therefore, the rte lw epression for this rection is: 0 = [cetone] 0 [] 0 [I ] 0 0 = [cetone] 0 [] 0 The ect mthemticl vlue of the rte lw orders cn lso be found to indicte the error in these mesurements. Compring the stndrd run to the double cetone run: Compring the stndrd run to the double cid run: = =.07 cetone I cetone I cetone I cetone I
4 Compring the stndrd run to the double iodine run: cetone I cetone I = These clculted orders re ll ver close to the qulittivel detered orders, so these eperimentl results do not hve significnt error, s reflected in the verge rection rtes in Tble 3. The vlue of the rte lw constnt is found b plugging the concentrtion nd rte dt bc into the rte lw epression nd solving for. Tble 4: lw constnts Ep t # [cetone] 0 [] 0 [I ] 0 ection ( / ) (   ) Cool Cool Cold Cold For Ep t : 0 = [cetone] 0 [] / = (.00) (0.48) = The vlue of should be constnt for rection t ech temperture, so the vlues re verged for ech temperture, results re shown in Tble 5. Tble 5: Averge rte lw constnts t three tempertures Temperture Averge, (K)   Error on verge ±0.00 (7.0%) ± (5.%) ± (0.5%) The ctivtion energ of this process cn be detered b using the Arrhenius eqution. Given the dt in Tble 5, the comprtive form of the Arrhenius eqution cn be used three times to detere the ctivtion energ of this process. E T T Compring the room temperture nd cool dt: molk 83.0K E = / mol = 03 / mol 94.0K
5 Compring the room temperture nd cold dt: molk 73.0K 94.0K E = / mol = 9.9 / mol Compring the cool nd cold dt: molk 73.0K 83.0K E = / mol = 80.8 / mol The verge ctivtion energ is 9 ± / mol bsed upon pirwise dt. This % error seems high, but this is lrgel result of using reltivel smll temperture rnge for the eperiments. As cn be seen in the dt, the clculted ctivtion energ for the lrgest temperture chnge (room temperture to cold) is most consistent with the verge, while the smller roomcool nd coolcold vlues vr significntl. The ctivtion energ cn lso be clculted grphicll using the liner form of the Arrhenius eqution. E T A Arrhenius Plot for Iodintion of Acetone = ² = E E E E E E E E03 /Temperture E slope 67K 8.34 molk E E = / mol = 9.8 / mol The vlue of the ctivtion energ detered from the liner form of the Arrhenius eqution is in ver close greement with tht found from the pirwise tretment of the dt, with less thn % difference between the two methods. A more relible nlsis of the ctivtion energ could be done with lrger temperture rnge nd/or more tempertures. Conclusions: Detertion of the rte lw nd ctivtion energ of chemicl rection requires number of steps. B vring the concentrtions of rectnts in the iodintion of cetone it ws detered tht the rection is first order with respect to both cetone nd hdrochloric cid concentrtion nd ero order with respect to iodine concentrtion. esuring the rection rte t multiple tempertures llows clcultion of the ctivtion energ of the process, in this cse the ctivtion energ of the rection is found to be 9 / mol. The error in ll prts of this eperiment is reltivel smll. This rection is fst enough to be performed in resonble mount of time, but not so fst tht it is difficult to mesure. This mens tht the clculted ctivtion energ, 9 / mol, is moderte brrier to rection.
Chemistry 141 Exploring Buffers Lab Lecture 11/13/2010 Dr. Abrash. Today we are going to study some of the properties of buffers.
Chemistry 141 Exploring Buffers Lb Lecture 11/13/2010 Dr. Abrsh Q: Wht is the purpose of tody s experiment? Tody we re going to study some of the properties of buffers. Q: Wht re buffers? Buffers re cidbse
More information= 2.4 x 10 3 at 2000 C. If a 2.0 L container holds 0.74 atm of N
1 SPRING 000 TEST solutions 1. The equilibrium constnt for the rection, NO(g) N (g) + O (g) is, K p =. x 10 t 000 C. If.0 L continer holds 0.7 tm of N, 0.10 tm of O nd 0.050 tm of NO, is the system t equilibrium?
