Infrared Spectroscopy: Functional Group Determination

Size: px
Start display at page:

Download "Infrared Spectroscopy: Functional Group Determination"

Transcription

1 nfrred pectroscopy: Functionl Group Determintion tch the infrred spectr below with the following compounds. ote tht one of the compounds does not mtch ny of the spectr. dentify ny spectrl fetures tht ssisted you in your determintion. B o mtch! (Would need both = nd =) o - sp 2 - o = = pectrum WVUB o - o sp 2 - = pectrum B WVUB o sp 2 - o = or = - pectrum WVUB 1

2 nfrred pectroscopy: tructure Determintion he infrred spectr for the following six compounds pper on the next two pges. Fill in ech box with the correct structure tht corresponds to ech spectrum. t () (b) t (c) 2

3 nfrred pectroscopy: tructure Determintion (continued) t (d) (e) (f) 3

4 nfrred pectroscopy: ore tructure Determintion Determine the structure of ech of the compounds on this nd the next pge using only the given moleculr formul nd infrred spectrum. Plce your nswer in the box below the corresponding spectrum. () oleculr formul: WVUB (b) oleculr formul: WVUB 4

5 nfrred pectroscopy: ore tructure Determintion (continued) (c) oleculr formul: WVUB (b) oleculr formul: B B WVUB 2. 5

6 nfrred pectroscopy: heory 1. nk the following three compounds in order of decresing crbonyl stretching frequency (1 = highest stretching frequency, 3 = lowest stretching frequency). xplin your nswer. e We consider the bility of ech heterotom to weken the neighboring crbonyl bond vi resonnce: e his resonnce structure cn never chieve the required overlp of p orbitls (they re effectively orthogonl), nd plys no role in reducing the crbonyl's double-bond chrcter. trongest crbonyl bond, so highest stretching frequency Between these two resonnce structures, the positive chrgeismorestbleonthenitrogenthnonthe oxygen. (lterntely, the nitrogen lone pir is higher in energy thn the oxygen lone pir, nd is thus more effective t donting electron density into the crbonyl.) hus, the mide crbonyl hs more single bond chrcter thn the ester crbonyl. ence, the mide crbonyl is weker bond nd hs lower stretching frequency thn the ester crbonyl. 2. Ketene, shown below, hs much higher crbonyl stretching frequency thn typicl ketone such s cetone. xplin why ketene's crbonyl stretching frequency is so high. ketene 18 cm -1 he crbonyl crbon of ketene is sp-hybridized, so the crbonyl bond should be shorter nd stronger. his strength of the crbonyl is lso reflected by the triple-bond resonnce structure shown below. hese fctors result in much higher crbonyl stretching frequency s compred to typicl ketone. 6

7 nfrred pectroscopy: ore heory 1. Phenylcetylene exhibits strong, shrp peks t 33 cm -1 nd cm -1 in the spectrum. dentify the bonds responsible for the presence of these peks. onversely, the compound diphenylcetylene, which you prepred in lb, shows neither of these peks in the infrred! xplin this observtion. Phenylcetylene shows shrp peks t 33 cm -1 nd cm -1 Diphenylcetylene shows neither pek in spectrum he f irst one is esy -- the 33 cm -1 pek results f rom terminl lkyne - stretch, nd diphenylcetylene is n internl lkyne nd lcks this type of - bond. For the second pek, spectroscopy relies on bond vibrtions tht chnge the dipole moment of those bonds. Bonds whose dipole moments do not chnge during vibrtion (nonpolr bonds) will not show pek in the spectrum. ince the triple bond in diphenylcetylene is completely symmetric, it should be no surprise tht this bond does not pper in the spectrum. 2. he infrred spectr shown below correspond to the compounds dicyclopropyl ketone nd dicyclohexyl ketone -- but which is which? xplin how cler understnding of bsic principles of spectroscopy cn mke this tsk less dunting. trin increses the s-chrcter of cyclopropne crbons f rom pure sp 3 lmost to sp 2. hus the - bonds re correspondingly stronger (s in lkenes) nd vibrte t higher Dicyclopropyl ketone f requency in the spectrum. Dicyclohexyl ketone Dicyclopropyl ketone WVUB (ote tht there is essentilly no dif f erence in their respective = peks!) Dicyclohexyl ketone WVUB 7

8 pectroscopy: Proton quivlence 1. Predict the number of 1 signls tht would be observed for ech of the following compounds. () (b) 3 6 signls 7signls (c) F (d) 2 3 signls 6signls (e) (f) 7 signls 3signls (g) (h) 5 signls 2signls (i) (j) 3 signls 5signls 8

9 pectroscopy: hemicl hift 1. By nlyzing the chemicl shifts nd integrtions, ssign the proton peks to the protons in ech molecule. b c c b 3 c 1 b f e d b 3 c 3 b 1 (exchnges with D 2 ) f e 1 2 c 3 d b d 3 c e b 2 e 3 c d

10 pectroscopy: pin/pin plitting nd the oupling onstnt 1. nlyze the expnded multiplets in the following proton spectrum, nd explin the observed splitting. hen write in the integrtion you expect for ech multiplet. b c 2 c b portion of the proton spectrum of methyl vinyl ketone is given below. ssign the three lkenyl proton resonnces in the spectrum by filling in ech box with, B,or s pproprite. methyl vinyl ketone B 3 B 3. n 2, Professor Brry rost nd coworkers t tnford University developed new method for prtil reduction of lkynes to lkenes. Given the coupling constnt between the two indicted hydrogens in the product, determine whether this rection produces the cis lkene or the trns lkene. n-bu e 1. [p*u(e) 3 ]PF 6,(t) 3 i 2. u, BF n-bu e J=15z he coupling constnt tells us tht the lkene product in this rection must end up trns.

