Chapter 13 Volumetric analysis (acid base titrations)

Save this PDF as:
 WORD  PNG  TXT  JPG

Size: px
Start display at page:

Download "Chapter 13 Volumetric analysis (acid base titrations)"

Transcription

1 Chpter 1 Volumetric lysis (cid se titrtios) Ope the tp d ru out some of the liquid util the tp coectio is full of cid d o ir remis (ir ules would led to iccurte result s they will proly dislodge durig the titrtio). Remove the fuel (stops drippig while you red the meiscus). Relese the liquid util the ottom of the meiscus is o the 0ml. Volumetric lysis is well estlished d verstile form of qutittive chemicl lysis. The purpose of this type of lysis is to use ccurtely kow volume d cocetrtio of oe solutio to fid the ccurte cocetrtio of secod. The experimetl procedure which llows us to do this is clled titrtio. This procedure is descried i detil elow. Preprig the pipette Titrtio procedure Fillig the urette Burette Cle the urette, rise it d dry the outside. Rise it with the solutio it is goig to coti (cid). Fill the urette to ove the 0ml mrk. Check for ir ules d ivert to remove y, if required. Wsh d rise well. Rise with the solutio it is to coti. Suck up solutio with pipette filler, ove the grd mrk. dry outside. Relese the solutio util the ottom of the meiscus is o the grd lie. Tip off y hgig drop (this should ot e couted). Allow to dri uder grvity (do ot low). Whe dried touch the tip off the side, y drops which should e ilcuded will dri i. Leve the rest.

2 Preprig the coicl flsk Coicl flsk Rise severl times with deioised wter. Dry outside. Add se solutio s descried ove, from the pipette. Rise dow wlls of the flsk with deioised wter (you kow exct volume dded of se) Titrtio procedure Add idictor to the flsk, or drops re eough ecuse ll idictors re wek cids or ses. Rise dow the sides with wter. Ru the solutio ito the flsk from the urette, slowly. Rise the sides of the flsk regulrly. Swirl the flsk costtly, to esure thorough mixig of regets. As the ed poit ers, dd the solutio drop y drop. Whe the ed-poit is reched the idictor will chge colour suddely. At this poit the cid will hve exctly eutrlised the se. Now red the meiscus of the urette, from the ottom, t eye level. Use filter pper, if ecessry, to mke the meiscus more redle. Record your result. Repet the titrtio severl times. Get the verge vlue. Oly iclude the vlues tht gree withi 0.ml of ech other. To prepre stdrd solutio of sodium crote. Weigh the smple Weigh 1.0 g of sodium crote o electroic lce, s ccurtely s you c. Use clock glss. Two plces of decimls would e est. Trsfer to eker Use sptul to trsfer the smple to eker of wrm wter (100ml). Rise the clock glss. Rise the remiig gris ito the eker with deioised wter. Rise the sptul ito the eker lso. All trces must e trsferred. Pour the wshigs ito the volumetric flsk. Pour the wshigs ito the volumetric flsk, usig fuel d glss rod. Wsh the rod s well. Rise the eker severl times with deioised wter. Pour these wshigs ito the volumetric flsk. Top up the volumetric flsk with deioised wter, util just elow the grdutio mrk.

3 Top up to the grdutio mrk with dropper. Red the ottom of the meiscus t eye level. Ivert d mix to esure proper mixig of the cotets. Clcultios Numer of moles of sodium crote moles 0.01 moles i50 cm moles i1 litre Molr Repet the titrtio severl times util two titrtio vlues gree to withi 0. ml of ech other. Equtio for the titrtio HCl N CO NCl HO CO Results Volume of the cid = 19. ml Fctor for the cid = (the umer i frot of HCl i the lced equtio) Molrity of the cid =? Volume of the se = 0 ml Fctor for the se = 1 (the umer i frot of sodium crote i the lced equtio) Molrity of the se = M To use this stdrd sodium crote solutio to fid the cocetrtio of (stdrdise) give hydrochloric cid solutio. Clcultios V M V M Plce 0 ml of Molr sodium crote ito coicl flsk usig pipette. Add two drops of methyl red idictor. This will give yellow colour to the solutio. Note; the umer of drops of idictor should e kept to miimum s most idictors re either wek cids or ses d will therefore tke prt i the eutrliztio process. Plce the hydrochloric cid i the urette d djust the level to zero, tkig ll of the usul precutios. Titrte i the usul mer. Record the volume of cid required to eutrlise the sodium crote. The poit of eutrlistio is reched whe the idictor just turs red (pik). 19. M M M moles per litre 0.1 Molr 0.1 M

