Chapter 10 Nonideal Solutions (2

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1、Chapter 10Nonideal SolutionsPhysical ChemistryPhysical ChemistrySimple SolutionModels for Nonelectrolyte Activity CoefficientsNonideal SolutionsW depends on T and P but not on the mole fractions.let z be the number of nearest neighbors of each molecule in the array.The intermolecular-interaction ene

2、rgy is approximated as the sum of nearest-neighbor interactions.)/()/()(21CBCBCBCBCCBBBCAmixnnnWnnnnnzNU,ln,ln2,2,BCICBIWxRTWxRT(10.31)If BB,CC,and BC are the interaction energies for adjacent B-B,C-C,and B-C pairs,respectively.The energy of mixingPhysical ChemistryPhysical ChemistryNonideal Solutio

3、nswhereFor two liquids B and C whose molecules have similar sizes and shapes,UHsoVmixmixmix,0)(21CCBBBCAzNW0,idmixmixEidmixmixSSSsoSSUHHTSHGmixmixEEEE),(PTWnnnnGCBCBEModels for Nonelectrolyte Activity CoefficientsPhysical ChemistryPhysical ChemistryNonideal SolutionsijnPTiEiInGRT,lnsimple solution m

4、odel(10.32)(Problem 10.4),(PTWnnnnGCBCBEModels for Nonelectrolyte Activity Coefficients)()()(12321nCBnCBCBCBCBEEmxxAxxAxxAARTxxnnGGRedlich-Kister equation(Margules equation)Physical ChemistryPhysical Chemistry,ln,ln2,2,BCICBIWxRTWxRT(10.31)Nonideal Solutionssimple solution modelsimple solution model

5、(10.32)Models for Nonelectrolyte Activity Coefficients)()()(12321nCBnCBCBCBCBEEmxxAxxAxxAARTxxnnGGRedlich-Kister equation(Margules equation),(PTWnnnnGCBCBEPhysical ChemistryPhysical ChemistrySolutions of ElectrolytesNonideal SolutionsNon-electrolyte solutionsThe solute is not present as ionsElectrol

6、yte solutionsThe solute is ionized and the ions generally interact strongly with each other.zzMMXM(10.33)s Numbers of ions in the chemical formula(integers)szCharges of ions in the chemical formula32232)(NOBaNOBa24422SONaSONa2424SOBaBaSO2:1 electrolyte1:2 electrolyte2:2 electrolytePhysical Chemistry

7、Physical ChemistryChemical Potentials in Electrolyte SolutionsNonideal SolutionsSince+and-are not measurable,define i(the chemical potentials of the electrolyte as a whole)in solutionzzMMXM(10.33)ijnPTiinG,jnPTnG,jnPTnG,AnPTiinG,(10.35)(10.34)Physical ChemistryPhysical ChemistryChemical Potentials i

8、n Electrolyte SolutionsNonideal SolutionsAnPTiinG,(10.35)AnPTiinVV,Similar definition for other partial molar properties of the electrolyte as a whole.dndndnVdPSdTdGAA(10.36)zzMMXM(10.33)fromiinnnnPhysical ChemistryPhysical ChemistryChemical Potentials in Electrolyte SolutionsNonideal SolutionsiAAdn

9、dnVdPSdTdG)(10.37)zzMMXM(10.33)Keep T,P,and nA constant and usingiinnnndndndnVdPSdTdGAA(10.36)AnPTiinG,(10.35)i(10.38)*1)(,ln),(,*AxAAxAAxRTPT(10.39)On the mole-fraction scale,the chemical potential of solventPhysical ChemistryPhysical ChemistryChemical Potentials in Electrolyte SolutionsNonideal So

10、lutions1)(,ln),(,*AxAAxAAxRTPT(10.39)mole-fraction activity coefficientinfinite dilutionOn the molality scale,the chemical potentials of electrolyte1,/1)/ln()/ln(kgmolmmmRTmmRTooooo(10.40)(10.41)i(10.38)*)/ln()/ln(ooooimmRTmmRT(10.42)/()/()()ln(ooooimmmmRTPhysical ChemistryPhysical ChemistryChemical

11、 Potentials in Electrolyte SolutionsNonideal SolutionsMolality-scale mean ionic activity coefficient(10.45)*(10.44)oooi)()()(10.43)*)/ln()/ln(ooooimmRTmmRT(10.42)/()/()()ln(ooooimmmmRT)/()/()ln(oooiimmmmRT(10.46)1(10.47)Physical ChemistryPhysical Chemistry(10.41)and(10.43)(10.41)1Chemical Potentials