11 opics in tructure Determintion: ymmetry dentify the unknown compound bsed on the spectrl dt given below. he correct structure will possess prticulr element of symmetry. From mss spectrometry, you deduce tht the moleculr formul is he infrred spectrum is: WVUB he 1 spectrum (with expnsions) is: Provide your best choice for the structure of the compound in the box below. emember tht the correct structure will possess n element of symmetry! ,2,3,3-tetrmethylbutne 11

12 opics in tructure Determintion: ymmetry dentify the unknown compound bsed on the spectrl dt given below. he correct structure will possess prticulr element of symmetry. From mss spectrometry, you deduce tht the moleculr formul is he infrred spectrum is: WVUB he 1 spectrum (with expnsions) is: Provide your best choice for the structure of the compound in the box below. emember tht the correct structure will possess n element of symmetry! dimethyl 2,2-diethylmlonte 12

13 opics in tructure Determintion: ings dentify the unknown compound bsed on the spectrl dt given below. he correct structure will possess non-romtic ring. From mss spectrometry, you deduce tht the moleculr formul is 4 9. he infrred spectrum is: WVUB he 1 spectrum (with expnsions) is: (exchnges with D 2 ) Provide your best choice for the structure of the compound in the box below. emember tht the correct structure will possess non-romtic ring! morpholine 13

14 opics in tructure Determintion: ings dentify the unknown compound bsed on the spectrl dt given below. he correct structure will possess non-romtic ring. From mss spectrometry, you deduce tht the moleculr formul is he infrred spectrum is: WVUB he 1 spectrum (with expnsions) is: 2 (ne dditionl pek t ; 1; exchnges with D 2 ) Provide your best choice for the structure of the compound in the box below. emember tht the correct structure will possess non-romtic ring! 1,1-cyclopropnedicrboxylic cid 14

15 opics in tructure Determintion: romtic ubstitution Ptterns dentify the unknown compound bsed on the spectrl dt given below. he correct structure will possess substituted romtic ring. From mss spectrometry, you deduce tht the moleculr formul is 8 9. he infrred spectrum is: WVUB he 1 spectrum (with expnsions) is: (exchnges with D 2 ) Provide your best choice for the structure of the compound in the box below. emember tht the correct structure will possess substituted romtic ring! 3 2 p-minocetophenone 15

16 opics in tructure Determintion: romtic ubstitution Ptterns dentify the unknown compound bsed on the spectrl dt given below. he correct structure will possess substituted romtic ring. From mss spectrometry, you deduce tht the moleculr formul is he infrred spectrum is: WVUB he 1 spectrum (with expnsions) is: Provide your best choice for the structure of the compound in the box below. emember tht the correct structure will possess substituted romtic ring! isophthlonitrile 16

17 opics in tructure Determintion: Geminl oupling dentify the unknown compound bsed on the spectrl dt given below. he correct structure will exhibit non-vinyl geminl coupling. From mss spectrometry, you deduce tht the moleculr formul is he infrred spectrum is: WVUB he 1 spectrum (with expnsions) is: (exchnges with D 2 ) Provide your best choice for the structure of the compound in the box below. emember tht the correct structure will exhibit non-vinyl geminl coupling! 3 1,2-propnediol 17

18 opics in tructure Determintion: Geminl oupling dentify the unknown compound bsed on the spectrl dt given below. he correct structure will exhibit non-vinyl geminl coupling. From mss spectrometry, you deduce tht the moleculr formul is he infrred spectrum is: WVUB he 1 spectrum (with expnsions) is: Provide your best choice for the structure of the compound in the box below. emember tht the correct structure will exhibit non-vinyl geminl coupling! 3 -butyrolctone 18

C Nuclear Magnetic Resonance

C Nuclear Magnetic Resonance Inherent Difficulties Low bundnce of 13 C (1.1% vs, 99.9% for 1 H) Lower gyromgnetic rtio (1/4 tht of 1 H) - 13 C: 67.28 vs. 1 H 267.53-1/2 1,000,000 nuclei t 60 MHz E ΔE +1/2 1,000,009 nuclei t 60 MHz

More information

Please write neatly!

Please write neatly! Nme Chem 130 Second Exm On the following pges re eight questions tht consider the structure of molecules, ions, nd solids, nd the different models we use to explin the nture of chemicl bonding. Red ech

More information

Chem 130 Third Exam. Total /100

Chem 130 Third Exam. Total /100 Nme Chem 130 Third Exm On the following pges you will find eight questions covering vries topics rnging from precipittion solubility, cid bse, nd oxidtion reduction rections to metl lignd complexes nd

More information

Organic Acids - Carboxylic Acids

Organic Acids - Carboxylic Acids Orgnic Acids - rboxylic Acids Orgnic cids - crboxylic cid functionl group rboxylic cids re redily deprotonted by bses such s NO eg 3 O O - + O - + O 3 O O Acid Bse onjugte Bse onjugte Acid This rection

More information

Key for Chem 130 Second Exam

Key for Chem 130 Second Exam Nme Key for Chem 130 Second Exm On the following pges you will find questions tht cover the structure of molecules, ions, nd solids, nd the different models we use to explin the nture of chemicl bonding.

More information

Read section 3.3, 3.4 Announcements:

Read section 3.3, 3.4 Announcements: Dte: 3/1/13 Objective: SWBAT pply properties of exponentil functions nd will pply properties of rithms. Bell Ringer: 1. f x = 3x 6, find the inverse, f 1 x., Using your grphing clcultor, Grph 1. f x,f

More information

Chem 130 Second Exam

Chem 130 Second Exam Nme Chem 130 Second Exm On the following pges you will find seven questions covering vries topics rnging from the structure of molecules, ions, nd solids to different models for explining bonding. Red

More information

BOND ORDER (BO): Single bond Þ BO = 1; Double bond Þ BO = 2; Triple bond Þ BO = 3 Bond Order Þ bond strength and bond length

BOND ORDER (BO): Single bond Þ BO = 1; Double bond Þ BO = 2; Triple bond Þ BO = 3 Bond Order Þ bond strength and bond length EMISTRY 104 elp Sheet #1 hem 103 Review (Text: h 6, h 7) Do topics pproprite for your lecture Prepred y Dr. Tony Jco http://www.chem.wisc.edu/res/clc (Resource pge) Nuggets: Electronegtivity (6.7), Bond