More informationBCHM461 Spring 2002 Solutions to ph and Buffers Problem Set
BCHM461 Spring 00 Solutions to ph nd Buffers Problem Set 1. Here I will provide nswers for the pk = 6.5 exmple only () For this problem, s well s for problems (b) nd (c), it is convenient to use the HendersonHsselblch
More informationDetermination of total Hardness
Determintion of totl Hrdness Equipment Bulb pipette 00 ml Bulb pipette 50 ml Bulb pipette 5 ml Bulb pipette 4 ml 3 Mesuring pipette 0 ml 2 Erlenmeyer flsks 300 ml Beker 600 ml Beker 250 ml Volumetric flsk
More informationOr more simply put, when adding or subtracting quantities, their uncertainties add.
Propgtion of Uncertint through Mthemticl Opertions Since the untit of interest in n eperiment is rrel otined mesuring tht untit directl, we must understnd how error propgtes when mthemticl opertions re
More informationPRACTICE 7: DETERMINATION BY VOLUMETRIC TECHNICS OF ALKALINITY IN WATER SAMPLES
Áre de Toxicologí PRACTICE 7: DETERMINATION BY VOLUMETRIC TECHNICS OF ALKALINITY IN WATER SAMPLES OVERVIEW Prcticl ctivity of the Áre of Toxicologí Universidd Miguel Hernández de Elche Environmentl Anlytic
More informationPHY 222 Lab 8 MOTION OF ELECTRONS IN ELECTRIC AND MAGNETIC FIELDS
PHY 222 Lb 8 MOTION OF ELECTRONS IN ELECTRIC AND MAGNETIC FIELDS Nme: Prtners: INTRODUCTION Before coming to lb, plese red this pcket nd do the prelb on pge 13 of this hndout. From previous experiments,
More informationHEATING TIME SIMULATION FOR FROZEN AND UNFROZEN WOOD
HEATING TIME SIMULATION FOR FROZEN AND UNFROZEN WOOD H. Peter Steinhgen Deprtment of Forest Products University of Idho Moscow, Idho INTRODUCTION The heting time simultion softwre LOGHEAT1 (Steinhgen et
More informationHomework #6 Chapter 7 Homework Acids and Bases
Homework #6 Chpter 7 Homework Acids nd Bses 18. ) H O(l) H 3O (q) OH (q) H 3 O OH Or H O(l) H (q) OH (q) H OH ) HCN(q) H O(l) H 3O (q) CN (q) H 3 O HCN CN Or HCN(q) H (q) CN (q) H CN HCN c) NH 3(q) H O(l)
More informationAs a companywide quality metrics, ISR pass/fail and observations are continuously documented and updated on a quarterly basis.
Appliction Note #2009LC/MS/MS001 >>> Incurred Smple Renlysis Introduction The Incurred Smple Renlysis (ISR) progrm hs been implemented in most bionlyticl lbortories s n dditionl mesure to evlute the
More information** Dpt. Chemical Engineering, Kasetsart University, Bangkok 10900, Thailand
Modelling nd Simultion of hemicl Processes in Multi Pulse TP Experiment P. Phnwdee* S.O. Shekhtmn +. Jrungmnorom** J.T. Gleves ++ * Dpt. hemicl Engineering, Ksetsrt University, Bngkok 10900, Thilnd + Dpt.hemicl
More informationCHAPTER 19 IONIC EQUILIBRIA IN AQUEOUS SYSTEMS
CHAPTER 19 IONIC EQUILIBRIA IN AQUEOUS SYSTEMS 19.1 The purpose of n cidbse buffer is to mintin reltively constnt ph in solution. 19.2 The wek cid component neutrlizes dded bse nd the wek bse component
More informationAcidic and Basic Solutes. Acidic and Basic Solutes. Acidic and Basic Solutes. Acidic and Basic Solutes
Acidic nd Bsic Solutes Acids lwys increse the concentrtion of 3 O nd decrese tht of O. Some cids relese ions directly when they dissocite: Acidic nd Bsic Solutes Other cids increse concentrtion by cusing
More informationMath 135 Circles and Completing the Square Examples
Mth 135 Circles nd Completing the Squre Exmples A perfect squre is number such tht = b 2 for some rel number b. Some exmples of perfect squres re 4 = 2 2, 16 = 4 2, 169 = 13 2. We wish to hve method for
More informationDIRECTCURRENT CIRCUITS
DTUNT UTS 6 6.7.DNTFY: First do s much seriesprllel reduction s possible. ST UP: The.Ω nd.ω resistors re in prllel, so first reduce them to single uivlent resistnce. Then find the uivlent series resistnce
More informationTaylor Polynomials with Error Term
