CHEM 120B - Spring 2010 - Geissler - Midterm 1 (solution)

CHEM 120B - Spring 2010 - Geissler - Midterm 1 (solution) -...

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KEY YOUR NAME HERE L!:ftjons ana Usefut Formdas: Inverse temPerature: Fbbruary 24,2010 1 k"T ' kB: P(u): 1.38 x g-98" t0-23 J /K Boltzmann distribution: a -BE" ,g: ks lnw, s : -keLr@rnP(u), Equilibrium averages: (E) : - (ffi," , (58\: (W),u,', :ksr2cv ! Equipartition PrinciPle: t (q : |keT per classical degree of freedom with quadratic energy. Entropy: , d dqr.u oo -T= First law of thermodYnamics: dE :dw *dq Partition function for noninteracting, indistinguishable molecules: Partition Factorials: a:# Chem 1208 Midterm #1 -lf! :,n/ x (l/ - 1) x (lr- 2) x . .. 1,
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l- euestions on this exam concern dilute solutes in a vesicle (which might be regarded as a crude model of a living cell), as sketched beiow' For purposes of counting, imagine dividing the vesicle into a lattice of M cells. A microstate is specified by detailing the presence or absence of solutes in every cell. The vesiele'-s ,envirr"',nment Serves as a heat bath at temneratttre 7 Q:rantrrrn mechanical effects can be ignored throughout. Neglect as weil contributions from solvent, particle velocities, and interactions among solute molecules unless explicitly stated otherwise. Many molecules in biological cells are synthesized in very small numbers- In this qrr"riiol we consider an extreme case: chemical species that are either completely absent or present as single molecules. Specifically, our vesicle contains one pa,rticle of type A and one particle of tYPe B' (i) Caiculate the partition function Qunbound for the collection of microstates in which A and B move independently within the vesicle, as depicted below. Take the energy of such "unbound" configurations to be zero. Your answer may involve some (but not necessarily all) of the following quantities: ?, M, and fundamentai constants. ''Mt \ 1. 8 pts 0,*ntoonl
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8 pts (ii) Calculate the partition function
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This note was uploaded on 09/12/2011 for the course CHEM 107B taught by Professor Jamesames during the Spring '09 term at UC Davis.

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CHEM 120B - Spring 2010 - Geissler - Midterm 1 (solution) -...

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