4 To mke up pproximte solutio of sodium hydroxide d stdrdise it (fid its exct cocetrtio) y titrtio with the stdrd hydrochloric cid solutio ove. Plce 0 ml of the sodium hydroxide i the coicl flsk. Note; Alwys plce the se i the coicl flsk s they my rect with the groud glss i the tp of the urette. Add two drops of methyl red idictor d yellow colour is imprted to the solutio. Put the hydrochloric cid (previously stdrdized) ito the urette. Adjust to the zero level i the usul wy. Titrte i the usul mer. Whe the colour of the solutio i the coicl flsk chges to fit trce of permet pik the ed-poit hs ee reched. Record the volume of cid required to do this. Repet the titrtio severl times util two titrtio vlues gree to withi 0. ml of ech other. Equtio for the titrtio NOH HCl NCl HO Results Volume of se = 0 ml Fctor for the se = 1 Molrity of the se =? Volume of the cid = 19.8 ml Fctor for the cid = 1 Molrity of the cid = 0.1 M Clcultio V M M 1 1 M M M V M moles per litre To determie the percetge of ethoic cid i viegr. Viegr is solutio of ethoic cid dissolved i wter. The purpose of this titrtio is to fid the percetge of this cid i the viegr. Add 50 ml of viegr to volumetric flsk usig 5 ml pipette twice. Mke up the solutio to the 50 ml mrk with deioised wter. This is the solutio which will e used for the titrtio. Note; dilutig the solutio i this mer is ecessry for two resos (i) you will use less regets this wy d (ii) if error is mde mesurig dilute solutio it will ot hve gret implictios for the fil swer. Add 0 ml of 0.1 M sodium hydroxide solutio to the coicl flsk usig pipette. Add two or three drops of pheolphthlei idictor, just eough to imprt pik tige to the sodium hydroxide solutio. Put the dilute viegr solutio i the urette.titrte i the usul mer.

5 The ed-poit is reched whe the pik colour chges to colourless. Record the volume of cid used from the urette.repet the titrtio severl times util two titrtio vlues gree to withi 0. ml of ech other. Equtio for titrtio CHCOOH NOH CHCOON HO Results Volume of cid used = 1 ml Fctor for the cid = 1 Molrity of the cid =? Volume of se used = 0 ml Fctor for the se = 1 Molrity = 0.1 M Clcultios V M V M 1 M M moles / litre moles 0.77 moles/ litreof solutio g/l 46. g/l 4.6 g i100 cm 4.6% (w/v) / litrei the origil viegr. To determie the percetge of wter of crystlliztio i hydrted sodium crote (wshig sod). Wter of crystlliztio is the wter which is foud s prt of the structure of crystllie sustce. It hs othig to do with eig wet. The wter molecules referred to i the term occupy positios i the crystl lttice of the sustce. This wter of crystlliztio is geerlly represeted i the chemicl equtios of such compouds, t the ed of the formul e.g. N CO.xH O The x here is umer which represets the umer of molecules of wter i the crystl. The purpose of this experimet is to determie the percetge of wter of crystlliztio i sustce y titrtio. Weigh out ccurtely 5 g of hydrted sodium crote o clock glss. Mke up the solutio to 50 ml i volumetric flsk. Follow the sme procedure s for mkig stdrd solutio previously outlied ove. Pipette out 5 ml of this solutio ito cle coicl flsk. Add few drops of methyl red idictor, eough to imprt fit yellow colour to the solutio i the coicl flsk. Plce 0. M HCl i the urette d djust the level to zero tkig ll the usul precutios. Titrte i the usul mer util the yellow colour is replced y permet pik tige. This is the ed-poit of the titrtio. Record the volume of cid required to rech the ed-poit d repet severl times util two redigs (titres) gree to withi 0. ml of ech other.

6 Results Volume of cid used =.5 ml Fctor for the cid = Molrity of the cid = 0. M Volume of se = 5 ml Fctor for the se = 1 Molrity of se =? moles of NCO ; moles HO 0.05 : : 10 x 10 Clcultios V M A V M M M Molr sodium crote moles i50 cm g.491g 6.7g -.491g 4.9 g % wter of crystllistio % We c ow clculte the vlue of 'x'i the formul N CO We lredy kow tht there re 0.05 moles preset i the crystls. of sodium crote We lso kow tht there re 4.9 g of wter preset. This is 4.9 equivlet to moles moles.xh O

A black- line master of Example 3 You Try is on provided on page 10 for duplication or use with a projection system.

A black- line master of Example 3 You Try is on provided on page 10 for duplication or use with a projection system. Grde Level/Course: Algebr Lesso/Uit Pl Nme: Geometric Sequeces Rtiole/Lesso Abstrct: Wht mkes sequece geometric? This chrcteristic is ddressed i the defiitio of geometric sequece d will help derive the

More information

Arithmetic Sequences

Arithmetic Sequences Arithmetic equeces A simple wy to geerte sequece is to strt with umber, d dd to it fixed costt d, over d over gi. This type of sequece is clled rithmetic sequece. Defiitio: A rithmetic sequece is sequece

More information

REVIEW QUESTIONS Chapter 16

REVIEW 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 information

MATHEMATICS FOR ENGINEERING BASIC ALGEBRA

MATHEMATICS FOR ENGINEERING BASIC ALGEBRA MATHEMATICS FOR ENGINEERING BASIC ALGEBRA TUTORIAL - INDICES, LOGARITHMS AND FUNCTION This is the oe of series of bsic tutorils i mthemtics imed t begiers or yoe wtig to refresh themselves o fudmetls.

More information

A Resource for Free-standing Mathematics Qualifications

A Resource for Free-standing Mathematics Qualifications A pie chrt shows how somethig is divided ito prts - it is good wy of showig the proportio (or frctio) of the dt tht is i ech ctegory. To drw pie chrt:. Fid the totl umer of items.. Fid how my degrees represet

More information

Well 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?