Tylor Polynomils with Error Term The functions e x, sinx, / x, etc re nice functions but they re not s nice s polynomils. Specificlly polynomils cn be evluted completely bsed on multipliction, subtrction
More informationREVIEW QUESTIONS Chapter 16
Chemistry 102 ANSWER EY REVIEW QUESTIONS Chpter 16 1. A buffer is prepred by dding 20.0 g of cetic cid (HC2HO2) nd 20.0 g of sodium cette (NC2HO2) in enough wter to prepre 2.00 L of solution. Clculte the
More informationExponential Functions
WS07.0 Eponentil Functions Aim: To study the properties of eponentil functions nd lern the fetures of their grphs Section A Activity : The Eponentil Function, f ( ).. For f ( ) : The bse of f ( ) is (ii)
More informationENTROPY OF MIXING FROM EMF MEASUREMENTS (10/30/ :57:00 AM)
ENTROPY OF MIXING FROM EMF MEASUREMENTS (0/30/0 :57:00 AM) INTRODUCTION Your ssignment is to mesure the potentil difference s voltges between two queous solutions of potssium ferricynide [K3] nd potssium
More informationSupplementary Materials: Direct Catalytic Conversion of Cellulose to 5Hydroxymethylfurfural Using Ionic Liquids
S1 of S5 Supplementry Mterils: Direct Ctlytic Conversion of Cellulose to 5Hydroxymethylfurfurl Using Ionic Liquids Snn Eminov, Prskevi Filippousi, Agnieszk Brndt, Jmes D. E. T. WiltonEly nd Json P. Hllett
More informationASTM E 1354 Caloric Content Determination of "3M ScotchWeld Low Odor Acrylic Adhesive DP8810NS Green"
UNCONTROLLED ELECTRONIC COPY ASTM E 1354 Cloric Content Determintion of "3M ScotchWeld Low Odor Acrylic Adhesive DP8810NS Green" A Report To: 3M Industril Adhesives nd Tpes Division 3M Center, Building
More informationMath 22B Solutions Homework 1 Spring 2008
Mth 22B Solutions Homework 1 Spring 2008 Section 1.1 22. A sphericl rindrop evportes t rte proportionl to its surfce re. Write differentil eqution for the volume of the rindrop s function of time. Solution
More informationK a. Exercise 10 SOLUBILITY PRODUCT CONSTANTS. a (2) AgX(s) Ag + (aq) + X  (aq)
Exercise 10 SOLUBILITY PRODUCT CONSTANTS Theory Solubility is physicl property referring to the bility for given substnce, the solute to dissolve in solvent. It is mesured in terms of the mximum mount
More informationOn the Meaning of Regression Coefficients for Categorical and Continuous Variables: Model I and Model II; Effect Coding and Dummy Coding
Dt_nlysisclm On the Mening of Regression for tegoricl nd ontinuous Vribles: I nd II; Effect oding nd Dummy oding R Grdner Deprtment of Psychology This describes the simple cse where there is one ctegoricl
More informationAcids and Bases  Answers
Acids nd Bses  Answers 1. It requires 3.0 ml of 0.0500 mol/l NOH(q) to neutrlize 100.0 ml of gstric juice. We cn ssume tht HCl(q) is the only cid present in gstric juice. ) Clculte the concentrtion of
More informationResearch Design   Topic 16 Multiple Regression: Applications 2010 R.C. Gardner, Ph.D. General Overview. General Overview.
Reserch Design   Topic 6 ultiple Regression: Applictions 00 R.C. Grdner, Ph.D. Generl Overview Curve Fitting edition nlsis Generl Overview As we hve seen multiple regression is ver powerful nd useful
More informationTopdressing Durum with Nitrogen to Manage Protein
Topdressing Durum with Nitrogen to Mnge Protein Bill My, Fernndo Selles, Guy Lfond, nd Myrim Fernndez Agriculture nd AgriFood Cnd Indin Hed Reserch Frm Semirid Pririe Agriculturl Reserch Centre Summry
More informationExponents. This suggests the following rule of multiplying like bases.
Eponents Objectives:. Using the product rule. Evluting epressions rised to the zero power. Using the quotient rule. Evluting epressions rised to the negtive powers. Rising power to power. Converting between
More informationSOLUTIONS FOR CHAPTER 21 PROBLEMS 4, 12, 19, 25, 33, 40, 50, 75, 89, 96.
