University of Washington Department of Chemistry Chemistry 453 Winter Quarter 2008

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1 Univrsity of Wasington Dpartmnt of Cmistry Cmistry 453 Wintr Quartr 008 Not: Exam answrs b writtn into Blu Books. T Final Examination will b ld on Monday, 17 Mar, , Bagly 154 T final xam will onsist of two parts. T first our ovrs all t matrial sin t midtrm. Tis inluds Captrs 18, 19, 0,, 3, 4 Lturs 13-4 All Problms in Homwork Assignmnts 5-8 T sond our is umulativ and will onntrat on matrial ovrd in t first alf of t ours i.. Captrs 1,13,14,15, , Lturs 1-1, and Homwork Assignmnts 1-4. Bring Calulator (any typ) Pnil/Pn Straigt Edg (for drawing graps) doubl-sidd pags of nots Blu or grn xamination book Format: Closd Book. Opn Nots. Grading: Grading of t xamination will b basd on t standards statd in t Cmistry 453 ours syllabus. Plas rviw t standards stion of t syllabus. Important points to kp in mind: Partial rdit is USUALLY givn in units of 3-5 points. Obtaining t orrt numrial answr is ountd in partial rdit grading. An answr tat is witin 10% of t orrt answr will b fully rditd. Calulations must inlud pysial units and a propr dimnsional analysis must b inludd in t alulation. Studnts ar xptd to undrstand ow to us tir alulators proprly. Studnts will NOT b forgivn for mistaks rsulting from alulator rrors. Wn you ar askd to xplain an answr or ar askd to dfin a trm, a wordd statmnt in omplt sntns is rquird. If you ar givn t option to oos from a list of problms (.g. answr tr of t following fiv qustions) you will NOT b rditd for answring mor tan t rqustd numbr. For xampl, if you ar allowd to slt tr problms out of fiv for answring and you answr all fiv t gradrs will NOT rdit you for t igst tr soring problms out of fiv. T first tr problms prsntd on t blu book will b gradd.

2 Examination Study Guidlins: Hr is a gnral outlin of t xamination tat will b prsntd to you on 1 Mar. Sampl qustions and answrs ar prsntd. Subjts to study for t first our wi will ovr all matrial sin t Midtrm: Ltur Atomi ltroni absorption: transition momnt alulations Molular lltroni absorption Fluorsn: Manism, maning of quantum yild Jablonski diagrams Fluosn quning and rat quations How to stimat transition intnsitis FRET: Rat quations, ow to alulat distans from FRET data, ompliations Ltur NMR: wat is it? Calulat a Larmor frquny. Spin angular momntum Torqu quations Rotating fram T 1 and T wat ar ty? Spin o: xplain Fourir transform: Wat is it? Prform simpl Fourir transform intgrals. Nular Ovrausr Efft: Explain it. Wat is a stady stat NOE. Wat is t NOE nanmnt fator for slow tumbling and fast tunbling moluls. Rogniz COSY sptr for simpl amino aids Explain wat information COSY givs Explain wat information about protis NOESY givs. Wat is HSQC? Wat do you larn from HSQC? Calulat a dipolar oupling onstant for two spin ½ nuli sparatd by a distan r. Ltur 19- Calulat W for a distribution Calulat probability for a distribution using t Boltzamann xprssion Calulat partition funtion of two lvl systm and nrgy laddr Calulat Q from q. Calulat singl partil partition funtions for translation, vibration, rotation Calulat ntropy, nrgy, Hlmoltz nrgy and quilibrium onstant from partition funtion Ltur -4 Fik s First and Sond Law Calulat man-squard-displamnt for random walk Calulat man squard displamnt from diffusion offiint.

3 Calulat fritional offiint for sprial molul from diffusion offiint. Calulat radius of sprial molul from fritional offiint and diffusion offiint. Calulat fritional offiint for ylindr/prolat llipsoid from aspt ratio Calulat Man End-to-nd distan for random polymr Vloity Sdimntation How to obtain sdimntation offiint from data How to alulat fritional offiint from sdimntation data Equilibrium Cntrifugation: How to alulat molular wigt from ntrifugation data. Cntrifugation in a dnsity gradint Not: Know t singl partil partition offiints for partils in a box (i.. translation in t ig tmpratur limit), quantum manial rigid rotor (ig tmpratur limit), and t quantum manial armoni osillator (low and ig tmpratur limit). Sampl Problms Problm 1 (8 points total) Dfin and disuss mayb two or tr out of four or fiv trms or prass providd. Exampls: 1) Dfin partition funtion. ) T at apaity of ydrogn gas at low dnsity is about 0.75 J K -1 mol -1. Assuming H bavs as an idal, diatomi gas wi undrgos translational, rotational, and vibrational motions, is tis at apaity in agrmnt wit t prditions of lassial statistial manis? Explain? Problm : (36 points) Sort alulations. In ts problms you ar usually askd to alulat on quantity or rad and intrprt a grap. A singl quation is usually involvd. Answr two problms out of four. I usually giv two ois for t sort alulation and two ois for t grap problm. Exampl: A protin tat is approximatly sprial in solution as a diffusion offiint of 1.1x10-6 m /s in watr at T93K. Assum t visosity is 0.01 pois. Calulat t Stoks radius of t protin. 16 kt kt rgs / Kb93Kg D R 6 6πηR 6πηD 6π 0. 01g / m s m /s b gb g m / s Problm 3 (36 points total) Ts will b a multi-stp alulations wr you av to us svral quations and alulat svral tings. T rlationsips you sould study ar t