More information

4 7x =250; 5 3x =500; Read section 3.3, 3.4 Announcements: Bell Ringer: Use your calculator to solve

4 7x =250; 5 3x =500; Read section 3.3, 3.4 Announcements: Bell Ringer: Use your calculator to solve Dte: 3/14/13 Objective: SWBAT pply properties of exponentil functions nd will pply properties of rithms. Bell Ringer: Use your clcultor to solve 4 7x =250; 5 3x =500; HW Requests: Properties of Log Equtions

More information

Chem 130 Second Exam

Chem 130 Second Exam Nme Chem 130 Second Exm On the following pges you will find questions tht cover the structure of molecules, ions, nd solids, nd the different models we use to explin the nture of chemicl bonding. Red ech

More information

Unique Solutions R. Amazing World of Carbon Compounds. C h a p t e r. G l a n c e

Unique Solutions R. Amazing World of Carbon Compounds. C h a p t e r. G l a n c e 9. C h p t e r t G l n c e Hydrocrbons - The fundmentl orgnic compounds : All orgnic compounds contin hydrogen long with crbon. They re the fundmentl orgnic compounds lso known s "Prent" compounds. These

More information

Chem 130 Second Exam

Chem 130 Second Exam Nme Chem 130 Second Exm On the following pges you will find questions tht cover the structure of molecules, ions, nd solids, nd the different models we use to explin the nture of chemicl bonding. Red ech

More information

Mechanisms: The Basics

Mechanisms: The Basics Mechnisms: The Bsics A) The orrect Use of Arrows to Indicte Electron Movement The bility to write n orgnic rection mechnism properly is key to success in orgnic chemistry clsses. rgnic chemists use technique

More information

Chem 130 Third Exam. ö ø. Name

Chem 130 Third Exam. ö ø. Name Nme Chem 130 Third Exm On the following pges re eight questions tht consider topics rnging from precipittion solubility, cid bse, nd oxidtion reduction rections to metl lignd complexes nd coordintion compounds.

More information

Module 2: Rate Law & Stoichiomtery (Chapter 3, Fogler)

Module 2: Rate Law & Stoichiomtery (Chapter 3, Fogler) CHE 309: Chemicl Rection Engineering Lecture-8 Module 2: Rte Lw & Stoichiomtery (Chpter 3, Fogler) Topics to be covered in tody s lecture Thermodynmics nd Kinetics Rection rtes for reversible rections

More information

Physics 9 Fall 2011 Homework 2 - Solutions Friday September 2, 2011

Physics 9 Fall 2011 Homework 2 - Solutions Friday September 2, 2011 Physics 9 Fll 0 Homework - s Fridy September, 0 Mke sure your nme is on your homework, nd plese box your finl nswer. Becuse we will be giving prtil credit, be sure to ttempt ll the problems, even if you

More information

CAAM 453 NUMERICAL ANALYSIS I Examination There are four questions, plus a bonus. Do not look at them until you begin the exam.

CAAM 453 NUMERICAL ANALYSIS I Examination There are four questions, plus a bonus. Do not look at them until you begin the exam. Exmintion 1 Posted 23 October 2002. Due no lter thn 5pm on Mondy, 28 October 2002. Instructions: 1. Time limit: 3 uninterrupted hours. 2. There re four questions, plus bonus. Do not look t them until you

More information

Chem 130 Third Exam Key

Chem 130 Third Exam Key Nme Chem 130 Third Exm Key On the following pges re eight questions tht consider topics rnging from precipittion solubility, cid bse, nd oxidtion reduction rections to metl lignd complexes nd coordintion

More information

Cu 3 (PO 4 ) 2 (s) 3 Cu 2+ (aq) + 2 PO 4 3- (aq) circle answer: pure water or Na 3 PO 4 solution This is the common-ion effect.

Cu 3 (PO 4 ) 2 (s) 3 Cu 2+ (aq) + 2 PO 4 3- (aq) circle answer: pure water or Na 3 PO 4 solution This is the common-ion effect. CHEM 1122011 NAME: ANSWER KEY Vining, Exm # SHORT ANSWER QUESTIONS ============= 4 points ech ============ All work must be shown. 1. Wht re [H O ] nd [OH ] for solution tht hs ph of 9.0? Choose one. ()

More information

CHAPTER 08: MONOPROTIC ACID-BASE EQUILIBRIA

CHAPTER 08: MONOPROTIC ACID-BASE EQUILIBRIA Hrris: Quntittive Chemicl Anlysis, Eight Edition CHAPTER 08: MONOPROTIC ACIDBASE EQUILIBRIA CHAPTER 08: Opener A CHAPTER 08: Opener B CHAPTER 08: Opener C CHAPTER 08: Opener D CHAPTER 08: Opener E Chpter

More information

UNIT 3 Indices and Standard Form Activities

UNIT 3 Indices and Standard Form Activities UNIT 3 Indices nd Stndrd Form Activities Activities 3.1 Towers 3.2 Bode's Lw 3.3 Mesuring nd Stndrd Form 3.4 Stndrd Inde Form Notes nd Solutions (1 pge) ACTIVITY 3.1 Towers How mny cubes re needed to build

More information

Math 113 Exam 2 Practice

Math 113 Exam 2 Practice Mth Em Prctice Februry, 8 Em will cover sections 6.5, 7.-7.5 nd 7.8. This sheet hs three sections. The first section will remind you bout techniques nd formuls tht you should know. The second gives number

More information

Hydrogen Bonding Interaction between 1-Propanol and Acrylic Esters in Non-polar Solvents: An FTIR Study

Hydrogen Bonding Interaction between 1-Propanol and Acrylic Esters in Non-polar Solvents: An FTIR Study RESEARCH ARTICLE K. Dhrmlingm, K. Rmchndrn nd P. Sivgurunthn, 75 S. Afr. J. Chem., 26, 59, 75 81, Hydrogen Bonding Interction between 1-Propnol nd Acrylic Esters in Non-polr Solvents: An FTIR Study Kurunthu

More information

The Predom module. Predom calculates and plots isothermal 1-, 2- and 3-metal predominance area diagrams. Predom accesses only compound databases.