SOLUTIONS FOR CHAPTER PROBLEMS 4,, 9, 5,, 4, 5, 75, 89, 96..4.IDENTIFY: Use the mss m of the ring nd the tomic mss M of gold to clculte the number of gold toms. Ech tom hs 79 protons nd n equl number of
More information7.2 Composite Trapezoidal and Simpson s Rule
364 CHAP. 7 NUMERICAL INTEGRATION 7. Composite Trpezoidl nd Simpson s Rule An intuitive method of finding the re under the curve y = f (x) over [, b] is by pproximting tht re with series of trpezoids tht
More informationMeasuring Distance Using Parallax
Mesuring Distnce Using Prllx Prllx is the pprent motion of sttionry object due to chnge in the observer s position. In stronomy prllx is the gold stndrd (best) wy to mesure distnces. Tht is, until it doesn
More informationForce and Acceleration on an Airtrack
Force nd Accelertion on n Airtrck Objectives: Experimentl objective Students will verify Newton s second lw of motion. Lerning objectives (students should lern ) The significnce nd use of Newton s second
More informationName: Lab Partner: Section:
Chpter 4 Newton s 2 nd Lw Nme: Lb Prtner: Section: 4.1 Purpose In this experiment, Newton s 2 nd lw will be investigted. 4.2 Introduction How does n object chnge its motion when force is pplied? A force
More information1 Numerical Solution to Quadratic Equations
cs42: introduction to numericl nlysis 09/4/0 Lecture 2: Introduction Prt II nd Solving Equtions Instructor: Professor Amos Ron Scribes: Yunpeng Li, Mrk Cowlishw Numericl Solution to Qudrtic Equtions Recll
More informationTopdressing Durum with Nitrogen to Manage Protein
Topdressing Durum with Nitrogen to Mnge Protein By Bill My, Fernndo Selles, Guy Lfond, nd Myrim Fernndez Agriculture nd AgriFood Cnd Indin Hed Reserch Frm Semirid Pririe Agriculturl Reserch Centre A.
More informationGraphs on Logarithmic and Semilogarithmic Paper
0CH_PHClter_TMSETE_ 3//00 :3 PM Pge Grphs on Logrithmic nd Semilogrithmic Pper OBJECTIVES When ou hve completed this chpter, ou should be ble to: Mke grphs on logrithmic nd semilogrithmic pper. Grph empiricl
More informationWorksheet 20 Polyprotic Acids and Salt Solutions
Worksheet 0 Polyprotic Acids nd Slt Solutions Acid Bse strong cid HNO, HI, HCl, etc NO, I, Cl, etc negligile sicity 1. HSO SO 7.7 1 7.1 HNO NO 1. 11 6.8 HF F 1.5 11 1.8 5 CH COOH CH COO 5.6.5 7 H CO HCO.
More informationWell say we were dealing with a weak acid K a = 1x10, and had a formal concentration of.1m. What is the % dissociation of the acid?
Chpter 9 Buffers Problems 2, 5, 7, 8, 9, 12, 15, 17,19 A Buffer is solution tht resists chnges in ph when cids or bses re dded or when the solution is diluted. Buffers re importnt in Biochemistry becuse
More informationProject Recovery. . It Can Be Done
Project Recovery. It Cn Be Done IPM Conference Wshington, D.C. Nov 47, 200 Wlt Lipke Oklhom City Air Logistics Center Tinker AFB, OK Overview Mngement Reserve Project Sttus Indictors Performnce Correction
More informationMoments of Inertia (Rotational Inertia)
Moments of nerti (ottionl nerti) his lb is cse sensitive. Plese do NO mix up nd r, nd M nd m. ntroduction ottionl motions involve more thn liner motions. nerti gives us n ide of how hrd or esy the object
More informationDr. Steward s CHM152 Exam #2 Review Spring 2014 (Ch ) KEY. 2. For the acid/base reactions determine the conjugate acid/base pairs for each.
