Midterm 2 Answers - 2008

Midterm 2 Answers - 2008 - UC Berkeley, Chem C13DIMCE 100A,...

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Unformatted text preview: UC Berkeley, Chem C13DIMCE 100A, Fall 2003, Mid«term Exam 2. Your Name QUESTION 1 (25 PTS TOTAL) 01. PartA (10 points) Shown below are short segments ofthree proteins, containing only the amino acids D. F, G. L and K. Protein 1: DFGLL Protein 2: KFDFK Protein 3: LGLFD Protein 1 is evolutionary related to only one of the two other proteins (i.e., it is related to either protein 2 or protein 3. but not both). (i) Using the BLOSUM substitution score matrix (given below), explain whether protein 1 is related to protein 2, or whether it is related to protein 3. Explain your reasoning completely. (4 points) Page 2 of 13 UC Berkeley, Chem C13OIMCB 100A, Fall 2003, Mid-term Exam 2. Your Name 01 Part A, continued (ii) What is the relatively likelihood that protein 1 is related to protein 2 versus protein 3? That is, how much more (or less) likely is the 1—2 alignment relative to the 1-3 alignment? Explain all the steps of how you work out the answer. (4 points) C) I.“ A h ‘ E): L 5/?“ J / 2. I '. - x ‘ w - '2 = = =2 z i rm la) ~ -»-- 2- . ; ( l _ 2 J ‘ ' —i5 5' 'i "3 4-” r. i /2. 7) 4'“ fi * ’ ‘ ‘ : 2 2 2. 4- or I" 1% i L”; _._ ~_ 5—- r— “ O i :35) .‘I. P i r ' . ‘ - i ' r I J ‘ j i" 1- 1. i .r' .v :5 “:r 4n. , ; g \ 1:} .FJ- ‘ :: I - H ‘5 ’ FA A‘ '-"\ / -' i i i i f 3 - .5 t 1 if“ it?“ 51} ".-\ 'J‘ut 1.ij IS ani- *‘ it ’-‘._ .J ’ ii ' i' t'. i" -‘ " Laue-4w i .3 . J? I . . . L . . (III) Why Is the leucrne—Ieucme substitution score lower than all the other self-substitution scores in the set of BLOSUM scores shown above? Explain your answer. (2 points) ) I . I) F I_ if” I / I If]; I. "/'/I‘ ii ow c if: no: . . -. . .1 45-» i '- .k a. K II; . - - I; ‘l' 'r' til: _ 3 I fl l A . . .-‘ . 1;, .- .- ‘ D I -' I: ' 4f a: r! {kn-$1,“ \ in. ,1 i}: L‘ ‘_ I’M: 1" ‘ - r2, ,r' y' 7/1 it.“ . nu E‘s-{7’ at; J C} ‘7‘ ‘1 ‘ {ts-t ‘ {I 5:431 4, ,, Page 3 of 13 UC Berkeley, Chem C1301MCB 100A, Fall 2008, Mid-term Exam 2. Your Name 01. Part B. (15 points) The interaction between two atoms separated by a distance r is described by the following parameters: (1) F: —k(r — r0) (when r560 A). r0 is the equilibrium bond length, which is 3.0 A. (2) The bond between the atoms "breaks" when r = 6.0 A. The magnitude of the force is 10.0 kJ mol" A" when r = 6.0 A. (3) F = 0 (when r > 6.0 A, i.e., the force is discontinous) (i) What is the bond dissociation energy for the interaction (i.e.. the difference in energy between the lowest point on the energy curve and when the atoms are completely separated). Specify the units that you use. (6 points) :} ‘ :‘3‘ y f r C \t K ’34} 1" 5 , I... '—“ t .l‘} i’ “I J" 3 :w\ .: ‘7’ .. i - { ‘ ,. f- ){lm A o A m z :0 l 40 r‘ r /<3 .- .r‘ . +1 :bjfij (@5154 file-(mflffi ill/“(.Leg- "Ld/a «. ' l mm Page 4 of 13 UC Berkeley, Chem C130IMCB 100A, Fall 2008, Mid-term Exam 2. Your Name 01. Part B, continued. (ii) What is the magnitude of the work done in moving the atoms from a separation of 4 A to 10 A? (3 points) - N work done : chime in {Fill/3ij \ j 1 3 _ 3:533 xi 2-, Ho? 14iwa g cm: may- 0 Uofifl: \6’ L3 /w\o’| NWL done 1 16'- [.Lo5i -: 179,35 Lj/m’i (iii) Sketch the energy, U(r), as as function of ron the graph below. Clearly indicate the numerical values (and units) of the grid points on the axes. (8 points) Page 5 of 13 UC Berkeley, Chem C130IMCB 100A, Fall 2008, Mid-term Exam 2. Your Name 02. 25 points total. Part A. (12 points) A molecule can exist in two conformations. A and B. Conformation B is higher in energy than B by 5 K] mol'1. (i) What fraction of the molecules will be in conformation A at 300 K? Calculate the concentration ratio: [AllillBl . Show all the steps of how you work out the answer. (4 points) Lel' [A] 3 X {3] _ ’S/Rr ,. 