The Predom module. Predom calculates and plots isothermal 1-, 2- and 3-metal predominance area diagrams. Predom accesses only compound databases. Section 1 Section 2 The module clcultes nd plots isotherml 1-, 2- nd 3-metl predominnce re digrms. ccesses only compound dtbses. Tble of Contents Tble of Contents Opening the module Section 3 Stoichiometric

More information

Period #2 Notes: Electronic Structure of Atoms

Period #2 Notes: Electronic Structure of Atoms Period # Notes: Electronic Structure of Atoms The logicl plce (for civil engineers) to begin in describing mterils is t the tomic scle. The bsic elements of the tom re the proton, the neutron, nd the electron:

More information

CHM Physical Chemistry I Chapter 1 - Supplementary Material

CHM Physical Chemistry I Chapter 1 - Supplementary Material CHM 3410 - Physicl Chemistry I Chpter 1 - Supplementry Mteril For review of some bsic concepts in mth, see Atkins "Mthemticl Bckground 1 (pp 59-6), nd "Mthemticl Bckground " (pp 109-111). 1. Derivtion

More information

CHEMISTRY. 31 (b) The term acid rain was coined by Robert Augus 32 (c)

CHEMISTRY. 31 (b) The term acid rain was coined by Robert Augus 32 (c) CHEMISTRY 31 (b) The term cid rin ws coined by Robert Augus 32 (c) Initil At (4-3 moles equilibrium mole mole Hence, mole Hence, number of moles of t equilibrium =2-1=1 mole Number of moles of t equilibrium

More information

Rel Gses 1. Gses (N, CO ) which don t obey gs lws or gs eqution P=RT t ll pressure nd tempertures re clled rel gses.. Rel gses obey gs lws t extremely low pressure nd high temperture. Rel gses devited

More information

Physics 24 Exam 1 February 18, 2014

Physics 24 Exam 1 February 18, 2014 Exm Totl / 200 Physics 24 Exm 1 Februry 18, 2014 Printed Nme: Rec. Sec. Letter: Five multiple choice questions, 8 points ech. Choose the best or most nerly correct nswer. 1. The totl electric flux pssing

More information

5.7 Improper Integrals

5.7 Improper Integrals 458 pplictions of definite integrls 5.7 Improper Integrls In Section 5.4, we computed the work required to lift pylod of mss m from the surfce of moon of mss nd rdius R to height H bove the surfce of the

More information

Anti-derivatives/Indefinite Integrals of Basic Functions

Anti-derivatives/Indefinite Integrals of Basic Functions Anti-derivtives/Indefinite Integrls of Bsic Functions Power Rule: In prticulr, this mens tht x n+ x n n + + C, dx = ln x + C, if n if n = x 0 dx = dx = dx = x + C nd x (lthough you won t use the second

More information

Physical Chemistry (II) CHEM Lecture 25. Lecturer: Hanning Chen, Ph.D. 05/01/2018

Physical Chemistry (II) CHEM Lecture 25. Lecturer: Hanning Chen, Ph.D. 05/01/2018 Physicl Chemistry (II) CHEM 372-80 Lecture 25 Nucler Overhuser Effect nd Electron Prmgnetic Resonnce Lecturer: Hnning Chen, Ph.D. 05/0/208 Quiz 24 0 minutes Plese stop writing when the timer stops! Spin

More information

Strong acids and bases. Strong acids and bases. Systematic Treatment of Equilibrium & Monoprotic Acid-base Equilibrium.

Strong acids and bases. Strong acids and bases. Systematic Treatment of Equilibrium & Monoprotic Acid-base Equilibrium. Strong cids nd bses Systemtic Tretment of Equilibrium & Monoprotic cid-bse Equilibrium onc. (M) 0.0.00 -.00-5.00-8 p Strong cids nd bses onc. (M) p 0.0.0.00 -.0.00-5 5.0.00-8 8.0? We hve to consider utoprotolysis

More information

Structure Determination. How to determine what compound that you have? One way to determine compound is to get an elemental analysis

Structure Determination. How to determine what compound that you have? One way to determine compound is to get an elemental analysis Structure Determination How to determine what compound that you have? ne way to determine compound is to get an elemental analysis -basically burn the compound to determine %C, %H, %, etc. from these percentages

More information

1. Predict the structure of the molecules given by the following spectral data: a Mass spectrum:m + = 116

1. Predict the structure of the molecules given by the following spectral data: a Mass spectrum:m + = 116 Additional Problems for practice.. Predict the structure of the molecules given by the following spectral data: a Mass spectrum:m + = IR: weak absorption at 9 cm - medium absorption at cm - NMR 7 3 3 C

More information

Fundamentals of Analytical Chemistry

Fundamentals of Analytical Chemistry Homework Fundmentls of nlyticl hemistry hpter 9 0, 1, 5, 7, 9 cids, Bses, nd hpter 9(b) Definitions cid Releses H ions in wter (rrhenius) Proton donor (Bronsted( Lowry) Electron-pir cceptor (Lewis) hrcteristic

More information

Which of the following describes the net ionic reaction for the hydrolysis. Which of the following salts will produce a solution with the highest ph?

Which of the following describes the net ionic reaction for the hydrolysis. Which of the following salts will produce a solution with the highest ph? 95. Which of the following descries the net ionic rection for the hydrolysis of NH4Cl( s)? A. NH4 ( q) Cl & ( q) NH4Cl( s) B. NH Cl & 4 ( s) NH4 ( q) Cl ( q) C. Cl ( q) H O & 2 ( l) HCl( q) OH ( q) D.