Dr. Stewrd s CHM15 Em # Review Spring 014 (Ch. 16. 17) KEY 1. For ech of the following cid / bse rections, determine if ech of the following will hve more products or rectnts (K HSO 4 = 1.10, K b NH =
More informationKinetic Modeling of Methanol to Olefins (MTO) Process on SAPO34 Catalyst
Simultion nd Optimiztion Chin Petroleum Processing nd Petrochemicl Technology 203, Vol., No. 3, pp 8690 September 30, 203 Kinetic Modeling of Methnol to Olefins (MTO) Process on SAPO34 Ctlyst Pu Jinglong;
More information3 Indices and Standard Form
MEP Y9 Prctice Book A Indices nd Stndrd Form. Inde Nottion Here we revise the use of inde nottion. You will lredy be fmilir with the nottion for squres nd cubes, nd this is generlised by defining: Emple
More informationCypress Creek High School IB Physics SL/AP Physics B 2012 2013 MP2 Test 1 Newton s Laws. Name: SOLUTIONS Date: Period:
Nme: SOLUTIONS Dte: Period: Directions: Solve ny 5 problems. You my ttempt dditionl problems for extr credit. 1. Two blocks re sliding to the right cross horizontl surfce, s the drwing shows. In Cse A
More informationThe laboratory received 4 samples, composed of a substrate board of 4 mm, finished with Hot Pipe Coating. Characteristics:
FACULTEIT INGENIEURSWETENSCHAPPEN DEPARTEMENT BURGERLIJKE BOUWKUNDE LABORATORIUM BOUWFYSICA KASTEELPARK ARENBERG 40 B3001 LEUVEN RAPPORT KATHOLIEKE UNIVERSITEIT LEUVEN Superior products NV Kmpweg, 13
More informationChapter 6 Solving equations
Chpter 6 Solving equtions Defining n eqution 6.1 Up to now we hve looked minly t epressions. An epression is n incomplete sttement nd hs no equl sign. Now we wnt to look t equtions. An eqution hs n = sign
More informationAP Statistics Testbank 8
AP Sttistics Testbnk 8 MultipleChoice Questions ) Suppose tht you re given sttistics s below: Smple size Smple men Smple Devition Smple 9.3.47 Smple 9.4.4 The Pvlue ssocited with the hypotheses is closest
More informationV (x) Box potential + bump. bump from  x to x Hight of bump V o
Problems: 5. (c) nd (d); 5.3 ; 5. (modified see below) ; 5.5 (see hints in problem 3 below) ; 5.30 (see hints in 4 below) ; (5.7 + problem five below) ; Prctice Test #4 1. 5. (Grded) () Replce (c) with
More informationFEASIBILITY OF USING PRESSED SUGAR CANE STALK FOR THE PRODUCTION OF CHARCOAL. D Ffoulkes, R Elliott and T R Preston
Trop Anim Prod 1980 5:2 125 FEASIBILITY OF USING PRESSED SUGAR CANE STALK FOR THE PRODUCTION OF CHARCOAL D Ffoulkes, R Elliott nd T R Preston Fcultd de Medicin Veterinri y Zootecni, University of Yuctn,
More informationAPPENDIX D Precalculus Review
APPENDIX D Preclculus Review SECTION D. Rel Numers nd the Rel Line Rel Numers nd the Rel Line Order nd Inequlities Asolute Vlue nd Distnce Rel Numers nd the Rel Line Rel numers cn e represented y coordinte
More informationCALMS Rating Scale for SchoolAge Children Who Stutter
CALMS Rting Scle for SchoolAge Children Who Stutter This rting scle is designed to evlute cognitive, ffective, linguistic, motor, nd socil (CALMS) components tht re relted to stuttering. It is recommended
More informationTests for One Poisson Mean
Chpter 412 Tests for One Poisson Men Introduction The Poisson probbility lw gives the probbility distribution of the number of events occurring in specified intervl of time or spce. The Poisson distribution
More informationTeaching Guide Zero and Negative Exponents
Teching Guide Zero nd Negtive Eponents Prepring for Your Clss Common Vocbulr Zero eponent, negtive eponent Instruction Tips In the more complicted eponentil epressions, it m be helpful to students if ou
More informationArc Length. P i 1 P i (1) L = lim. i=1
Arc Length Suppose tht curve C is defined by the eqution y = f(x), where f is continuous nd x b. We obtin polygonl pproximtion to C by dividing the intervl [, b] into n subintervls with endpoints x, x,...,x
More informationOperations with Polynomials
38 Chpter P Prerequisites P.4 Opertions with Polynomils Wht you should lern: Write polynomils in stndrd form nd identify the leding coefficients nd degrees of polynomils Add nd subtrct polynomils Multiply
More informationAppendix C Derivation of Equations for an AirWater Mixture
Appendix C Derivtiof Equtions for n AirWter Mixture The following ssumptions were mde for this nlysis. We will ssume initil sturtion levels re greter thn 85 percent, which implies tht ll ir bubbles re
More informationChapter 5. Exponential and Logarithmic Functions. 5.1 Exponential Functions
Chpter 5. Exponentil nd Logrithmic Functions 5. Exponentil Functions The exponentil function with bse is defined by f (x) = x where > 0 nd. Its domin is the set of ll rel numbers, nd its rnge is the set
More informationStraight pipe model. Orifice model. * Please refer to Page 3~7 Reference Material for the theoretical formulas used here. Qa/Qw=(ηw/ηa) (P1+P2)/(2 P2)
Air lek test equivlent to IX7nd IX8 In order to perform quntittive tests Fig. shows the reltionship between ir lek mount nd wter lek mount. Wter lek mount cn be converted into ir lek mount. By performing
More informationDISSOLVED INORGANIC CARBON DIC
1 Chpter 2 Geochemicl Rections DISSOLVED INORGANIC CARBON Inorgnic or minerlized crbon in its most oxidized stte crries vlence of 4. In minerls C 4 coordintes covlently with oxygen toms s the crbonte nion
More information1. Set up and test the hypothesis that GPA does not contribute to prediction of SCORE for students who are homogeneous on NHS and NHR.
