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prelim_1_solutions2

prelim_1_solutions2 - Chemistry 288 Preliminary Exam I...

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Unformatted text preview: Chemistry 288 Preliminary Exam I Spring 2005, Mamhn '1. Estimating the cell potential. Suppose that the concentration of K+ ions inside a cell is 100. mil! while the concentration of K+ outside the cell is 5.011)!” i What is the voltage difference, in millivoltsi between the inside and the outside of the cell? 77/“ :: /abmm Chemistry 288 Preliminary EXflIH I Spring 2005, Marohn ‘ . Ion channel protein. An ion—channel protein can be in one of two configurations, “open” or “closed.” In a control experiment, it is found that‘ when fully opened“ the ion—channel protein admits an ion current of [open = 10 HA. In a separate control experiment, it is found that in its closed state, the ion channel still admits an ion current of [Closed = 211A. In a cell, it is found that. the ion-channel protein at room temperature (I = 300 K) admits a current of I = 5 HA. What is the energy difference between the open and closed forms of the ion-channel protein? ::?f\ 7F : A9,”? IWW =1“ .244? £11437 0 E Chemistry 288 Preliminary Exam I Spring 2005, Marohn 3. Polymer elasticity. (a) Consider a polymer chain comprised of N monomeric units or “links,” each of length (0. with each link equally likely to be directed to the left or the right. If the polymer chain is stretched, the restoring force is given by 3F 30 f — (W). ~ ”(5). where we have used that the Helmholtz free energy is F E U — TO' and where we have neglected the energy associated with stretching the polymer. We can thus calculate the restoring force of a. polymer if we know its entropy as a function of length. Derive an expression for f in terms of 'r, l. N, and [0. '--~ —- ;a "' 5:852 a—t 0* har— W’” ’ 7;"; - WW/~—,§/fi/‘ “Jewry,“ “We“! .-.~ 13.2.5- _-.a ! l A We... 1:. ,. ’ L z: _+ 7“,? . /A/m. m a? ,y/] (b) On the homework we considered DNA length fluctuations, and derived that the root—mean—square variation in the length of a. polymer is [mm = VN [0. Use this result to write down the root—mean—squere restoring force. How does it depend on the polymer’s molecular weight and on the length of the monomer unit? ’Ww WM ‘ .. ”an. (W459- " f =- —- 7‘14? . £1? :- zv V] /m I m K1 v r M“ 4443' 7‘4“,” 96 V3964) 2 61;” w 5.9738943. 4 d Chemistry 288 Spring 2005, Marohn w...»..-.m r-‘l‘u‘ 4. A neurotransmitter binding to a cell surface. A certggnEUrotransmitter i'holecule binds to a receptor site on a cell surface, and it is known that this binding liberat 15,0le moi—1 of energy. If the fraction of receptor sites that have a neurotransmitter bound is observed to be 0.20, what is the activity of the neurotransmitter in the extracellular fluid? Recall that we defined the activity as A E 43“", where p is chemical potential, 7' = kBT, and T is temperature in kelvin. éfl «“11 J2}? .Z. “*6 phédwu‘l c3 o Mywm 5/ C’ J /l e 7‘ ” _ . - E/ ”Fifi“? ”term; I / r ’7‘ i ......_:i.f:.,.m..:m 1”” sze""" = 0- 80 =- 0,30 2+» away a“ Mr xi amt/W ‘1?!" 11.-., , “A-“ ‘ "New“ *{A z c, :2 m - V M e» w, x 6’ \ a: €9.37 \ ,1l Chemistry 288 Preliminary Exam I Spring 2005, Marohn 5. Multiple choice, mostly. (a) We introduced temperature as (b) The Gibbs free energy is a function of the variables 0,301}; T,V,N ((1) Two systems free to exchange only energy have reached equilibrium once they have a. common ,@ temperature 85 pressure chemical potential 85 temperature pressure (e) What were the approximations we used in deriving the ideal gas law? / 6614— Law a. imagine flmv/yw ._ m Wvéétrmf fifizw / M 71,,” I A”; M Q‘ (RI/9%"; W‘ ((1450 ...
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