Well 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 information

UNIT FIVE DETERMINANTS

UNIT FIVE DETERMINANTS UNIT FIVE DETERMINANTS. INTRODUTION I uit oe the determit of mtrix ws itroduced d used i the evlutio of cross product. I this chpter we exted the defiitio of determit to y size squre mtrix. The determit

More information

Repeated multiplication is represented using exponential notation, for example:

Repeated multiplication is represented using exponential notation, for example: Appedix A: The Lws of Expoets Expoets re short-hd ottio used to represet my fctors multiplied together All of the rules for mipultig expoets my be deduced from the lws of multiplictio d divisio tht you

More information

A function f whose domain is the set of positive integers is called a sequence. The values

A function f whose domain is the set of positive integers is called a sequence. The values EQUENCE: A fuctio f whose domi is the set of positive itegers is clled sequece The vlues f ( ), f (), f (),, f (), re clled the terms of the sequece; f() is the first term, f() is the secod term, f() is

More information

n Using the formula we get a confidence interval of 80±1.64

n Using the formula we get a confidence interval of 80±1.64 9.52 The professor of sttistics oticed tht the rks i his course re orlly distributed. He hs lso oticed tht his orig clss verge is 73% with stdrd devitio of 12% o their fil exs. His fteroo clsses verge

More information

Application: Volume. 6.1 Overture. Cylinders

Application: Volume. 6.1 Overture. Cylinders Applictio: Volume 61 Overture I this chpter we preset other pplictio of the defiite itegrl, this time to fid volumes of certi solids As importt s this prticulr pplictio is, more importt is to recogize

More information

Math Bowl 2009 Written Test Solutions. 2 8i

Math Bowl 2009 Written Test Solutions. 2 8i Mth owl 009 Writte Test Solutios i? i i i i i ( i)( i ( i )( i ) ) 8i i i (i ) 9i 8 9i 9 i How my pirs of turl umers ( m, ) stisfy the equtio? m We hve to hve m d d, the m ; d, the 0 m m Tryig these umers,

More information

m n Use technology to discover the rules for forms such as a a, various integer values of m and n and a fixed integer value a.

m n Use technology to discover the rules for forms such as a a, various integer values of m and n and a fixed integer value a. TIth.co Alger Expoet Rules ID: 988 Tie required 25 iutes Activity Overview This ctivity llows studets to work idepedetly to discover rules for workig with expoets, such s Multiplictio d Divisio of Like

More information

Chapter 04.05 System of Equations

Chapter 04.05 System of Equations hpter 04.05 System of Equtios After redig th chpter, you should be ble to:. setup simulteous lier equtios i mtrix form d vice-vers,. uderstd the cocept of the iverse of mtrix, 3. kow the differece betwee

More information

Chapter 3 Section 3 Lesson Additional Rules for Exponents

Chapter 3 Section 3 Lesson Additional Rules for Exponents Chpter Sectio Lesso Additiol Rules for Epoets Itroductio I this lesso we ll eie soe dditiol rules tht gover the behvior of epoets The rules should be eorized; they will be used ofte i the reiig chpters

More information

We will begin this chapter with a quick refresher of what an exponent is.

We will begin this chapter with a quick refresher of what an exponent is. .1 Exoets We will egi this chter with quick refresher of wht exoet is. Recll: So, exoet is how we rereset reeted ultilictio. We wt to tke closer look t the exoet. We will egi with wht the roerties re for

More information

Released Assessment Questions, 2015 QUESTIONS

Released Assessment Questions, 2015 QUESTIONS Relesed Assessmet Questios, 15 QUESTIONS Grde 9 Assessmet of Mthemtis Ademi Red the istrutios elow. Alog with this ooklet, mke sure you hve the Aswer Booklet d the Formul Sheet. You my use y spe i this

More information

Chapter 9: Quadratic Equations

Chapter 9: Quadratic Equations Chpter 9: Qudrtic Equtions QUADRATIC EQUATIONS DEFINITION + + c = 0,, c re constnts (generlly integers) ROOTS Synonyms: Solutions or Zeros Cn hve 0, 1, or rel roots Consider the grph of qudrtic equtions.

More information

EXPONENTS AND RADICALS

EXPONENTS AND RADICALS Expoets d Rdicls MODULE - EXPONENTS AND RADICALS We hve lert bout ultiplictio of two or ore rel ubers i the erlier lesso. You c very esily write the followig, d Thik of the situtio whe is to be ultiplied

More information

FOURIER SERIES PART I: DEFINITIONS AND EXAMPLES. To a 2π-periodic function f(x) we will associate a trigonometric series. a n cos(nx) + b n sin(nx),

FOURIER SERIES PART I: DEFINITIONS AND EXAMPLES. To a 2π-periodic function f(x) we will associate a trigonometric series. a n cos(nx) + b n sin(nx), FOURIER SERIES PART I: DEFINITIONS AND EXAMPLES To -periodic fuctio f() we will ssocite trigoometric series + cos() + b si(), or i terms of the epoetil e i, series of the form c e i. Z For most of the

More information

Chapter 18 Superposition and Standing Waves

Chapter 18 Superposition and Standing Waves hpter 8 Superpositio d Stdig Wves 8. Superpositio d Iterereces y '(, y(, + y (, Overlppig wves lgericlly dd to produce resultt wve (or et wve). Overlppig wves do ot i y wy lter the trvel o ech other. Superpositio

More information

A. Description: A simple queueing system is shown in Fig. 16-1. Customers arrive randomly at an average rate of

A. Description: A simple queueing system is shown in Fig. 16-1. Customers arrive randomly at an average rate of Queueig Theory INTRODUCTION Queueig theory dels with the study of queues (witig lies). Queues boud i rcticl situtios. The erliest use of queueig theory ws i the desig of telehoe system. Alictios of queueig

