1、Physical ChemistryPhase EquilibriumPhase EquilibriumBinary mixturesliq vap Eq.in Binary MixturesBoth the liquid and the vapor phase are binary mixtures of A and B.x A,x B are the mole fractions in the liquid.y A,y B are the mole fractions in the vapor.p A,p B are the partial pressures in the vapor.E
2、thyl Acetate in Acetic Anhydride01002003004005006007008000.00.20.40.60.81.0 xethyl acetatep/torrThe vapor pressure of a substance varies linearly with its mole fraction in solution.pA=xA pA*Raoults Law becomes exact as xA 1.Raoults Law becomes increasingly valid as the components of the mixture beco
3、me more structurally similar.Raoults Lawn-Pentane in Methyl Acetate01002003004005006000.00.20.40.60.81.0p/torrxpentaneIdeal Solution ModelAAAAAAAAAAAAlglRTpplRTppRTxlRTx()()()ln(/)()ln(/)ln()ln*,at equilibrium0000where A*is the chemical potential of the pure liquidIdeal Heat of MixingGnnnnn RTxn RTx
4、SGTn Rxn RxHGT SmixingAABBAABBAABBmixingmixingpAABBmixingmixingmixing()lnlnlnln*0Molecular Basis for Ideal Solns.In pure liquid A,there are only A-A interactions.In pure liquid B,there are only B-B interactions.In solutions of A and B,there are A-B interactions as well.Hmixing=0 says that all three
5、interactions are of equal strength.Ethyl Acetate-Acetic Anhydride01002003004005006007008000.00.10.20.30.40.50.60.70.80.91.0p/torrxethyl acetatepacetic andydridepethyl acetateptotaln-Pentane and Methyl Acetate01002003004005006000.00.20.40.60.81.0 xpentanep/torrpmethyl acetateppentaneptotalColligative
6、 Properties Definition:colligative properties depend only on the concentration of solute particles,not on their identity.Assumptions:the solute is non-volatile,i.e.the vapor phase is pure solvent.the solute is insoluble in the solid solvent,i.e.solid phases are pure substances.Boiling Point Elevatio
7、nAAAAvapvapvapBvapBvapvapBlRTxgRTxGHT SRxHTTxHRTTHRTTTKx*2()ln()lnln()(/)011111Molality and Mole Fractionxnnnnnmnnn MxMmBBABBABBBABB1 kg ATherefore,where M is the molecular weight in kg/mole.=k(mB/mB0)Freezing Point DepressionAAAAfusfusfusBfusBfusvapBlRTxsRTxGHT SRxHTTxHRTTHRTTTKx*2()ln()lnln()(/)01
8、1111SolubilityBBBBfusfusfusBfusBfusfuslRTxsRTxGHT SRxHTTxHRTTHsolute*()ln()lnln()(/)ln.01111where and T are properties of the*Osmotic PressureAAAAAABmppmBppppRTxRTxG ppRTxV dpVVn RT*()()()()lnln()pp+puresolventsolutionMolality and Mole Fraction)/(10BBABABABBBAABAABBbbMxMxMxxbMxxMnnb05001000150020000
9、.00.10.20.30.40.50.60.70.80.91.0n-Pentane in Methyl AcetateHenrys LawRaoults LawKp*xpentanep/torrThe vapor pressure of a substance varies linearly with its mole fraction in solution.pA=xA KAwhere KA is the Henrys Law constantHenrys Law becomes exact as xA 0.KA is the hypothetical vapor pressure of p
10、ure A,assuming that it behaved in its pure form as it does at infinite dilution.Henrys LawDilute-Ideal Solution ModelBBBBBBBBBBBBlglgRTpplgRTKpRTxlRTx()(),()()ln(/)()()ln(/)ln()ln at equilibrium0000where A+is the hypothetical chemical potential of theliquid as xB approaches unity.Molality Scale BBBB
11、BBBBBBBBBBBBBlRTxxM mmmlRTM mmlRTmmRTM()ln(/)()ln(/)()ln(/)ln,in the dilute-ideal model,where molal,where 0000001Solvent ActivityThe exact chemical potential is given byA=A*+RT ln(pA/pA*)The solvent activity is defined aA=pA/pA*Therefore,A=A*+RT ln aA is exact.The activity coefficient gA is defined
12、aA=gA xA As xA 1,aA xA and gA 1Solute ActivityThe exact chemical potential is given byB=B+RT ln(pB/KB)The solute activity is defined aB=pB/KB Therefore,B=B+RT ln aB is exact.The activity coefficient gB is defined aB=gB xB As xB 0,aB xB and gB 1 Molality Scale ActivityThe exact chemical potential is