More information

7.2 The Definite Integral

7.2 The Definite Integral 7.2 The Definite Integrl the definite integrl In the previous section, it ws found tht if function f is continuous nd nonnegtive, then the re under the grph of f on [, b] is given by F (b) F (), where

More information

CHEMICAL KINETICS

CHEMICAL KINETICS CHEMICAL KINETICS Long Answer Questions: 1. Explin the following terms with suitble exmples ) Averge rte of Rection b) Slow nd Fst Rections c) Order of Rection d) Moleculrity of Rection e) Activtion Energy

More information

Advanced Calculus: MATH 410 Notes on Integrals and Integrability Professor David Levermore 17 October 2004

Advanced Calculus: MATH 410 Notes on Integrals and Integrability Professor David Levermore 17 October 2004 Advnced Clculus: MATH 410 Notes on Integrls nd Integrbility Professor Dvid Levermore 17 October 2004 1. Definite Integrls In this section we revisit the definite integrl tht you were introduced to when

More information

Chem 3502/4502 Physical Chemistry II (Quantum Mechanics) 3 Credits Spring Semester 2006 Christopher J. Cramer. Lecture 25, March 29, 2006

Chem 3502/4502 Physical Chemistry II (Quantum Mechanics) 3 Credits Spring Semester 2006 Christopher J. Cramer. Lecture 25, March 29, 2006 Chem 3502/4502 Physicl Chemistry II (Quntum Mechnics) 3 Credits Spring Semester 2006 Christopher J. Crmer Lecture 25, Mrch 29, 2006 (Some mteril in this lecture hs been dpted from Crmer, C. J. Essentils

More information

SOLUTIONS FOR ADMISSIONS TEST IN MATHEMATICS, COMPUTER SCIENCE AND JOINT SCHOOLS WEDNESDAY 5 NOVEMBER 2014

SOLUTIONS FOR ADMISSIONS TEST IN MATHEMATICS, COMPUTER SCIENCE AND JOINT SCHOOLS WEDNESDAY 5 NOVEMBER 2014 SOLUTIONS FOR ADMISSIONS TEST IN MATHEMATICS, COMPUTER SCIENCE AND JOINT SCHOOLS WEDNESDAY 5 NOVEMBER 014 Mrk Scheme: Ech prt of Question 1 is worth four mrks which re wrded solely for the correct nswer.

More information

Math 8 Winter 2015 Applications of Integration

Math 8 Winter 2015 Applications of Integration Mth 8 Winter 205 Applictions of Integrtion Here re few importnt pplictions of integrtion. The pplictions you my see on n exm in this course include only the Net Chnge Theorem (which is relly just the Fundmentl

More information

2FAMILIES OF CARBON COMPOUNDS:

2FAMILIES OF CARBON COMPOUNDS: P1: PBU/VY P2: PBU/VY Q: PBU/VY T1: PBU Printer: Bind Rite JWL338-02 JWL338-Solomons-v1 April 23, 2010 21:49 2AMILIES ARB MPUDS: UTIAL GRUPS, ITERMLEULAR RES, AD IRARED (IR) SPETRSPY SLUTIS T PRBLEMS 2.1

More information

Data Provided: A formula sheet and table of physical constants is attached to this paper.

Data Provided: A formula sheet and table of physical constants is attached to this paper. PHY106 PHY47 Dt Provided: Formul sheet nd physicl constnts Dt Provided: A formul sheet nd tble of physicl constnts is ttched to this pper. DEPARTMENT OF PHYSICS & Autumn Semester 009-010 ASTRONOMY DEPARTMENT

More information

Introduction to Astrophysics

Introduction to Astrophysics PHY472 Dt Provided: Formul sheet nd physicl constnts Dt Provided: A formul sheet nd tble of physicl constnts is ttched to this pper. DEPARTMENT OF PHYSICS & Autumn Semester 2009-2010 ASTRONOMY DEPARTMENT

More information

Improper Integrals. Type I Improper Integrals How do we evaluate an integral such as

Improper Integrals. Type I Improper Integrals How do we evaluate an integral such as Improper Integrls Two different types of integrls cn qulify s improper. The first type of improper integrl (which we will refer to s Type I) involves evluting n integrl over n infinite region. In the grph

More information

APPROXIMATE INTEGRATION

APPROXIMATE INTEGRATION APPROXIMATE INTEGRATION. Introduction We hve seen tht there re functions whose nti-derivtives cnnot be expressed in closed form. For these resons ny definite integrl involving these integrnds cnnot be

More information

Construction of Gauss Quadrature Rules

Construction of Gauss Quadrature Rules Jim Lmbers MAT 772 Fll Semester 2010-11 Lecture 15 Notes These notes correspond to Sections 10.2 nd 10.3 in the text. Construction of Guss Qudrture Rules Previously, we lerned tht Newton-Cotes qudrture

More information

Calculus 2: Integration. Differentiation. Integration

Calculus 2: Integration. Differentiation. Integration Clculus 2: Integrtion The reverse process to differentition is known s integrtion. Differentition f() f () Integrtion As it is the opposite of finding the derivtive, the function obtined b integrtion is

More information

Orthogonal Polynomials

Orthogonal Polynomials Mth 4401 Gussin Qudrture Pge 1 Orthogonl Polynomils Orthogonl polynomils rise from series solutions to differentil equtions, lthough they cn be rrived t in vriety of different mnners. Orthogonl polynomils

More information

( dg. ) 2 dt. + dt. dt j + dh. + dt. r(t) dt. Comparing this equation with the one listed above for the length of see that

( dg. ) 2 dt. + dt. dt j + dh. + dt. r(t) dt. Comparing this equation with the one listed above for the length of see that Arc Length of Curves in Three Dimensionl Spce If the vector function r(t) f(t) i + g(t) j + h(t) k trces out the curve C s t vries, we cn mesure distnces long C using formul nerly identicl to one tht we

More information

MATH FIELD DAY Contestants Insructions Team Essay. 1. Your team has forty minutes to answer this set of questions.

