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Prelim_III_solutions - Prelifll III ll Chemistrv Phvsical...

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Prelifll III Chem 3900: Phvsical Chemistrv ll Spring 2009 9 April 2009 Name: So/,,hbns Problem l: /20 Problem2: /25 Problem 3: /20 Problem 4: /20 Problem 5: /15 Total: /100 Contants and relations vou misht need: R: 8.314 J/ (mol K) ks= I .38lxl0t3 J/K I bar: 0.987 atm = l0) Pa N, (Avogadro #) = 6.02x1023 mol-r I joule = 6.24x10r8eV 9ibbs-Duhem equation: ln,dp, =o Raoult's law fldeal Solution): 1 = 1'x, fugacitv. fusacitv coefncient: { P., -7 lnr- lnl= l' i ap' p 6p entroDy: /ano\ S = fr- lnO+ k"Tl " "-' I " \ ar )r., Clausius-Clanevron eq uation : ' P, Luor,"uofr(l l) In'"- - l---l pr R (.4 Tr) Definition of Thermodvnamic Enersies: U(S,V) dU =TdS - pdV H(S,p)=U + pV dH =TdS +Vdp A(T,V)=U -TS dA=-SdT * pdv G(T,p)= H -TS dG:-SdT +Vdp Maxwell Relations: f as) =( A\ [ut] =_( y\ \av ),-\ar ),'lao ),--\ar ), (av\ _( ar\ ( A\ =_({\ [*,J, =[ooJ-'[asl" \av )r
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Problem 1- (20 points) Since benzene (CoFIr) and toluene (CzHs) are very similar molecules, their liquid mixtures are well represented by the ideal solution model. The vapor pressures of benzene and toluene have the following values for several temperatures as shown below: Temperature ('C) 79.4 88 94 r00 ll0 Prrr" lbar 1.000 r.285 1.526 1.801 P[,r" I bar 0.508 0.616 0.742 1.000 Use this to answer thefollowing questions. @.o) "* "b f5-1 (a) Sketch a pressure/composition (p, zrcu*) phase diagram at T = 100"C. Clearly labelthe axes and r-r the regions where liquid, vapor, and coexisting phases are stable. At /ooc' f:* = /.&t bF & er, = d-v+z L^n P chc.) o.?44. o TGnr / If a solution containing 0.5mol of benzene and 0.5mol of tolueneis heated at p : I .0 bar, at what temperature will the first bubble of vapor appear, and what will be its composition? A simple linear interpolation will be sufficient for the estimate of the boiling remperature.
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