PracticeMidterm2

PracticeMidterm2 - YOUR NAME HERE April 7, 2010 Chem 120B...

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YOUR NAME HERE April 7, 2010 Chem 120B Midterm #2 Defnitions and UseFul ±ormulas: Inverse temperature: β = 1 k B T ,k B =1 . 38 × 10 - 23 J / K ±irst law oF thermodynamics: dE = TdS - pdV + ± i μ i dN i Entropy and the second law: S = k B ln W, S = - k B ± ν P ( ν )ln P ( ν ) ,d S = ¯ dq rev T ¯ dq T S ) E,V,N 0 , A ) T,V,N 0 , G ) T,p,N 0 ±unctions oF state: H = E + pV, A = E - TS, G = H - TS Clausius-Clapeyron equation: dp dT = Δ s Δ v Intensive variables: sdT - vdp + ± i x i i =0 ,x i = N j N Chemical potential: μ i = μ (0) i ( T,p )+ k B T ln x i Colligative properties: Δ T b = k B T * b Δ s x sol π = x sol ρ = ρ sol 1
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Questions on this exam concern dilute amphiphilic moleculesin(andatthe surface of) aqueous solutions. One such molecule (denoted “A” for “amphiphile”), consisting of a polar head and a nonpolar tail, is sketched below. polar head nonpolar tail A = 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) A n = Each micelle (denoted A n )ismadeupo f n amphiphile molecules. We will not specify a value for n ,excepttosaythatitismuchgreaterthanone . Let μ 1 be the chemical potential of an individual amphiphile A that is well separated from other solutes. Let μ n be the chemical potential of an entire micelle A n .S im i l a r ly ,w ew i l ld en o t eth enumb e ro fun a s s o c i a t edamph iphiles per unit volume as ρ 1 ,andthenumbero fm ice l lesperun itvo lumeas ρ n .F ina l ,l e t N be the total number of amphiphiles (including those in micelles), so that c = N/V = ρ 1 + n is their total concentration. Temperature T and pressure p will be ±xed throughout this problem.
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PracticeMidterm2 - YOUR NAME HERE April 7, 2010 Chem 120B...

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