MATH FIELD DAY Contestants Insructions Team Essay. 1. Your team has forty minutes to answer this set of questions. MATH FIELD DAY 2012 Contestnts Insructions Tem Essy 1. Your tem hs forty minutes to nswer this set of questions. 2. All nswers must be justified with complete explntions. Your nswers should be cler, grmmticlly

More information

STRAND B: NUMBER THEORY

STRAND B: NUMBER THEORY Mthemtics SKE, Strnd B UNIT B Indices nd Fctors: Tet STRAND B: NUMBER THEORY B Indices nd Fctors Tet Contents Section B. Squres, Cubes, Squre Roots nd Cube Roots B. Inde Nottion B. Fctors B. Prime Fctors,

More information

ENGI 9420 Lecture Notes 7 - Fourier Series Page 7.01

ENGI 9420 Lecture Notes 7 - Fourier Series Page 7.01 ENGI 940 ecture Notes 7 - Fourier Series Pge 7.0 7. Fourier Series nd Fourier Trnsforms Fourier series hve multiple purposes, including the provision of series solutions to some liner prtil differentil

More information

AP Calculus Multiple Choice: BC Edition Solutions

AP Calculus Multiple Choice: BC Edition Solutions AP Clculus Multiple Choice: BC Edition Solutions J. Slon Mrch 8, 04 ) 0 dx ( x) is A) B) C) D) E) Divergent This function inside the integrl hs verticl symptotes t x =, nd the integrl bounds contin this

More information

Riemann Sums and Riemann Integrals

Riemann Sums and Riemann Integrals Riemnn Sums nd Riemnn Integrls Jmes K. Peterson Deprtment of Biologicl Sciences nd Deprtment of Mthemticl Sciences Clemson University August 26, 2013 Outline 1 Riemnn Sums 2 Riemnn Integrls 3 Properties

More information

PAPER No.12 :Organic Spectroscopy MODULE No.30: Combined problem on UV, IR, 1 H NMR, 13 C NMR and Mass - Part II

PAPER No.12 :Organic Spectroscopy MODULE No.30: Combined problem on UV, IR, 1 H NMR, 13 C NMR and Mass - Part II Subject Chemistry Paper No and Title Module No and Title Module Tag 12 : rganic Spectroscopy 30: Combined problem on UV, IR, 1 H NMR, 13 C NMR and Mass Part-II CHE_P12_M30 TABLE F CNTENTS 1. Learning utcomes

More information

8 Laplace s Method and Local Limit Theorems

8 Laplace s Method and Local Limit Theorems 8 Lplce s Method nd Locl Limit Theorems 8. Fourier Anlysis in Higher DImensions Most of the theorems of Fourier nlysis tht we hve proved hve nturl generliztions to higher dimensions, nd these cn be proved

More information

PHY 140A: Solid State Physics. Solution to Midterm #1

PHY 140A: Solid State Physics. Solution to Midterm #1 PHY 140A: Solid Stte Physics Solution to Midterm #1 TA: Xun Ji 1 October 24, 2006 1 Emil: jixun@physics.ucl.edu Problem #1 (20pt)Clculte the pcking frction of the body-centered cubic lttice. Solution:

More information

Vibrational Relaxation of HF (v=3) + CO

Vibrational Relaxation of HF (v=3) + CO Journl of the Koren Chemicl Society 26, Vol. 6, No. 6 Printed in the Republic of Kore http://dx.doi.org/.52/jkcs.26.6.6.462 Notes Vibrtionl Relxtion of HF (v3) + CO Chng Soon Lee Deprtment of Chemistry,

More information

#6A&B Magnetic Field Mapping

#6A&B Magnetic Field Mapping #6A& Mgnetic Field Mpping Gol y performing this lb experiment, you will: 1. use mgnetic field mesurement technique bsed on Frdy s Lw (see the previous experiment),. study the mgnetic fields generted by

More information

ANSWERS TO REVIEW PROBLEM SET CH F

ANSWERS TO REVIEW PROBLEM SET CH F ANSWERS T REVIEW PRBLEM SET C41-018F [1] () The chirl isomer is stilized y intrmoleculr hydrogen onding etween the two guche groups. Such n rrngement lso keeps the ulky tert-utyl groups frther prt s they

More information

Markscheme May 2016 Mathematics Standard level Paper 1

Markscheme May 2016 Mathematics Standard level Paper 1 M6/5/MATME/SP/ENG/TZ/XX/M Mrkscheme My 06 Mthemtics Stndrd level Pper 7 pges M6/5/MATME/SP/ENG/TZ/XX/M This mrkscheme is the property of the Interntionl Bcclurete nd must not be reproduced or distributed

More information

1. Weak acids. For a weak acid HA, there is less than 100% dissociation to ions. The B-L equilibrium is:

1. Weak acids. For a weak acid HA, there is less than 100% dissociation to ions. The B-L equilibrium is: th 9 Homework: Reding, M&F, ch. 15, pp. 584-598, 602-605 (clcultions of ph, etc., for wek cids, wek bses, polyprotic cids, nd slts; fctors ffecting cid strength). Problems: Nkon, ch. 18, #1-10, 16-18,

More information

f(x) dx, If one of these two conditions is not met, we call the integral improper. Our usual definition for the value for the definite integral

f(x) dx, If one of these two conditions is not met, we call the integral improper. Our usual definition for the value for the definite integral Improper Integrls Every time tht we hve evluted definite integrl such s f(x) dx, we hve mde two implicit ssumptions bout the integrl:. The intervl [, b] is finite, nd. f(x) is continuous on [, b]. If one

More information

Riemann Sums and Riemann Integrals

Riemann Sums and Riemann Integrals Riemnn Sums nd Riemnn Integrls Jmes K. Peterson Deprtment of Biologicl Sciences nd Deprtment of Mthemticl Sciences Clemson University August 26, 203 Outline Riemnn Sums Riemnn Integrls Properties Abstrct

More information

Recitation 3: More Applications of the Derivative

Recitation 3: More Applications of the Derivative Mth 1c TA: Pdric Brtlett Recittion 3: More Applictions of the Derivtive Week 3 Cltech 2012 1 Rndom Question Question 1 A grph consists of the following: A set V of vertices. A set E of edges where ech

More information

New Expansion and Infinite Series

New Expansion and Infinite Series Interntionl Mthemticl Forum, Vol. 9, 204, no. 22, 06-073 HIKARI Ltd, www.m-hikri.com http://dx.doi.org/0.2988/imf.204.4502 New Expnsion nd Infinite Series Diyun Zhng College of Computer Nnjing University

More information

LECTURE 14. Dr. Teresa D. Golden University of North Texas Department of Chemistry