More information

The Math Learning Center PO Box 12929, Salem, Oregon 97309 0929 Math Learning Center

The Math Learning Center PO Box 12929, Salem, Oregon 97309 0929  Math Learning Center Resource Overview Quntile Mesure: Skill or Concept: 1010Q Determine perimeter using concrete models, nonstndrd units, nd stndrd units. (QT M 146) Use models to develop formuls for finding res of tringles,

More information

Basic Math Review. Numbers. Important Properties. Absolute Value PROPERTIES OF ADDITION NATURAL NUMBERS {1, 2, 3, 4, 5, }

Basic 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 information

Strong acids and bases

Strong acids and bases Monoprotic Acid-Bse 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 information

Lecture 15 - Curve Fitting Techniques

Lecture 15 - Curve Fitting Techniques Lecture 15 - Curve Fitting Techniques Topics curve fitting motivtion liner regression Curve fitting - motivtion For root finding, we used given function to identify where it crossed zero where does fx

More information

Binary Representation of Numbers Autar Kaw

Binary Representation of Numbers Autar Kaw Binry Representtion of Numbers Autr Kw After reding this chpter, you should be ble to: 1. convert bse- rel number to its binry representtion,. convert binry number to n equivlent bse- number. In everydy

More information

Homework #6 Chapter 7 Homework Acids and Bases

Homework #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 information

Solutions for the problems about Calculation of ph in the case of monoprotic acids and bases. 1. What is the ph of a 0.1 M acetic acid solution?

Solutions for the problems about Calculation of ph in the case of monoprotic acids and bases. 1. What is the ph of a 0.1 M acetic acid solution? Solutions for the prolems out Clcultion of ph in the cse of monoprotic cids nd ses 1. Wht is the ph of 0.1 M cetic cid solution? Acetic cid is wek cid with = 1.86 5 nd in this cse c wek cid >>>, tht is

More information

4 Geometry: Shapes. 4.1 Circumference and area of a circle. FM Functional Maths AU (AO2) Assessing Understanding PS (AO3) Problem Solving HOMEWORK 4A

4 Geometry: Shapes. 4.1 Circumference and area of a circle. FM Functional Maths AU (AO2) Assessing Understanding PS (AO3) Problem Solving HOMEWORK 4A Geometry: Shpes. Circumference nd re of circle HOMEWORK D C 3 5 6 7 8 9 0 3 U Find the circumference of ech of the following circles, round off your nswers to dp. Dimeter 3 cm Rdius c Rdius 8 m d Dimeter

More information

Basic Arithmetic TERMINOLOGY

Basic Arithmetic TERMINOLOGY Bsic Arithmetic TERMINOLOGY Absolute vlue: The distce of umber from zero o the umber lie. Hece it is the mgitude or vlue of umber without the sig Directed umbers: The set of itegers or whole umbers f,,,

More information

Math 113 HW #11 Solutions

Math 113 HW #11 Solutions Math 3 HW # Solutios 5. 4. (a) Estimate the area uder the graph of f(x) = x from x = to x = 4 usig four approximatig rectagles ad right edpoits. Sketch the graph ad the rectagles. Is your estimate a uderestimate

More information

MATHEMATICS SYLLABUS SECONDARY 7th YEAR

MATHEMATICS SYLLABUS SECONDARY 7th YEAR Europe Schools Office of the Secretry-Geerl Pedgogicl developmet Uit Ref.: 2011-01-D-41-e-2 Orig.: DE MATHEMATICS SYLLABUS SECONDARY 7th YEAR Stdrd level 5 period/week course Approved y the Joit Techig

More information

Lecture 34: The `Density Operator. Phy851 Fall 2009

Lecture 34: The `Density Operator. Phy851 Fall 2009 Lecture 3: The `Deity Opertor Phy85 Fll 9 The QM `deity opertor HAS NOTHING TO DO WITH MASS PER UNIT VOLUME The deity opertor forli i geerliztio of the Pure Stte QM we hve ued o fr. New cocept: Mixed tte

More information

Surface Area and Volume

Surface Area and Volume Surfce Are nd Volume Student Book - Series J- Mthletics Instnt Workooks Copyright Surfce re nd volume Student Book - Series J Contents Topics Topic - Surfce re of right prism Topic 2 - Surfce re of right

More information

Math 135 Circles and Completing the Square Examples

Math 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 information

Graphs on Logarithmic and Semilogarithmic Paper

Graphs 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 information

Summation Notation The sum of the first n terms of a sequence is represented by the summation notation i the index of summation

Summation Notation The sum of the first n terms of a sequence is represented by the summation notation i the index of summation Lesso 0.: Sequeces d Summtio Nottio Def. of Sequece A ifiite sequece is fuctio whose domi is the set of positive rel itegers (turl umers). The fuctio vlues or terms of the sequece re represeted y, 2, 3,...,....

More information

Assuming all values are initially zero, what are the values of A and B after executing this Verilog code inside an always block? C=1; A <= C; B = C;

Assuming all values are initially zero, what are the values of A and B after executing this Verilog code inside an always block? C=1; A <= C; B = C; B-26 Appendix B The Bsics of Logic Design Check Yourself ALU n [Arthritic Logic Unit or (rre) Arithmetic Logic Unit] A rndom-numer genertor supplied s stndrd with ll computer systems Stn Kelly-Bootle,

More information

Sequences and Series

Sequences and Series Secto 9. Sequeces d Seres You c thk of sequece s fucto whose dom s the set of postve tegers. f ( ), f (), f (),... f ( ),... Defto of Sequece A fte sequece s fucto whose dom s the set of postve tegers.

