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1、Chapter 10Nonideal SolutionsPhysical Chemistry1Ideal SolutionsSolutionsB at T, PC at T, PB + C at T, PB-B, C-CB-B, C-C, B-CPhysical ChemistryIf B-B, C-C and B-C interactions are all all differentdifferent2Nonideal SolutionsSolutionsB at T, PC at T, PB + C at T, PB-B, C-CB-B, C-C, B-CPhysical Chemist
2、ryIf B-B, C-C and B-C interactions are all all differentdifferentThe molecules of one type cluster togetherReorganization of the molecules: orderly mixtureSeparation is spontaneousLiquids become immiscible or partially miscible3The chemical potentialchemical potential () does more than show how G va
3、ries with composition.The Wide Significance of Chemical PotentialNonideal SolutionsA general infinitesimal change in U for a system of variable composition can be writtenAt constant V and SPhysical Chemistry4The Wide Significance of Chemical PotentialNonideal SolutionshenceIn the same way, it is eas
4、y to deducePhysical Chemistry5Activity and Activity CoefficientsNonideal Solutions(9.59)*ideally dilute solution(9.60)*ideally dilute solutionideal ideal solutionsolution(9.42)*ideal ideal solutionsolution(9.43)*ideal or ideally dilute solution(10.1)*ideal or ideally dilute solution(10.2)Physical Ch
5、emistry6Activity and Activity CoefficientsNonideal Solutionsideal or ideally dilute solution(10.2)When the solution is neither ideal nor ideally dilute solution, every solution(10.3)ai is defined as activityactivity, a kind of “effective” mole fraction.every solution(10.4)*The difference between and
6、Physical Chemistry7Activity and Activity CoefficientsNonideal SolutionsThe ratio is the measure of the departuredeparture from ideal behavior.every solution(10.5)*activity coefficientThe activity coefficient i measures the degree of departure of substance is behavior from ideal or ideally dilute beh
7、avior. The activity ai is obtained from the mole fraction xi by correcting for nonideality.Physical Chemistry8Activity and Activity CoefficientsNonideal SolutionsNote from (10.3) and (10.5) that ai and i are dimensionless and nonnegative.(10.6)*Since i depends on T and P, and the mole fraction xi, t
8、he activity ai and the activity coefficient i depend on these variables:The task of thermodynamics: show how ai and i can be obtained from experimental data.The task of statistical mechanics: show how ai and i can be found from the intermolecular interactions in the solution. Physical Chemistry9Acti
9、vity and Activity CoefficientsNonideal SolutionsLike the chemical potential, ai is a measure of the escaping tendency of i from the solution.The activity ai is a measure of the chemical potential i in the solution. The activity The activity a ai i is more convenient to is more convenient to use in n
10、umerical calculations than use in numerical calculations than i ievery solution(10.3)Physical Chemistry10Activity and Activity CoefficientsNonideal Solutions(c) ai can be compared with xi (and i with 1) to judge the degree of nonideality.(a) we can not determine absolute value of i (more relative va
11、lues). The activity ai is more convenient to use in numerical calculations than i. (b)Physical Chemistry11Standard States for Nonideal-Solution ComponentsNonideal SolutionsConvention I(10.7)*for all componentsConvention I is the same convention as that used for ideal solutions.is independent of the
12、choice of standard statedepends on the choice of standard stateevery solution(10.3)depends on the choice of standard statePhysical Chemistry12Standard States for Nonideal-Solution ComponentsNonideal SolutionsConvention I(10.7)*for all componentsdepends on the choice of standard stateevery solution(1
13、0.3)depends on the choice of standard statedepends on the choice of standard stateTherefore, we denote as convention Iconvention I activities, activity coefficients and standard chemical potentials. Physical Chemistry13Standard States for Nonideal-Solution ComponentsNonideal SolutionsConvention Iide
14、al or ideally dilute solution(10.1)*(10.6)*nonideal solutionFor a nonideal solution, the deviation of the from 1 measure the deviation of the solutions behavior from ideal-solution behavior.(10.7)*for all components(10.8)*for each iPhysical Chemistry14Standard States for Nonideal-Solution Components
15、Nonideal SolutionsConvention ISince the Convention I standard state of each solution is the pure substance, the Convention I standard state thermodynamic properties of i equal the corresponding properties of pure i.Convention I puts all the components on the same footing and does not single out one
16、component as the solvent. Convention I is often called the symmetrical symmetrical conventionconvention. Physical Chemistry15Standard States for Nonideal-Solution ComponentsNonideal SolutionsConvention IIConvention II is chosen when one wants to treat one solution component (the solvent A) different
17、ly from the other components (the solutes i). Common cases are: solid or gases solutions in a liquid solvent Convention II is often called the unsymmetrical unsymmetrical conventionconvention. The Convention II standard state of the solvent A is pure liquid A at the T and P of the solution.(10.6)*no
