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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‘—§' (")(‘U070%) 34.5 IJ/LJ S’ 68’ ’“SLU/ #3 Fe/ 0/ PW (law] k't an u Qr— («I/r (“C4 "a" '
AG : MAW£0) —?6,u7ﬂ+1}(~0.o7o) 4/51 It I‘dDad‘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
selfinteractions; 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 rootmeansquared endto—end distance of the polymer? mzw :m/l:/é”0 ”"‘" 7777.57,... ...
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 Winter '10
 Brown
 Physical chemistry, pH, Statistical Mechanics, Entropy, Ligand binding site, binding sites, ligand binding equilibrium, random polymer

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