1 1. Set up nd test the hypothesis tht GPA does not contriute to prediction of SCOE for students who re homogeneous on NHS nd NH. First Approch test of specific hypothesis: t test Y NH NHS GPA 1 3 H0 :
More informationPrediction of Reoxidation Inclusion Composition in Casting of Steel
Prediction of Reoxidtion Inclusion Composition in Csting of Steel LIANG WANG nd CHRISTOPH BECKERMANN A model is developed to clculte the composition of reoxidtion inclusions tht form during pouring of
More informationUnit #9 : Definite Integral Properties, Fundamental Theorem of Calculus
Unit #9 : Definite Integrl Properties, Fundmentl Theorem of Clculus Gols: Identify properties of definite integrls Define odd nd even functions, nd reltionship to integrl vlues Introduce the Fundmentl
More informationSubstituting the righthand side of eq 3 into eq 2 we obtain:
ph, pk, Solver, nd ll Tht This hndout contins four prts. In Prt I we derive n expression tht reltes the erved sornce of molecule (e.g., dye, cidse indictor, or fluorescent molecule to the frctionl sornce
More informationMing Ha Lee. School of Engineering, Computing and Science Swinburne University of Technology (Sarawak Campus), Malaysia.
http://sjie.journls.c.z VRIBLE SMPLING RTE HOTELLING S T 2 CONTROL CHRT WITH RUNS RULES Ming H Lee School of Engineering, Computing nd Science Swinburne University of Technology (Srwk Cmpus), Mlysi mhlee@swinburne.edu.my
More informationSECTION 59 Inverse Trigonometric Functions
59 Inverse Trigonometric Functions 47 In Problems 7 3, grph t lest two ccles of the given eqution in grphing utilit, then find n eqution of the form A tn B, A cot B, A sec B, or A csc B tht hs the sme
More informationLinear Functions. (1) Let F denote the Fahrenheit temperature and C the Celsius temperature of an object. F and C are related by
Liner Functions A. Definition nd Exmples A function f is liner if it cn be expressed in the form f ( x) = mx + b where m nd b re constnts nd x is n rbitrry member of the domin of f. Often the reltionship
More informationSection 2.3. Motion Along a Curve. The Calculus of Functions of Several Variables
The Clculus of Functions of Severl Vribles Section 2.3 Motion Along Curve Velocity ccelertion Consider prticle moving in spce so tht its position t time t is given by x(t. We think of x(t s moving long
More informationACIDBASE BASICS Stephen Wright, Ph.D. Dept of Physiology
Foundtions Lerning Objectives for the selflerning module on ACIDBASE Bsics 1. Define ph. 2. Clculte the hydrogen ion concentrtion from ph nd vice vers. 3. List the mjor body buffer systems. ACIDBASE
More informationDate: solutions. b) [OWj = 3.0 x. [OW) = 7.5 x. [Hj f) ph = 0.03
N. Nme: Dte: Block: 1. Clculte nd poh for following solutions: ) [H] = 1.0 x i0 b) [OWj = 3.0 x 108 c) [Hj = 2.5 x 102 d) [OW) = 7.5 x i0 e) [Hj = 1.2 x i0 f) [Hj = 6.0 2. Clculte [OW] for following
More informationControl transformers ST, DTZ, Multiwinding transformers UTI, Universal power supplies AING
Contents 12/1 Control trnsformers ST, DTZ, Multiwinding trnsformers UTI, Universl power supplies AING Multipurpose power supplies All trnsformers re built nd tested to the newest stndrds of IEC/EN 61558.