More information

Reasoning to Solve Equations and Inequalities

Reasoning to Solve Equations and Inequalities Lesson4 Resoning to Solve Equtions nd Inequlities In erlier work in this unit, you modeled situtions with severl vriles nd equtions. For exmple, suppose you were given usiness plns for concert showing

More information

MerCarb 2 bbl Carburetor

MerCarb 2 bbl Carburetor TO: SERVICE MANAGER TECHNICIANS PARTS MANAGER No. 97-8 Revised June 1999. Informtion underlined is new. MerCr 2 l Cruretor 8 Point Cruretor Check List To ensure tht the cruretor is the cuse of the engine

More information

Appendix D: Completing the Square and the Quadratic Formula. In Appendix A, two special cases of expanding brackets were considered:

Appendix D: Completing the Square and the Quadratic Formula. In Appendix A, two special cases of expanding brackets were considered: Appendi D: Completing the Squre nd the Qudrtic Formul Fctoring qudrtic epressions such s: + 6 + 8 ws one of the topics introduced in Appendi C. Fctoring qudrtic epressions is useful skill tht cn help you

More information

AP CALCULUS FORMULA LIST. f x + x f x f x + h f x. b a

AP CALCULUS FORMULA LIST. f x + x f x f x + h f x. b a AP CALCULUS FORMULA LIST 1 Defiitio of e: e lim 1+ x if x 0 Asolute Vlue: x x if x < 0 Defiitio of the Derivtive: ( ) f x + x f x f x + h f x f '( x) lim f '( x) lim x x h h f ( + h) f ( ) f '( ) lim derivtive

More information

Titrations. x C A V B V A. n A n B. x C B C A C B. Acid-base titrations:

Titrations. x C A V B V A. n A n B. x C B C A C B. Acid-base titrations: Acid-base titrations: Titrations n A A + n B B products Where: n A moles of acid (A) are neutralised by n B moles of base (B). If we have a solution of known acid but of unknown concentration then we can

More information

SECTION 1.5 : SUMMATION NOTATION + WORK WITH SEQUENCES

SECTION 1.5 : SUMMATION NOTATION + WORK WITH SEQUENCES SECTION 1.5 : SUMMATION NOTATION + WORK WITH SEQUENCES Read Sectio 1.5 (pages 5 9) Overview I Sectio 1.5 we lear to work with summatio otatio ad formulas. We will also itroduce a brief overview of sequeces,

More information

INVESTIGATION OF PARAMETERS OF ACCUMULATOR TRANSMISSION OF SELF- MOVING MACHINE

INVESTIGATION OF PARAMETERS OF ACCUMULATOR TRANSMISSION OF SELF- MOVING MACHINE ENGINEEING FO UL DEVELOENT Jelgv, 28.-29.05.2009. INVESTIGTION OF ETES OF CCUULTO TNSISSION OF SELF- OVING CHINE leksdrs Kirk Lithui Uiversity of griculture, Kus leksdrs.kirk@lzuu.lt.lt bstrct. Uder the

More information

CHAPTER-10 WAVEFUNCTIONS, OBSERVABLES and OPERATORS

CHAPTER-10 WAVEFUNCTIONS, OBSERVABLES and OPERATORS Lecture Notes PH 4/5 ECE 598 A. L Ros INTRODUCTION TO QUANTUM MECHANICS CHAPTER-0 WAVEFUNCTIONS, OBSERVABLES d OPERATORS 0. Represettios i the sptil d mometum spces 0..A Represettio of the wvefuctio i

More information

Ae2 Mathematics : Fourier Series

Ae2 Mathematics : Fourier Series Ae Mthemtics : Fourier Series J. D. Gibbon (Professor J. D Gibbon, Dept of Mthemtics j.d.gibbon@ic.c.uk http://www.imperil.c.uk/ jdg These notes re not identicl word-for-word with my lectures which will

More information

MATH 90 CHAPTER 5 Name:.

MATH 90 CHAPTER 5 Name:. MATH 90 CHAPTER 5 Nme:. 5.1 Multiplictio of Expoets Need To Kow Recll expoets The ide of expoet properties Apply expoet properties Expoets Expoets me repeted multiplictio. 3 4 3 4 4 ( ) Expoet Properties

More information

OPTIMA QUADRANT / OFFSET QUADRANT

OPTIMA QUADRANT / OFFSET QUADRANT OPTIMA QUADRANT / OFFSET QUADRANT 71799 00 / Issue 1 / 15 Y Z DIMENSIONS Check the enclosure size in the tle elow mtches the showertry instlltion. = Widths: 800 Door = 780-805mm 900 Door = 880-905mm Y

More information

Multiplication and Division - Left to Right. Addition and Subtraction - Left to Right.

