MT_solutions_yellow

MT_solutions_yellow - Chem 112B Midterm Feb. 10, 2010

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Unformatted text preview: Chem 112B Midterm Feb. 10, 2010 NAMEifiw_//EzfiPERM:_—_ Instructions: The last two pages of the exa contain some useful information. Please verify that your exam contains 6 pages (5 of exam and l of information; one of the exam pages is intentionally blank). Show all work and box your final answers to receive full credit. Question I, 20 points: The resting membrane potential of neurons is about -90 millivolts. The concentrations of K+ and Na+ within neurons are lOOmM and 10 mM, respectively. The concentrations of K+ and Na" outside the cell are SmM and 140 mM respectively. Neurons expend energy to maintain this ion gradient. More specifically, the Na+/K+ ATPase pump simultaneously sends 3 Na+ ions out of the cell while bringing in 2 K” ions. What is AG for this process? (Assume T = 298K) + ‘l' — ‘f 3 Q Cr'ag‘r/c) —i akfwfig/d 5 3/14 m”);:/:) +0.2k-(f/‘1z‘t/é) A64“: 4&th 1* Ffigéam 7‘ \I My/{S 9% Click/Id 4.515447% ‘0 (521R 41".“ :Cefl"¢gf) «I ll § ,_ 3 Ab- 3.3/144/ x19$k[q(/‘fl (£03 7L%/¢55‘—§' (")(‘U-070%) 34.5- IJ/LJ S’- 68’ ’“SLU/ #3 Fe/ 0/ PW (la-w] k't an u -Qr— («I/r (“C4 "a" ' AG : MAW-£0) —?6,u7fl+1}(~0.o7o) 4/51 It I‘d-Dad‘f ,o 1 gin/W, +fi8? fez“, = 5702 521.! “OJ—x". : K714 +%3 “3744 [‘0'07") = #6744 —2?‘3W/ = J75 ’64” we,“ Mask 2 45 6 m awe/14+ 0/ Rae/F AG Question II, 20 points: The data below describe the binding of ligand A to a macromolecule. Calculate the number of binding sites per macromolecule and the binding constant (KA from class). You can assume that the binding sites are independent of each other. Concentration of unbound A (mM)£./,] # of bound A per macromoleculeV E .70 1),: L J 0.05 1.6 0.11 2.5 3 a, 000 0.20 3.2 a a, 7 10 0.49 4.0 / (,1 000 g, lea Question 111, 35 points: A small ligand has 5 total microstates. Three of the microstates have energy E0 and two of the microstates have energy El (E1 > E0). A) (7 pts.) What are the entropies associated with energy levels E0 and El (you need to give two answers here)? B) (7 pts.) What is the total Helmholtz free energy for the ligand at temperature T? Leave your answer in terms of 130,El and T. C) (7 pts.) Assume E0=0.5kJ/mol and El=3.0kJ/mol and T=300°K. What is the probability, Po, that the ligand has energy E0? D) (7 pts.) Imagine that you have one billion (10°) copies of the ligand in solution at T=300°K. How many of the ligands do you expect to have energy E0, on average? ‘ E) (7 pts.) What is the standard deviation associated with the average number you just calculated in part D? A) 55% Srw g) [hr/(6771C? : _k67’/4(3C_fl>5o+;€dgg. Question IV, 25 points (5 points each): A) Fill in the blank(s): 1) Eadégfi constant relates the number of electrons in a mole to the number of electrons in a coulomb of charge. M ‘ +4» 2) Boltzmann’s constant is the gas constant divided by [I vat/(w) j 3) A $3 /(4g¢c/{ plot is useful to determine ligand binding equilibrium constants for systems with a single ligand binding site er macromolecule or for systems with multiple independent binding sites per macromolecule. A E} // plot is used to quantify the effects of cooperativity between ligand binding sites on the same macromolecule. 4) Maximizing the Q, figs entropy formula subject to the constraints of normalization of probability and a constant average energy leads to the Boltzmann distribution. B) Linear polymers get larger as more and more monomers are added. Let “N” be the number of monomers in the polymer. If we define size as the root—mean—square end to end distance of the polymer, indicate how each of these four types of polymers grows with N: a completely rigid polymer; a completely random polymer with no self-interactions; a flexible polymer that is attracted to itself in solution; a flexible polymer that repels itself in solution. (your answers should be some function of N, for example N, e”, etc.. Do not worry about constants and assume the polymers are large enough to exhibit the limiting, large N, behaviors discussed in class). rt‘ift/(J 17/ 4 flat 4V! - fl/ Z3 riflvé'fl'. “WU/Wat 1/}(r C) You grab a random polymer by its ends and pull. Is it more difficult to stretch at 350 K or 300 K? Provide a brief explanation. D) Consider a two state system (for example, the spin of a proton in a magnetic field): What is the probability to find the system in the state with lower energy when T = 0 and when T = oo? 62.4 3/ a. 4 E) A random polymer is synthesized that has a Kuhn length of 3 nm and a contour length of 2000 nm. What is the root-mean-squared end-to—end distance of the polymer? mzw :m/l:/é”0 ”"‘" 7777.57,... ...
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This note was uploaded on 03/01/2010 for the course CHEM 112b taught by Professor Brown during the Winter '10 term at UCSB.

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MT_solutions_yellow - Chem 112B Midterm Feb. 10, 2010

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