CHEM 120B - Spring 2010 - Geissler - Midterm 2 (solution)

CHEM 120B - Spring 2010 - Geissler - Midterm 2 (solution) -...

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KEY YOUR NAME HERE April 7, 20L0 Chem 1208 Midterm #2 Definitions and Useful Fqrmulas: Inverse temPerature: P:#' ke:1'38 xro-23JfK First law of thermodYnamics: dE=Td,S-pd'V +t FfiNr, Entropy and the second law: .g: ke lnw, s : -keLrr4itnP(u), d,s :w aE (AS)e,v,ru Z 0, (AA)r,4iv < 0, (AG)7,p,ry S 0 F\rnctions of state: H:E*PV, A:E-TS, G:H_TS Clausius- ClapeYron equation: dP -Ls dT Lu Intensive variables: sd,T - ud,p *lrld,1't.i:0, *n: # i Chemical potential: Colligative proPerties: pn : pto) (T,p) * kB,Trnu ATu : $"""t, on :
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wt,;L 4a , : Questions on this exam concern dilute amphiphilic molecules in (and at the surface of) aqueous solutions. One such molecule (denoted "A" for "amphiphile"), consisting of a polar head and a nonpola,r tail, is sketched below. A = ?*0"" n"': ., )-nonRolar tail 1. These amphiphilic solutes can shield their hydrophobic tails from solvent by forming micelles, roughly spherical clusters of solutes whose head groups point outward toward solvent. micelle (cross section) Each micelle (denoted A,) is made up of n amphiphile molecules. We will not specify a value for n,.except to say that it is much greater than one. Let p,1be the chemical potential of an individual amphiphile A that is well separated from other solutes. Let p,n be the chemical potential of an entire micelle A,o. Similarly, we will denote the number of unassociated amphiphiles per unit volume # pr, and the number of'micelles per unit volume 6 Pn. Finally, let N be the total number of amphiphiles (including those in micelles), so that c : NIV : h * npn is their total concentration' Temperature ? and pressure p will be fixed throughout this problem. (i) What is the change AG,, in Gibbs free energy when ri, amphiphiles a,re brought iogether to form a micelle, i.e., resulting from a single instance of the reaction ni --+ Arr. Your answer should involve some (but not necessarily all) of the following quantitles: the chemical potentials p1 and 1.rn, the size n of a micelle, ?, p, N, c, and fundamental constants.
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CHEM 120B - Spring 2010 - Geissler - Midterm 2 (solution) -...

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