Multiplication and Division - Left to Right. Addition and Subtraction - Left to Right. Order of Opertions r of Opertions Alger P lese Prenthesis - Do ll grouped opertions first. E cuse Eponents - Second M D er Multipliction nd Division - Left to Right. A unt S hniqu Addition nd Sutrction

More information

Introduction to Hypothesis Testing

Introduction to Hypothesis Testing Itroductio to Hypothesis Testig I Cosumer Reports, April, 978, the results of tste test were reported. Cosumer Reports commeted, "we do't cosider this result to be sttisticlly sigifict." At the time, Miller

More information

Rate and Activation Energy of the Iodination of Acetone

Rate and Activation Energy of the Iodination of Acetone 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

More information

Helicopter Theme and Variations

Helicopter 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 information

STUDENT S COMPANIONS IN BASIC MATH: THE SECOND. Basic Identities in Algebra. Let us start with a basic identity in algebra:

STUDENT S COMPANIONS IN BASIC MATH: THE SECOND. Basic Identities in Algebra. Let us start with a basic identity in algebra: STUDENT S COMPANIONS IN BASIC MATH: THE SECOND Bsic Idetities i Algebr Let us strt with bsic idetity i lgebr: 2 b 2 ( b( + b. (1 Ideed, multiplyig out the right hd side, we get 2 +b b b 2. Removig the

More information

Vectors. The magnitude of a vector is its length, which can be determined by Pythagoras Theorem. The magnitude of a is written as a.

Vectors. The magnitude of a vector is its length, which can be determined by Pythagoras Theorem. The magnitude of a is written as a. Vectors mesurement which onl descries the mgnitude (i.e. size) of the oject is clled sclr quntit, e.g. Glsgow is 11 miles from irdrie. vector is quntit with mgnitude nd direction, e.g. Glsgow is 11 miles

More information

58.08 g 1 mol. 1 mol

58.08 g 1 mol. 1 mol Chem 338 Homework Set #6 solutios October 17, 001 From Atkis: 6.8, 6.1, 6.14, 6.16, 6.17, 6.19, 6. 6.8) The partial molar volumes of propaoe ad trichloromethae i a mixture i which the mole fractio of CHCl

More information

Present and future value formulae for uneven cash flow Based on performance of a Business

Present and future value formulae for uneven cash flow Based on performance of a Business Advces i Mgemet & Applied Ecoomics, vol., o., 20, 93-09 ISSN: 792-7544 (prit versio), 792-7552 (olie) Itertiol Scietific Press, 20 Preset d future vlue formule for ueve csh flow Bsed o performce of Busiess

More information

Acetic Acid Content of Vinegar: An Acid-Base Titration E10-1

Acetic Acid Content of Vinegar: An Acid-Base Titration E10-1 Experiment 10 Acetic Acid Content of Vinegar: An Acid-Base Titration E10-1 E10-2 The task The goal of this experiment is to determine accurately the concentration of acetic acid in vinegar via volumetric

More information

Introduction to Mathematical Reasoning, Saylor 111

Introduction to Mathematical Reasoning, Saylor 111 Frction versus rtionl number. Wht s the difference? It s not n esy question. In fct, the difference is somewht like the difference between set of words on one hnd nd sentence on the other. A symbol is

More information

Gray level image enhancement using the Bernstein polynomials

Gray level image enhancement using the Bernstein polynomials Buletiul Ştiiţiic l Uiersităţii "Politehic" di Timişor Seri ELECTRONICĂ şi TELECOMUNICAŢII TRANSACTIONS o ELECTRONICS d COMMUNICATIONS Tom 47(6), Fscicol -, 00 Gry leel imge ehcemet usig the Berstei polyomils

More information

Mathematics Higher Level

Mathematics Higher Level Mthemtics Higher Level Higher Mthemtics Exmintion Section : The Exmintion Mthemtics Higher Level. Structure of the exmintion pper The Higher Mthemtics Exmintion is divided into two ppers s detiled below:

More information

CS99S Laboratory 2 Preparation Copyright W. J. Dally 2001 October 1, 2001

CS99S Laboratory 2 Preparation Copyright W. J. Dally 2001 October 1, 2001 CS99S Lortory 2 Preprtion Copyright W. J. Dlly 2 Octoer, 2 Ojectives:. Understnd the principle of sttic CMOS gte circuits 2. Build simple logic gtes from MOS trnsistors 3. Evlute these gtes to oserve logic

More information

Warm-up for Differential Calculus

Warm-up for Differential Calculus Summer Assignment Wrm-up for Differentil Clculus Who should complete this pcket? Students who hve completed Functions or Honors Functions nd will be tking Differentil Clculus in the fll of 015. Due Dte:

More information

AntiSpyware Enterprise Module 8.5

AntiSpyware Enterprise Module 8.5 AntiSpywre Enterprise Module 8.5 Product Guide Aout the AntiSpywre Enterprise Module The McAfee AntiSpywre Enterprise Module 8.5 is n dd-on to the VirusScn Enterprise 8.5i product tht extends its ility

More information

Chapter 2 Decimals. (A reminder) In the whole number chapter, we looked at ones, tens, hundreds, thousands and larger numbers. = 1

Chapter 2 Decimals. (A reminder) In the whole number chapter, we looked at ones, tens, hundreds, thousands and larger numbers. = 1 Chpter 2 Decimls Wht is Deciml? (A reminder) In the whole numer chpter, we looked t ones, tens, hundreds, thousnds nd lrger numers. When single unit is divided into 10 (or 100) its, we hve deciml frctions

More information

EQUATIONS OF LINES AND PLANES

EQUATIONS OF LINES AND PLANES EQUATIONS OF LINES AND PLANES MATH 195, SECTION 59 (VIPUL NAIK) Corresponding mteril in the ook: Section 12.5. Wht students should definitely get: Prmetric eqution of line given in point-direction nd twopoint