4 sam as listd abov for problm. Tis problm will b styld aftr t supplmntary omwork problms or aftr som of t multi-stp alulations givn in t Ltur. 1 Exampl: Carbon monoxid absorbs radiation at a wav numbr ν 144m baus of its intrnal vibration. a) Calulat t nrgy lvl spaing for CO. Assum t vibration of CO an b modld as a armoni osillation. E 34 8 J m m 1 ν m m s / s b / g. J λ b) Calulat k B T for T300K. Basd on tis valu and your answr in part a, will CO vibrations b trmally xitd at T300K? Explain. kb T J / K 300K J 1/10 of t vibrational nrgy lvl spaing and so vibrations will not b appriably xitd by trmal nrgy at T300K. b g. Trfor k B T is only about ) At wat tmpratur will trmal xitation of CO vibrations bom important? Vibrations will b xitd wn k B T Eν. So for tis to appn t 0 E J tmpratur must b T 3086K. 3 k J / K B d) Calulat t vibrational at apaity of 1 mol of CO at t tmpratur alulatd in part. From t ltur t at apaity for 1 mol of armoni osillators is C V F HG ν N AkB kbt ν 1, so k B T C V ν N AkB kbt Anotr Exampl: F HG I KJ ν / kbt I KJ ν / k T B ν / kbt ν / k T B, wr N A is Avagadro s numbr. And at T3086K b g 1 R 1 b gb g b g 831. J / K J / K 79. J / K

5 (36 points total) T molular wigt of a small protin is 1,000 g/mol. T protin is blivd to aggrgat in solution at T77K..T spifi volum of t protin is m 3 /g. At T77K t diffusion offiint masurd from solutions of t protin is 5.03x10-7 m /s. Assum t visosity of watr at T77K is 1.57x10 - g-m -1 -s -1. a) From t molular wigt and t spifi volum, alulat t radius of t unydratd protin in solution. Assum t monomri protin is an unydratd spr in solution. V MW / g 1, 000 g / mol MolularVolum 3 Avagadro' s numbr moluls / mol 3 0 4πr 7 Vmolul r m. 3 b gb g / molul b) From t diffusion offiint, alulat t fritional offiint of t protin (wi may b aggrgatd in solution). Assuming t protin (or its aggrgat) as a rougly sprial sap in solution, alulat t radius. D kt kt f f D J / Kb77Kg rg / Kb77Kg g/ s m / s m / s 8 8 f g/ s f 6πηr g/ s r 6πη 6π g m s m. ) By omparing your answrs in parts a and b, dtrmin if t protin aggrgats in solution and dtrmin t numbr of protins in t aggrgat. Again, trat t aggrgat as an unydratd spr T volum sals as t ub of t radius V F aggrgat raggrgat Vmolul H G I rmolul K J F 3 H G I K J 5. Trfor t aggrgat onsists of about protins. Parts 4-6 ar umulativ: Us study guid from t midtrm xam and t study guid for Parts 1-3. Part: 4 (8 points); Qustions: Answr 4 out of 6. Part 5 (a. 36 points): Sort Calulations: Prform tr out of fiv

6 Part 6 (a. 36 points) Multi-stp alulation: Prform 1 out of. Exam Outlin/Study Guid for Cumulativ Exam Part 4: 8 points. Answr 4 out of 6 qustions daling wit t following topis: Eltromagnti Sptrum and Sptrosopy Hat Capaity and molular motions Bor Atom Partil-in-Box Harmoni Osillator Sdimntation and Equilibrium Cntrifugation Absorption, Fluorsn Masurmnt of Maromolular Proprtis from Transport Proprtis Cntrifugation (vloity and quilibrium) Diffusion offiint/fritional offiint Partil-in-a-box Harmoni Osillator Hydrogn Atom + Hydrogn Molul Ion (H ) Sptrosopy transition frqunis transition momnt Part 5: 36 points. Prform tr out of fiv alulations Exptation valus and probabilitis alulatd from wavfuntions Eltroni transitions Calulation of partition funtions How to alulat t partition funtion for translational motion and ow to alulat t nrgy and at apaity from t partition funtion. How to alulat t partition funtion for vibrational motion and ow to alulat t nrgy and at apaity from t partition funtion. Calulations involving wav funtions and nrgis for partil-in-a-box, ydrogn atom, and linar armoni osillator Calulation of transition dipol momnts and transition probabilitis Part 6 (36 points) Prform on out of two multi-stp problms Linar Harmoni Osillator and/or rigid rotor: Rdud mass, spring onstant, momnt of inrtia, fundamntal vibrational/rotational frquny Calulation of partition funtion, trmodynami nrgy, at apaity, t. Masurmnt of diffusion offint, frition offiint byligt sattring and/or sdimntation.

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