LECTURE 14. Dr. Teresa D. Golden University of North Texas Department of Chemistry LECTURE 14 Dr. Teres D. Golden University of North Texs Deprtment of Chemistry Quntittive Methods A. Quntittive Phse Anlysis Qulittive D phses by comprison with stndrd ptterns. Estimte of proportions of

More information

CHEMISTRY 3.5 Paper 1. Describe the structure and reactions of organic compounds containing selected organic groups

CHEMISTRY 3.5 Paper 1. Describe the structure and reactions of organic compounds containing selected organic groups CHEMISTRY 3.5 Pper 1 Describe the structure nd rections of orgnic compounds contining selected orgnic groups Credits: Five INSTRUCTIONS Answer ALL questions NZQA/Person Eduction 2006 - 2 - You re dvised

More information

13.4. Integration by Parts. Introduction. Prerequisites. Learning Outcomes

13.4. Integration by Parts. Introduction. Prerequisites. Learning Outcomes Integrtion by Prts 13.4 Introduction Integrtion by Prts is technique for integrting products of functions. In this Section you will lern to recognise when it is pproprite to use the technique nd hve the

More information

. Double-angle formulas. Your answer should involve trig functions of θ, and not of 2θ. sin 2 (θ) =

. Double-angle formulas. Your answer should involve trig functions of θ, and not of 2θ. sin 2 (θ) = Review of some needed Trig. Identities for Integrtion. Your nswers should be n ngle in RADIANS. rccos( 1 ) = π rccos( - 1 ) = 2π 2 3 2 3 rcsin( 1 ) = π rcsin( - 1 ) = -π 2 6 2 6 Cn you do similr problems?

More information

University of Washington Department of Chemistry Chemistry 453 Winter Quarter 2009

University of Washington Department of Chemistry Chemistry 453 Winter Quarter 2009 University of Wshington Deprtment of Chemistry Chemistry Winter Qurter 9 Homework Assignment ; Due t pm on //9 6., 6., 6., 8., 8. 6. The wve function in question is: ψ u cu ( ψs ψsb * cu ( ψs ψsb cu (

More information

Lecture 1. Functional series. Pointwise and uniform convergence.

Lecture 1. Functional series. Pointwise and uniform convergence. 1 Introduction. Lecture 1. Functionl series. Pointwise nd uniform convergence. In this course we study mongst other things Fourier series. The Fourier series for periodic function f(x) with period 2π is

More information

CH 3. mirror plane. CH c d

CH 3. mirror plane. CH c d CAPTER 20 Practice Exercises 20.1 The index of hydrogen deficiency is two. The structural possibilities include two double bonds, a double do 20.3 (a) As this is an alkane, it contains only C and and has

More information

Math 1B, lecture 4: Error bounds for numerical methods

Math 1B, lecture 4: Error bounds for numerical methods Mth B, lecture 4: Error bounds for numericl methods Nthn Pflueger 4 September 0 Introduction The five numericl methods descried in the previous lecture ll operte by the sme principle: they pproximte the

More information

Chapter 5. , r = r 1 r 2 (1) µ = m 1 m 2. r, r 2 = R µ m 2. R(m 1 + m 2 ) + m 2 r = r 1. m 2. r = r 1. R + µ m 1

Chapter 5. , r = r 1 r 2 (1) µ = m 1 m 2. r, r 2 = R µ m 2. R(m 1 + m 2 ) + m 2 r = r 1. m 2. r = r 1. R + µ m 1 Tor Kjellsson Stockholm University Chpter 5 5. Strting with the following informtion: R = m r + m r m + m, r = r r we wnt to derive: µ = m m m + m r = R + µ m r, r = R µ m r 3 = µ m R + r, = µ m R r. 4

More information

Jack Simons, Henry Eyring Scientist and Professor Chemistry Department University of Utah

Jack Simons, Henry Eyring Scientist and Professor Chemistry Department University of Utah 1. Born-Oppenheimer pprox.- energy surfces 2. Men-field (Hrtree-Fock) theory- orbitls 3. Pros nd cons of HF- RHF, UHF 4. Beyond HF- why? 5. First, one usully does HF-how? 6. Bsis sets nd nottions 7. MPn,

More information

Mathcad Lecture #1 In-class Worksheet Mathcad Basics

Mathcad Lecture #1 In-class Worksheet Mathcad Basics Mthcd Lecture #1 In-clss Worksheet Mthcd Bsics At the end of this lecture, you will be ble to: Evlute mthemticl epression numericlly Assign vrible nd use them in subsequent clcultions Distinguish between

More information

Math 31S. Rumbos Fall Solutions to Assignment #16

Math 31S. Rumbos Fall Solutions to Assignment #16 Mth 31S. Rumbos Fll 2016 1 Solutions to Assignment #16 1. Logistic Growth 1. Suppose tht the growth of certin niml popultion is governed by the differentil eqution 1000 dn N dt = 100 N, (1) where N(t)

More information

5 Polyatomic molecules

5 Polyatomic molecules s manual for Burrows et.al. Chemistry 3 Third edition 5 Polyatomic molecules Answers to worked examples WE 5.1 Formal charges in N 2 (on p. 221 in Chemistry 3 ) Use formal charges to decide whether oxygen

More information

MATH 144: Business Calculus Final Review

MATH 144: Business Calculus Final Review MATH 144: Business Clculus Finl Review 1 Skills 1. Clculte severl limits. 2. Find verticl nd horizontl symptotes for given rtionl function. 3. Clculte derivtive by definition. 4. Clculte severl derivtives

More information

Data Provided: A formula sheet and table of physical constants are attached to this paper.