More information

Measures of Spread and Boxplots Discrete Math, Section 9.4

Measures of Spread and Boxplots Discrete Math, Section 9.4 Measures of Spread ad Boxplots Discrete Math, Sectio 9.4 We start with a example: Example 1: Comparig Mea ad Media Compute the mea ad media of each data set: S 1 = {4, 6, 8, 10, 1, 14, 16} S = {4, 7, 9,

More information

Section 2.3. Motion Along a Curve. The Calculus of Functions of Several Variables

Section 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 information

Fourier Series (Lecture 13)

Fourier Series (Lecture 13) Fourier Series (Lecture 3) ody s Objectives: Studets will be ble to: ) Determie the Fourier Coefficiets for periodic sigl b) Fid the stedy-stte respose for system forced with geerl periodic forcig Rrely

More information

TRENDS IN THE PERIODIC TABLE

TRENDS IN THE PERIODIC TABLE MODULE WORKSHEET0 TRENDS IN THE PERIODIC TABLE Syllus reference.. Complete the following with word or phrse to check your understnding. In the nineteenth century, s more elements ecme known, chemists serched

More information

Chapter. Contents: A Constructing decimal numbers

Chapter. Contents: A Constructing decimal numbers Chpter 9 Deimls Contents: A Construting deiml numers B Representing deiml numers C Deiml urreny D Using numer line E Ordering deimls F Rounding deiml numers G Converting deimls to frtions H Converting

More information

Unit 6: Exponents and Radicals

Unit 6: Exponents and Radicals Eponents nd Rdicls -: The Rel Numer Sstem Unit : Eponents nd Rdicls Pure Mth 0 Notes Nturl Numers (N): - counting numers. {,,,,, } Whole Numers (W): - counting numers with 0. {0,,,,,, } Integers (I): -

More information

State the size of angle x. Sometimes the fact that the angle sum of a triangle is 180 and other angle facts are needed. b y 127

State the size of angle x. Sometimes the fact that the angle sum of a triangle is 180 and other angle facts are needed. b y 127 ngles 2 CHTER 2.1 Tringles Drw tringle on pper nd lel its ngles, nd. Ter off its orners. Fit ngles, nd together. They mke stright line. This shows tht the ngles in this tringle dd up to 180 ut it is not

More information

Sequences II. Chapter 3. 3.1 Convergent Sequences

Sequences II. Chapter 3. 3.1 Convergent Sequences Chapter 3 Sequeces II 3. Coverget Sequeces Plot a graph of the sequece a ) = 2, 3 2, 4 3, 5 + 4,...,,... To what limit do you thik this sequece teds? What ca you say about the sequece a )? For ǫ = 0.,

More information

Simple Annuities Present Value.

Simple Annuities Present Value. Simple Auities Preset Value. OBJECTIVES (i) To uderstad the uderlyig priciple of a preset value auity. (ii) To use a CASIO CFX-9850GB PLUS to efficietly compute values associated with preset value auities.

More information

Confidence Intervals for One Mean with Tolerance Probability

Confidence Intervals for One Mean with Tolerance Probability Chapter 421 Cofidece Itervals for Oe Mea with Tolerace Probability Itroductio This procedure calculates the sample size ecessary to achieve a specified distace from the mea to the cofidece limit(s) with

More information

m, where m = m 1 + m m n.

m, where m = m 1 + m m n. Lecture 7 : Moments nd Centers of Mss If we hve msses m, m 2,..., m n t points x, x 2,..., x n long the x-xis, the moment of the system round the origin is M 0 = m x + m 2 x 2 + + m n x n. The center of

More information

Burning Issues. OBJECTIVES: Visitors learn about products of combustion reactions and how these products contribute to pollution.

Burning Issues. OBJECTIVES: Visitors learn about products of combustion reactions and how these products contribute to pollution. EXPERIMENT Burning Issues Visitors use a candle to investigate the products of combustion. The candle flame deposits carbon on a glass rod and water on the sides of a jar: Carbon dioxide gas reacts with

More information

Repeating Decimals are decimal numbers that have number(s) after the decimal point that repeat in a pattern.

Repeating Decimals are decimal numbers that have number(s) after the decimal point that repeat in a pattern. 5.5 Fractios ad Decimals Steps for Chagig a Fractio to a Decimal. Simplify the fractio, if possible. 2. Divide the umerator by the deomiator. d d Repeatig Decimals Repeatig Decimals are decimal umbers

More information

.04. This means $1000 is multiplied by 1.02 five times, once for each of the remaining sixmonth

.04. This means $1000 is multiplied by 1.02 five times, once for each of the remaining sixmonth Questio 1: What is a ordiary auity? Let s look at a ordiary auity that is certai ad simple. By this, we mea a auity over a fixed term whose paymet period matches the iterest coversio period. Additioally,

More information

Homework 3 Solutions

Homework 3 Solutions CS 341: Foundtions of Computer Science II Prof. Mrvin Nkym Homework 3 Solutions 1. Give NFAs with the specified numer of sttes recognizing ech of the following lnguges. In ll cses, the lphet is Σ = {,1}.