More information14.2. The Mean Value and the RootMeanSquare Value. Introduction. Prerequisites. Learning Outcomes
he Men Vlue nd the RootMenSqure Vlue 4. Introduction Currents nd voltges often vry with time nd engineers my wish to know the men vlue of such current or voltge over some prticulr time intervl. he men
More informationSUPPLEMENTARY MATERIALS RASCH ANALYSIS. Rasch analyses were used to estimate item and person measures for three sets of questions,
SUPPLEMENTARY MATERIALS RASCH ANALYSIS Rsch nlyses were used to estimte item nd person mesures for three sets of questions, detiled below (Tble S1), nd to exmine response ctegory functioning, person nd
More informationBasic Math Review. Numbers. Important Properties. Absolute Value PROPERTIES OF ADDITION NATURAL NUMBERS {1, 2, 3, 4, 5, }
ƒ Bsic Mth Review Numers NATURAL NUMBERS {1,, 3, 4, 5, } WHOLE NUMBERS {0, 1,, 3, 4, } INTEGERS {, 3,, 1, 0, 1,, } The Numer Line 5 4 3 1 0 1 3 4 5 Negtive integers Positive integers RATIONAL NUMBERS All
More informationTrigonometric Review Part 2
1 Trigonometric Review Prt Identities If, y is point on the unit circle corresponding to the ngle, we know nd y, y is point on the unit circle, then Becuse y 1 This mens tht 1 This is usully denoted s
More information1. Find the zeros Find roots. Set function = 0, factor or use quadratic equation if quadratic, graph to find zeros on calculator
AP Clculus Finl Review Sheet When you see the words. This is wht you think of doing. Find the zeros Find roots. Set function =, fctor or use qudrtic eqution if qudrtic, grph to find zeros on clcultor.
More informationNewton s Three Laws. d dt F = If the mass is constant, this relationship becomes the familiar form of Newton s Second Law: dv dt
Newton s Three Lws For couple centuries before Einstein, Newton s Lws were the bsic principles of Physics. These lws re still vlid nd they re the bsis for much engineering nlysis tody. Forml sttements
More informationOblique Triangles and The Law of Sines Congruency and Oblique Triangles Derivation of the Law of Sines Solving SAA and ASA Triangles (Case 1)
Olique Tringles nd The Lw of Sines Congruency nd Olique Tringles Derivtion of the Lw of Sines Solving SAA nd ASA Tringles (Cse 1) Are of Tringle Lw of Sines In ny tringle ABC, with sides,, nd c, sin A
More informationREVIEW QUESTIONS Chapter 16
Chemistry 102 ANSWER EY REVIEW QUESTIONS Chpter 16 1. A buffer is prepred by dding 20.0 g of cetic cid (HC 2 H O 2 ) nd 20.0 g of sodium cette (NC 2 H O 2 ) in enough wter to prepre 2.00 L of solution.
More informationHelicopter Theme and Variations
Helicopter Theme nd Vritions Or, Some Experimentl Designs Employing Pper Helicopters Some possible explntory vribles re: Who drops the helicopter The length of the rotor bldes The height from which the
More informationStudy on enzymeassisted aqueous extraction of oil from soybean
8 Journl Scientific & Industril Reserch J SCI IND RES VOL 69 NOVEMBER 2010 Vol. 69, November 2010, pp. 8865 Study on enzymessisted queous extrction oil from soyben JunQing Qin*, DeHui Qin, XingMo
More informationEconomics Letters 65 (1999) 9 15. macroeconomists. a b, Ruth A. Judson, Ann L. Owen. Received 11 December 1998; accepted 12 May 1999
Economics Letters 65 (1999) 9 15 Estimting dynmic pnel dt models: guide for q mcroeconomists b, * Ruth A. Judson, Ann L. Owen Federl Reserve Bord of Governors, 0th & C Sts., N.W. Wshington, D.C. 0551,
More informationExperiment 6: Friction
Experiment 6: Friction In previous lbs we studied Newton s lws in n idel setting, tht is, one where friction nd ir resistnce were ignored. However, from our everydy experience with motion, we know tht
More informationa, a 1, and x is any real
MA 131 Lecture Notes Eponentil Functions, Inverse Functions, nd Logrithmic Functions Eponentil Functions We sy tht unction is n lgebric unction i it is creted by combintion o lgebric processes such s ddition,
More informationHomework #6: Answers. a. If both goods are produced, what must be their prices?
Text questions, hpter 7, problems 12. Homework #6: Answers 1. Suppose there is only one technique tht cn be used in clothing production. To produce one unit of clothing requires four lborhours nd one
More informationHomework #4: Answers. 1. Draw the array of world outputs that free trade allows by making use of each country s transformation schedule.