Data Provided: A formula sheet and table of physical constants are attached to this paper. PHY40 Dt Provided: A formul sheet nd tble of physicl constnts re ttched to this pper. DEPARTMENT OF PHYSICS & ASTRONOMY Spring Semester 015-016 PHYSICS OF MUSIC 1.5 HOURS ANSWER ANY QUESTIONS. All questions

More information

OAT Organic Chemistry - Problem Drill 19: NMR Spectroscopy and Mass Spectrometry

OAT Organic Chemistry - Problem Drill 19: NMR Spectroscopy and Mass Spectrometry OAT Organic Chemistry - Problem Drill 19: NMR Spectroscopy and Mass Spectrometry Question No. 1 of 10 Question 1. Which statement concerning NMR spectroscopy is incorrect? Question #01 (A) Only nuclei

More information

Test , 8.2, 8.4 (density only), 8.5 (work only), 9.1, 9.2 and 9.3 related test 1 material and material from prior classes

Test , 8.2, 8.4 (density only), 8.5 (work only), 9.1, 9.2 and 9.3 related test 1 material and material from prior classes Test 2 8., 8.2, 8.4 (density only), 8.5 (work only), 9., 9.2 nd 9.3 relted test mteril nd mteril from prior clsses Locl to Globl Perspectives Anlyze smll pieces to understnd the big picture. Exmples: numericl

More information

Chapter 9 Molecular Geometry and Bonding Theories

Chapter 9 Molecular Geometry and Bonding Theories Chapter 9 Molecular Geometry and Bonding Theories molecular shapes the VSEPR model molecular shape and molecular polarity covalent bonding and orbital overlap hybrid orbitals multiple bonds 9.1 Molecular

More information

Topics Covered AP Calculus AB

Topics Covered AP Calculus AB Topics Covered AP Clculus AB ) Elementry Functions ) Properties of Functions i) A function f is defined s set of ll ordered pirs (, y), such tht for ech element, there corresponds ectly one element y.

More information

The graphs of Rational Functions

The graphs of Rational Functions Lecture 4 5A: The its of Rtionl Functions s x nd s x + The grphs of Rtionl Functions The grphs of rtionl functions hve severl differences compred to power functions. One of the differences is the behvior

More information

2. My instructor s name is T. Snee (1 pt)

2. My instructor s name is T. Snee (1 pt) Chemistry 342 Exm #1, Feb. 15, 2019 Version 1 MY NAME IS: Extr Credit#1 1. At prissy Hrvrd, E. J. Corey is Nobel Prize (1990 winning chemist whom ll students cll (two letters 2. My instructor s nme is

More information

1. Which is the most electronegative atom in the compound below?

1. Which is the most electronegative atom in the compound below? 1. Which is the most electronegative atom in the compound below? A) Carbon C) Oxygen B) Nitrogen D) Bromine 2. Which of the following correctly describes the electrons of a carbon atom in its ground state?

More information

The Properties of Stars

The Properties of Stars 10/11/010 The Properties of Strs sses Using Newton s Lw of Grvity to Determine the ss of Celestil ody ny two prticles in the universe ttrct ech other with force tht is directly proportionl to the product

More information

Experiment 9: WEAK ACID IONIZATION CONSTANT & PROPERTIES OF A BUFFERED SOLUTION

Experiment 9: WEAK ACID IONIZATION CONSTANT & PROPERTIES OF A BUFFERED SOLUTION Experiment 9: WEAK ACID IONIZATION CONSTANT & PROPERTIES OF A BUFFERED SOLUTION Purpose: Prt I: The cid ioniztion constnt of wek cid is to be determined, nd the cid is identified ccordingly. Prt II: The

More information

Version 001 HW#6 - Electromagnetic Induction arts (00224) 1 3 T

Version 001 HW#6 - Electromagnetic Induction arts (00224) 1 3 T Version 001 HW#6 - lectromgnetic Induction rts (00224) 1 This print-out should hve 12 questions. Multiple-choice questions my continue on the next column or pge find ll choices efore nswering. AP 1998

More information

UNIT 1 FUNCTIONS AND THEIR INVERSES Lesson 1.4: Logarithmic Functions as Inverses Instruction

UNIT 1 FUNCTIONS AND THEIR INVERSES Lesson 1.4: Logarithmic Functions as Inverses Instruction Lesson : Logrithmic Functions s Inverses Prerequisite Skills This lesson requires the use of the following skills: determining the dependent nd independent vribles in n exponentil function bsed on dt from

More information

A REVIEW OF CALCULUS CONCEPTS FOR JDEP 384H. Thomas Shores Department of Mathematics University of Nebraska Spring 2007

A REVIEW OF CALCULUS CONCEPTS FOR JDEP 384H. Thomas Shores Department of Mathematics University of Nebraska Spring 2007 A REVIEW OF CALCULUS CONCEPTS FOR JDEP 384H Thoms Shores Deprtment of Mthemtics University of Nebrsk Spring 2007 Contents Rtes of Chnge nd Derivtives 1 Dierentils 4 Are nd Integrls 5 Multivrite Clculus

More information

A-level Mathematics. Paper 3 Mark scheme. Practice paper Set 1. Version 1.0

A-level Mathematics. Paper 3 Mark scheme. Practice paper Set 1. Version 1.0 A-level Mthemtics Pper 3 Mrk scheme Prctice pper Set 1 Version 1.0 Mrk schemes re prepred by the Led Assessment Writer nd considered, together with the relevnt questions, by pnel of subject techers. This

More information

Lesson 1: Quadratic Equations

Lesson 1: Quadratic Equations Lesson 1: Qudrtic Equtions Qudrtic Eqution: The qudrtic eqution in form is. In this section, we will review 4 methods of qudrtic equtions, nd when it is most to use ech method. 1. 3.. 4. Method 1: Fctoring

More information

DIRECT CURRENT CIRCUITS

DIRECT CURRENT CIRCUITS DRECT CURRENT CUTS ELECTRC POWER Consider the circuit shown in the Figure where bttery is connected to resistor R. A positive chrge dq will gin potentil energy s it moves from point to point b through

More information

7/19/2011. Models of Solution Chemistry- III Acids and Bases

7/19/2011. Models of Solution Chemistry- III Acids and Bases Models of Solution Chemistry- III Acids nd Bses Ionic Atmosphere Model : Revisiting Ionic Strength Ionic strength - mesure of totl concentrtion of ions in the solution Chpter 8 1 2 i μ ( ) 2 c i z c concentrtion

More information