18、nideal solutionPhysical Chemistry16Standard States for Nonideal-Solution ComponentsNonideal SolutionsConvention II(10.6)*nonideal solution(10.9)*For each solute iA, Convention II chooses the standard state so that II,i goes to 1 in the limit of infinite dilution:(10.10)*Physical Chemistry17Standard
19、States for Nonideal-Solution ComponentsNonideal Solutions-6-4-20Fig. 9.20When xA is near 1 and the solute mole fractions are small, then by (10.10) the activity coefficient II,i, is close to 1.Setting in (10.6) equals to , get in the standard stateWe choose the standard state of each solute i as the
20、 fictitious state.Pretend that the behavior of that holds in the limit of infinite dilution holds for all values of xi.Physical Chemistry18Standard States for Nonideal-Solution ComponentsNonideal Solutions-6-4-20Fig. 9.20The Convention II solute standard state is the same as that used for solutes in
21、 an ideally dilute solution.(9.67)(9.68)The deviations of II,A and II,i from 1 measure the deviation of the solutions behavior from ideally dilute behavior.Physical Chemistry19Excess FunctionsNonideal Solutions(10.11)(10.12)The thermodynamic properties of nonideal (real) solutions may be expressed i
22、n terms of the excess functions, the difference between the observed thermodynamic function of solution and the function for a hypothetical ideal solution.Physical Chemistry20Excess FunctionsNonideal SolutionsExcess functions are found from mixing quantities.(9.44)ideal solution, const. T, P(9.46)Ph
23、ysical Chemistry21Regular SolutionNonideal Solutionswhen Deviations of the excess functions from zero indicate the extent to which the solutions are non-ideal. In this connection, a useful model system is the regular solution. or then A regular solutionregular solution can be thought of as one in wh
24、ich the two kinds of molecules are distributed randomly (as in an ideal solution) but have different energies of interaction with each other.Regular solutionPhysical Chemistry22Regular SolutionNonideal Solutionsnote excess chemical potentialIn a regular solution, lni is proportional to the inverse o
25、f T.Physical Chemistry23Athermal SolutionNonideal Solutionswhen or then The nonideality of regular solution is caused by the enthalpy effect (due to HE 0). Athermal solutionThe nonideality of athermal solution is caused by the entropy effect (due to SE 0). Physical Chemistry24Athermal SolutionNonide
26、al SolutionsthenIn an athermal solution, lni is independent of T.Physical Chemistry25Determination of activities and activity coefficientsNonideal Solutions(10.6)*nonideal solutionFrom data on phase equilibriuaFrom vapor-pressure measurementsConvention I(10.13)*ideal vapor, P not very high(10.14)orP
27、hysical Chemistry26Determination of activities and activity coefficientsNonideal Solutionsnonideal solutionConvention IIandideally dilute solution(9.63)*solute in ideally dilute solution, ideal vapor(9.64)*solvent in ideally dilute solution, ideal vapor(10.15)for i A, ideal vapor(10.16)ideal vapor,
28、P not very highVapor measurements find Ki since II,i=1 in very dilute solutionPhysical Chemistry27The Gibbs-Duhem EquationNonideal Solutions(4.73)*(9.23)The use of(10.17)(10.18)const. T, PPhysical Chemistry28The Gibbs-Duhem EquationNonideal Solutions(10.17)(10.18)const. T, PThe Gibbs-Duhem equationT
29、he significance of Gibbs-Gibbs-DuhemDuhem equationequation is that the chemical potentials of a mixture cannot change independently: in a binary mixture, if one increases the other must decreases. The same applies to all partial molar quantities.Physical Chemistry29Activity CoefficientsNonideal Solu
30、tions(10.23)On the Molality Scale(9.3)*The molality of solute imo 1 mol/kgPhysical Chemistry30Activity CoefficientsNonideal Solutionsmo 1 mol/kgdimensionlessdefine(10.24)(10.25)*(10.26)The molality-scale activity coefficient of solute iThe molality-scale standard state chemical potential of iPhysica
31、l Chemistry31Activity CoefficientsNonideal Solutions-6-4-202Fig. 10.5-6-4-20Fig. 9.20Physical ChemistryextrapolationIdeally dilute solution32Standard States for Nonideal-Solution ComponentsNonideal SolutionsSimilarly, solute molality-scale standard-state properties(9.67)(9.68)(10.27)The mole-fractio
32、n scale for solvent A(10.28)Physical Chemistry33Activity CoefficientsNonideal Solutions(10.23)On the Molar Concentration Scaleco 1 mol/dm3(9.1)*(10.29)The mole-fraction scale is used for solvent.(10.30)*Physical Chemistry34Activity CoefficientsNonideal Solutions(10.30)*(10.5)*0123456710.9Fig. 10.6He
33、nrys-law activity coefficientsmeasure deviations from Henrys lawRaoults-law activity coefficientmeasure deviations from Raoults lawPhysical Chemistry35SubstanceStandard stateConvention ISolvent AConvention IImolality scaleconcentration scalePure i at T, PPure A at T, PFictitious state Fictitious stateFictitious stateSummary of Standard States & Chemical PotentialsNonideal SolutionsTable 11.1 (P. 333, part)Physical Chemistry36HomeworkNonideal SolutionsPhysical ChemistryP314, Section 10.110.2, 10.3P315, Section 10.210.4P315, Section 10.310.6, 10.8P315, Section 10.410.12, 10.1337