13、also given by B=B0+RT ln(pB/kKB)The molality scale activity is defined by aB=pB/kKB Therefore,B=B0+RT ln aB is exact.The activity coefficient gB is defined aB=gB(mB/m0)As xB 0,aB mB/m0 and gB 1 Benzene-Acetic Acid05010015020025030000.10.20.30.40.50.60.70.80.91BenzeneAcetic Acidxacetic acidp/torrBenz
14、ene-Acetic Acid Raoult Activitiesxacetic acidActivity0.00.20.40.60.81.01.20.00.20.40.60.81.0BenzeneAcetic AcidBenzene-Acetic Acid Benzene Activitiesxacetic acidActivity0.000.200.400.600.801.001.200.000.200.400.600.801.00Raoults Law BasisHenrys Law BasisBenzene-Acetic Acid Activity Coefficientsxaceti
15、c acidActivity Coefficients0.00.51.01.52.00.00.20.40.60.81.0BenzeneAcetic AcidExcess G of MixingGGactualGidealGidealn RTxn RTxGactualn RTan RTaGn RTn RTmixingEmixingmixingmixingAABBmixingAABBmixingEAABB()()()lnln()lnlnlnlnggPhase EquilibriumPhase DiagramsDefinitionsuF:the number of degrees of freedo
16、m,i.e.the number of independent variables needed to describe the state of the system.uC:the number of independent substances in the system.uP:the number of phases in the system,where a phase is a form of matter that is uniform throughout in composition and state.The Phase RuleuEach phase needs C-1 c
17、omposition variables plus T and p to describe its state.Therefore,the total number of state variables is P(C-1)+2uFor each substance,there are P-1 equil.constraints of the form(uTherefore F=P(C-1)+2-C(P-1)or F=C-P+2Phase DiagramsolidliquidgaspTcritical pointtriple point1 atmTbCooling Curve:Pure Subs
18、tancetimeTTfarrestliquid coolingsolid coolingliquid freezingBoiling Pt./Composition DiagramliquidxATb vaporTA*TB*yAxA Tb for the liquidwith composition xAcomposition of the vapor that boils off at Tb boiling pt.of pure Aboiling pt.of pure BLever RuleuLet z be the total mole fraction of A,both phases
19、 combined.uLet n and n be the moles in phases and.unz=nx+nyA =nz+nzAun(z-x)=n(y-z)unl=nl zAphase phase llTyAxAliquidvaporTb TA*TB*xA Azeotropesazeotropiccompositionazeotropicboiling pt.Ideal Boiling Pt./Composition)(11)(expn,eqClapeyron-Clausius thefrom where)(0*ATTRAHppxppppxppybvapAABABAAAAImmisci
20、ble LiquidsxA T uppercriticaltemperatureTxxcomposition of phase at Tcomposition of phase at T2 liquid phases1 liquid phaseBoiling of Immiscible LiquidsxA T 2 liquid phases1 liquid phasevapor phasel+vl+vzABoiling of Immiscible LiquidsxA T 2 liquid phasesvapor phasel+vl+vzAllMelting of Solid Mixturesx
21、A T 2 solid phasesliquid phases+ls+lzAEutectic pointIntermediate CompoundxA T solid B+solid ABliquid phases+ls+lBABAsolid AB+solid As+lliquid phases+lSpinelxA T SolidSoln.liquid phaseBA2 solid phases and liquid+solid SolidSoln.liquid+solid Immiscible Melts:Ex 8.17mole fraction CF4 T solid B+solid AT
22、wo phase liquidCH4CF4liquid phases+ls+lsolid B+liquid9186848994Incongruent MeltingxA T solid B+solid ABliquid phaseB(s)+lBABAsolid AB+solid AA(s)+lAB(s)+lTriangular CoordinatesuEach vertex corresponds to a pure substance.uThe side opposite a vertex corresponds to a mixture of the other two substance
23、s.uThe mole fraction of A is proportional to the distance from the opposite side.ABCxA=0.65xB=0.15xC=0.20Triangular Phase Diagramsfixed T and PABCP=1P=2composition of B-rich phasecomposition of C-rich phasetie line“Salting Out”H2OCH3OHK2CO3 P=1liquidP=2K2CO3(s)+solnP=2K2CO3(s)+solnP=2immiscible liquidsP=3K2CO3(s)and2 immiscible liquidsDouble Solubility DiagramH2OP=2NH4Cl(s)&satd.soln.(NH4)2SO4NH4Cl P=1solnP=2(NH4)2SO4(s)&satd.soln.P=3 both solids&satd.soln.