Text questions, Chpter 5, problems 15: Homework #4: Answers 1. Drw the rry of world outputs tht free trde llows by mking use of ech country s trnsformtion schedule.. Drw it. This digrm is constructed
More informationLinear Inequalities A linear inequality in one variable is an inequality such as
7.4 Liner Inequlities A liner inequlity in one vrile is n inequlity such s x 5 2, y 3 5, or 2k 5 10. Archimedes, one of the gretest mthemticins of ntiquity, is shown on this Itlin stmp. He ws orn in the
More informationHomework 10. Problems: 19.29, 19.63, 20.9, 20.68
Homework 0 Prolems: 9.29, 9.63, 20.9, 20.68 Prolem 9.29 An utomoile tire is inlted with ir originlly t 0 º nd norml tmospheric pressure. During the process, the ir is compressed to 28% o its originl volume
More informationTHERMAL EXPANSION OF TUNGSTEN
. THERMAL EXPANSION OF TUNGSTEN S515 By Peter Hidnert nd W. T. Sweeney ABSTRACT This pper gives the results of n investigtion on the therml expnsion of tungsten (99.98 per cent) over vrious temperture
More informationStrong acids and bases
Monoprotic AcidBse Equiliri (CH ) ϒ Chpter monoprotic cids A monoprotic cid cn donte one proton. This chpter includes uffers; wy to fi the ph. ϒ Chpter 11 polyprotic cids A polyprotic cid cn donte multiple
More informationAlternate hamburger binding methods and their effects on flavor. Angela Jacquay, Corrie Beaver, and Stephen Fisher. Food Chemistry FN 453 Dr.
Alternte hmburger binding methods nd their effects on flvor. Angel Jcquy, Corrie Bever, nd Stephen Fisher Food Chemistry FN 453 Dr. Dniel Lbortory Wednesdy t 2:30 5:20p.m. Aku Reserch Project Fll 2011
More informationThe Analytic Hierarchy Process
The Anlytic Hierrchy Process The Anlytic Hierrchy Process (AHP), introduced by Thoms Sty (980), is n effective tool for deling with complex decision mking, nd my id the decision mker to set priorities
More information2.2 Power Functions with Modeling
174 CHAPTER 2 Polynomil, Power, nd Rtionl Functions Wht you ll lern bout Power Functions nd Vrition Monomil Functions nd Their Grphs Grphs of Power Functions Modeling with Power Functions... nd why Power
More information1. 1 m/s m/s m/s. 5. None of these m/s m/s m/s m/s correct m/s
Crete ssignment, 99552, Homework 5, Sep 15 t 10:11 m 1 This printout should he 30 questions. Multiplechoice questions my continue on the next column or pge find ll choices before nswering. The due time
More informationChem 116 POGIL Worksheet  Week 9 Weak Acid and Base Equilibria
Chem 116 POGIL Worksheet  Week 9 Wek Acid nd Bse Equilibri Why? We hve seen tht the clcultion of [HO ] nd ph for solutions of strong cids nd bse. To crry out clcultion of ll species present in solution
More informationIntegral calculus usage for conductor length determination on the basis of known maximal sag of a parabola
Ŕ periodic polytechnic Electricl Engineering nd Computer Science 56/ 01) 35 41 doi: 10.3311/PPee.7076 http:// periodicpolytechnic.org/ ee Cretive Commons Attribution RESEARCH ARTICLE Integrl clculus usge
More informationEffect of viscosity on C sugar in Beet sugar factories
ANNUAL TRANSACTIONS OF THE NORDIC RHEOLOGY SOCIETY, VOL. 16, 2008 Effect of on C sugr in Beet sugr fctories Mohmmd Hojjtoleslmy 1, Rez Shokrni 2 nd Ahmd Krsi 3 1 Deprtment of food technology, College of
More informationUnit 29: Inference for TwoWay Tables
Unit 29: Inference for TwoWy Tbles Prerequisites Unit 13, TwoWy Tbles is prerequisite for this unit. In ddition, students need some bckground in significnce tests, which ws introduced in Unit 25. Additionl
More informationSingle electrode potentials. Standard reduction potentials (E 0 )
25 Single electrode potentils Stndrd reduction potentils ( ) 26 Single electrode potentils Which is the strongest reducing gent mong the following metls: Cu, N, Au, Zn? Stndrd reduction potentils ( ) 27
More information