6-9 , o 135 “t [A]+[B] = l [A] " 44mm {3] = | —- x l- x X __[_A-L_ ._—, I 0 . g 8 I [fix :O.l35X | :' l . l 35 X ' O. ‘88 = K (ii) At what temperature will 99.9% of the molecules be in conformation A? (4 points) [Pl]=x : 0.9991 [8] = l-x = 0.001 ' -—AU £311.: WOOL]: o.ooi:e_ /RT [A 0.99 in o OOI = "AU/RT T = —AU _ -5‘ooo Incl" R. [no.om mm 18.314 Tmol"K" (iii) A different molecule has two conformations C and D. At 300 K, 30% of the molecules are in conformation C. What is the difference in energy between conformations C and D? 4 oints Efilwc : 03‘ p )E: : e-AU/RT E5] = l-x r 0-—7 [M 0'3 [n = "AP. 3 RT "RTln {-33.13 : AL) =3 -62.H KS Moi" Page60f13 (l) is lower M W) \LAUl: 2m KS moi" UC Berkeley, Chem C1301MCB 100A, Fall 2008, Mid-term Exam 2. Your Name Q2. Part B. (13 points) (i) One mole of an ideal monatomic gas is initially at 300K, with the internal pressure being 2000 JL". The gas undergoes isothermal expansion to a final pressure of 1000 JL“. The expansion is carried out reversibly. Calculate the change in energy (AU), the heat transferred to the system (q), the work done by the system (w), and the entropy change (AS). Show your reasoning and all the steps of your calculation, and write the final answers, with units, in the box provided. (8 points) rr 9 i Q { EJM‘QIW" Ll AU: 0 z T V 2 £1 : galaxy}?! : F2417 ‘ _ _ pl/ “(2 I P "Piggy-“FM— q:/’72é’1rfl0{!K, iii/v EV; => v2 = fl; : MW {21? :Qa‘ifi Wzmzérmflkl” F; "ii—‘9 5757:3553?” r e — AS: r - _ - _ _. i i“ :grsiqsz/flwléjbl 5775 Jane-“16 [grim] “ grail? jam/<4 / if swam = /.7212Jm34"r<" ,/’ grew (ii) The same amount of gas undergoes adiabatic (isolated) expansion against a constant external pressure of 1000 JL“. In this case, the piston is suddenly released so that the expansion is against the constant external pressure. Calculate the change in energy (AU), the heat transferred to the system (q) and the work done by the system (w). Show your reasoning and all the steps of your calculation, and write the final answers, with units, in the box provided. (5 points) 7; $981M r/aéjfi‘xm‘, 59/1/751‘460, flaw/1;.” 2 JJ{7%A/ 0 {'50 '61/waj fl/iflws’” ’43 V297: flow—fig MWAJA'QZH- l . jarW P; r was” fife/MW in Phi/2;; @ WSTIW - ? “A, 5 ’41” k rm , [and 93-! * AU: M)”: 51,5347) lz-W >< (24%50”) ,5 g-PWM. C”) Page 7 of 13 I UC Berkeley, Chem C1301'MCB 100A, Fall 2008. Mid-term Exam 2. Your Name 03 (25 points total) Part A (8 points) A small peptide forms a dimer with three hydrogen bonds, as shown schematically in the diagram below. Each hydrogen bond has a stabilization energy of —5.0 kJ mol". What is the relative population of dimers, at 300K, in which all 3 hydrogen bonds are formed versus dimers in which any one hydrogen bond is broken? That is, calculate the following ratio of concentrations: , [dimers with all three hydrogen bonds formed] [dimers with the 1:1 bond or the 2% bond or the 3—3 bond broken] Show how you work out the answer. + Z .. / .755 z 79 q 35’” z: 6 -» 6 {/1 i”..- I H 4 e—l Page80f13 UC Berkeley, Chem C13OIMCB 100A. Fall 2008, Mid-term Exam 2. Your Name Q3. Part B. (6 points) A heating system stores heat by depositing energy into two kinds of solutions. One solution contains type A molecules, the other contains type B molecules. The potential energy levels of the two kinds of molecules are shown below. Given equal volume vessels containing A or B at the same temperature, which vessel will deliver more heat to a system at lower temperature? Explain the reasoning behind your answer. Energy _____.___.___ Energy Molecule A Molecule B l I"? /f} l 1‘ fl “.0. './" erl/l'ti’ f. 4.,» 120 W‘ /q A! - a i 10 vita/«Amy ' r /V 41"? v’ E 3 :l t ' Q “a I) " dc?) 171‘ M a fix “a” ct ' 01/113 ’ %Mf 2m awe/7 0 W w_,w ’ " I? n jut/[125” MM, / W/Mfigrw in; 2": 64¢“??? ‘* u/ 57:7 Page 9 of 13 UC Berkeley, Chem C130IMCB 100A, Fall 2003, Mid-term Exam 2. Your Name 03 Part C 11 Points (i) Consider the system above, in which 3 A—type molecules, 3 B-type molecules and 4 C-type molecules are present in a 5X5 grid. What is the entropy of the system? Assume that the value of the Boltzmann constant (k3) is 1.0. (7 points). :1 L’flmow (ii) Assume that C-type molecules can convert to D-type molecules through an isomerization reaction. Will the entropy go up or down if one C-type molecule converts to a D-type molecule? Justify your answer. (4 points) 7/6“ x :0 {A}: r 5-4in g : it“ Séiciéxtom 2%? aim (16 :[0 g T Page 10 of 13 UC Berkeley. Chem C13OIMCB 100A, Fall 2008, Mid-term Exam 2. Your Name Question 4. (25 points total) Part A. (15 points) Shown below is a system inside which two chambers are separated by a movable piston. The size of each chamber and the number of molecules (of two types, A and B) are indicated in the diagram. 