More information

2 DIODE CLIPPING and CLAMPING CIRCUITS

2 DIODE CLIPPING and CLAMPING CIRCUITS 2 DIODE CLIPPING nd CLAMPING CIRCUITS 2.1 Ojectives Understnding the operting principle of diode clipping circuit Understnding the operting principle of clmping circuit Understnding the wveform chnge of

More information

Titration of Hydrochloric Acid with Sodium Hydroxide

Titration of Hydrochloric Acid with Sodium Hydroxide Cautions: Hydrochloric acid solution is a strong acid. Sodium hydroxide solution is a strong base. Both are harmful to skin and eyes. Affected areas should be washed thoroughly with copious amounts of

More information

Variable Dry Run (for Python)

Variable Dry Run (for Python) Vrile Dr Run (for Pthon) Age group: Ailities ssumed: Time: Size of group: Focus Vriles Assignment Sequencing Progrmming 7 dult Ver simple progrmming, sic understnding of ssignment nd vriles 20-50 minutes

More information

Determination of the amount of sodium carbonate and sodium hydroxide in a mixture by titration.

Determination of the amount of sodium carbonate and sodium hydroxide in a mixture by titration. Module 9 : Experiments in Chemistry Lecture 38 : Titrations : Acid-Base, Redox and Complexometric Objectives In this lecture you will learn the techniques to do following Determination of the amount of

More information

FEASIBILITY OF USING PRESSED SUGAR CANE STALK FOR THE PRODUCTION OF CHARCOAL. D Ffoulkes, R Elliott and T R Preston

FEASIBILITY 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 information

Geometry and Measure. 12am 1am 2am 3am 4am 5am 6am 7am 8am 9am 10am 11am 12pm

Geometry and Measure. 12am 1am 2am 3am 4am 5am 6am 7am 8am 9am 10am 11am 12pm Reding Scles There re two things to do when reding scle. 1. Mke sure you know wht ech division on the scle represents. 2. Mke sure you red in the right direction. Mesure Length metres (m), kilometres (km),

More information

LECTURE #05. Learning Objectives. How does atomic packing factor change with different atom types? How do you calculate the density of a material?

LECTURE #05. Learning Objectives. How does atomic packing factor change with different atom types? How do you calculate the density of a material? LECTURE #05 Chpter : Pcking Densities nd Coordintion Lerning Objectives es How does tomic pcking fctor chnge with different tom types? How do you clculte the density of mteril? 2 Relevnt Reding for this

More information

Section 5-4 Trigonometric Functions

Section 5-4 Trigonometric Functions 5- Trigonometric Functions Section 5- Trigonometric Functions Definition of the Trigonometric Functions Clcultor Evlution of Trigonometric Functions Definition of the Trigonometric Functions Alternte Form

More information

Modified Line Search Method for Global Optimization

Modified Line Search Method for Global Optimization Modified Lie Search Method for Global Optimizatio Cria Grosa ad Ajith Abraham Ceter of Excellece for Quatifiable Quality of Service Norwegia Uiversity of Sciece ad Techology Trodheim, Norway {cria, ajith}@q2s.tu.o

More information

Searching Algorithm Efficiencies

Searching Algorithm Efficiencies Efficiecy of Liear Search Searchig Algorithm Efficiecies Havig implemeted the liear search algorithm, how would you measure its efficiecy? A useful measure (or metric) should be geeral, applicable to ay

More information

Confidence Intervals and Sample Size

Confidence Intervals and Sample Size 8/7/015 C H A P T E R S E V E N Cofidece Itervals ad Copyright 015 The McGraw-Hill Compaies, Ic. Permissio required for reproductio or display. 1 Cofidece Itervals ad Outlie 7-1 Cofidece Itervals for the

More information

THE REGRESSION MODEL IN MATRIX FORM. For simple linear regression, meaning one predictor, the model is. for i = 1, 2, 3,, n

THE REGRESSION MODEL IN MATRIX FORM. For simple linear regression, meaning one predictor, the model is. for i = 1, 2, 3,, n We will cosider the liear regressio model i matrix form. For simple liear regressio, meaig oe predictor, the model is i = + x i + ε i for i =,,,, This model icludes the assumptio that the ε i s are a sample

More information

www.mathsbox.org.uk e.g. f(x) = x domain x 0 (cannot find the square root of negative values)

www.mathsbox.org.uk e.g. f(x) = x domain x 0 (cannot find the square root of negative values) www.mthsbo.org.uk CORE SUMMARY NOTES Functions A function is rule which genertes ectl ONE OUTPUT for EVERY INPUT. To be defined full the function hs RULE tells ou how to clculte the output from the input

More information

Even and Odd Functions

Even and Odd Functions Eve d Odd Fuctios Beore lookig t urther emples o Fourier series it is useul to distiguish two clsses o uctios or which the Euler- Fourier ormuls or the coeiciets c be simpliied. The two clsses re eve d

More information

P.3 Polynomials and Factoring. P.3 an 1. Polynomial STUDY TIP. Example 1 Writing Polynomials in Standard Form. What you should learn

P.3 Polynomials and Factoring. P.3 an 1. Polynomial STUDY TIP. Example 1 Writing Polynomials in Standard Form. What you should learn 33337_0P03.qp 2/27/06 24 9:3 AM Chpter P Pge 24 Prerequisites P.3 Polynomils nd Fctoring Wht you should lern Polynomils An lgeric epression is collection of vriles nd rel numers. The most common type of

More information

The Velocity Factor of an Insulated Two-Wire Transmission Line

The Velocity Factor of an Insulated Two-Wire Transmission Line The Velocity Fctor of n Insulted Two-Wire Trnsmission Line Problem Kirk T. McDonld Joseph Henry Lbortories, Princeton University, Princeton, NJ 08544 Mrch 7, 008 Estimte the velocity fctor F = v/c nd the

More information