20,000 gridhoxes 20,000 gridboxes 1.000 type A molecules 2,000 type A molecules 1,000 type B molecules no type B molecules (i) What is the entropy of the left chamber in the system? Use the statistical definition of the entropy (S = k3 an , where Wis the multiplicity). In order to calculate the multiplicity, use the number of grid boxes indicated for each chamber, and also use Stirl'mg's approximation (lnN ! = N In N — N). Assume that the value of the Boltzmann constant (k3) is 1.0. (8 points) 3 - “.08ch -* “1C5 Elmo's) — Lea/«35:1 k3 Lapi— —' Ix EM ST—Ke lh \xJ _. KB E ln C14 ot' grcdfllw lnL—fi AhoOKE ' 1 {Us 0% was — #Aml ‘flBle-j —" V\ in 10,090l£tfl<3><l0§ LOOO :ibofl KLO'B In .4. ln 1600f. = \‘BEX‘Q Page 11 of 13 UC Berkeley, Chem C1301MCB 100A, Fall 2008, Mid-term Exam 2. Your Name Question 4, Part A, continued. (ii) The entropy ofthe right chamber is 6502 (entropy units). What is the combined entropy of the system? Explain your answer. (4 points) Sm 2: 8(00 ka't' 63020 '—= ‘46“) KB tha; is WVHWL (iii) Will the piston move spontaneously to the right or the left? Justify your explanation without doing any further calculation. (3 points) \ “\sfin \UlU MOT MOVE 34rd WW9? )5 Cir W7 V‘OQd 9‘" 3% bacctwae, C‘Bual WWWBU 0% MOLth Per (array gm both state. 1% 04. PART B (10 pts). Multiple choice and True/False questions. Circle the correct option (or circle either TRUE or FALSE). +2 points for each correct answer, -2 points for each wrong answer. To get the maximum score you do not need to answer all the questions, so be careful not to answer questions incorrectly. Unanswered questions do not change the score. Maximum points: 10. Minimum points: 0. (i) The fold recognition method known as the 3D—1D profile method compares: - the sequence of an unknown protein to the sequences of known proteins th€§ifi€rfi€6fififikfi6fifiproféfififithe three—dimensional environmen a I, .u___ each position in KQQM‘LSJEJELQLeflg . " - the hydrophobicity at each position in the unknown protein to the hydrophobicity of known proteins - the predicted structure of an unknown protein to the actual structure of known proteins (ii) For a process occurring under constant ressure conditions the energy change is equal to the enthalpy change (TRUE 'FALS (iii) For a process occurring under reversible conditions the heat transferred is a state function FALSE) (iv) The density of a system is an intensive property'of the system @/ FALSE) Page 12 of13 UC Berkeley. Chem C1301MCB 100A. Fall 2008, Mid-term Exam 2. Your Name (v) The molar heat capacity of a system is an extensive property of the system (TRUE/flee) (vi) A piston contains protein molecules dissolved in water. During an isothermal and reversible egpansion of the system the total energy of the system stays constant. (TRUE/ ALSE (vii) The combined potenti nergy of the system and the surroundings is always conserved. (TRUE ALS (viii) The entro a system can decrease spontaneously if it is coupled to an energy source. RU FALSE) (ix) The work done in a reversible process is always the work done in an irreversible process. ;le.ss,.than.. C-greeeefirfi - equal to (x) The entropy of a system is property of the system: — an ' 've 5/” - an additive”) - poorly determined - conserved —-—END OF EXAM—3 Page 13 of13 ...
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This note was uploaded on 02/23/2011 for the course MCB 100A taught by Professor Kuryian during the Spring '09 term at Berkeley.

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Midterm 2 Answers - 2008 - UC Berkeley, Chem C13DIMCE 100A,...

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