12、 in Electrolyte SolutionsNonideal Solutions1(10.47)Aiiwnm(10.48)Stoichiometric molalityiimmmm)/()/()ln(oooiimmmmRT(10.46)iiimmmmm)()()()()()(10.49)(10.45)*)()()(10.50)()()(10.43)*definePhysical ChemistryPhysical ChemistryChemical Potentials in Electrolyte SolutionsNonideal Solutionsiiimmmmm)()()()()

13、()(10.49)()()(10.50)1/1oiimmandThe standard state of i as a whole is taken as the fictitious state witheelectrolytstrongmmRTmmmmmmoioiioioo)/ln()/()/()/()(10.51)()()(immm(10.49)/()/()ln(oooiimmmmRT(10.46)kgmolmi/)/1(hasPhysical ChemistryPhysical ChemistryChemical Potentials in Electrolyte SolutionsN

14、onideal Solutions)/(oiimma(10.52)Gibbs Energy of an Electrolyte SolutioneelectrolytstrongmmRToioii)/ln(10.51)givesThe activity ai of electrolyte i as a whole ioiiaRT ln(10.4)iAAdndnVdPSdTdG)(10.37)i(10.38)*iiAAdndnVdPSdTdG(10.53)iiAAnnG(10.54)PTconstdndniiAA,.0(10.55)Gibbs-Duhem Eq.Physical Chemistr

15、yPhysical ChemistryThe Debye-Hckel Theory of Electrolyte SolutionsNonideal SolutionswhereThe Debye-Hckel treatment assumes that the solution is very dilute.2/12/122/12/121ln,1lnmmmmBaIAIzBaIAIz(10.60)2/1,2/3,22/12,4)2(kTNeBkTeNAAroAAAroAA(10.61)jjjmmzI221(10.62)*(10.63)lnlnlnIonic strengthPhysical C

16、hemistryPhysical Chemistrylog of(10.43)The Debye-Hckel Theory of Electrolyte SolutionsNonideal Solutions(10.64)z+The electrolyte neutrality gives(10.64)0zzzzz2(10.64)z-zzz2+)(10.65)(|)(22zzzzzz2/12/122/12/121ln,1lnmmmmBaIAIzBaIAIz(10.60)(10.63)lnlnln(10.66)2/12/11|lnmmBaIAIzzPhysical ChemistryPhysic

17、al ChemistryThe Debye-Hckel Theory of Electrolyte SolutionsNonideal SolutionsFor very dilute solutions,Im is very small(10.66)2/12/11|lnmmBaIAIzz(10.67)2/12/1)/)(/(328.01)/(|510.0logomoommIAamIzz(10.68)2/1|lnmAIzz(10.69)2/1)/(|510.0logommIzzvery dilute aqueous solution,25oCvery dilute aqueous soluti

18、on,25oCvery dilute solutionPhysical ChemistryPhysical ChemistryThe Debye-Hckel Theory of Electrolyte SolutionsNonideal Solutions(10.69)2/1)/(|510.0logommIzzDebye-Hckel limiting law(10.67)2/12/1)/)(/(328.01)/(|510.0logomoommIAamIzz(10.70)2/12/1)/(1)/(|510.0logomommImIzzdilute aqueous solution,25oC(10

19、.71)/(30.0)/(1)/(|51.0log2/12/1omomommImImIzzat higher concentrations in H2O at 25oCPhysical ChemistryPhysical ChemistryHomeworkNonideal SolutionsPhysical ChemistryPhysical ChemistryP315-316,Section 10.510.16,10.18P316,Section 10.610.31,10.32,10.33P316,Section 10.810.38,10.39,10.40 Ionic Association

20、Nonideal Solutions(10.72)()()(solutionMXsolutionXsolutionMzzzzThe equilibrium for ion-pair formation(10.73)IPIPAAdndndndnVdPSdTdGIf no ion pairs were found,With ion-pair formation,zzMMXM(10.33)iinnnnIPiIPinnnnnn(10.74)IPIPIPiIPiAAdndndndndndnVdPSdTdG)()(Physical ChemistryPhysical ChemistryIonic Asso

21、ciationNonideal Solutions(10.72)()()(solutionMXsolutionXsolutionMzzzzUse of the equilibrium condition for the ion-pair formation(10.72)(10.75)dndnVdPSdTdGAA)(Same as(10.37)IPPhysical ChemistryPhysical ChemistryNonideal Gas MixturesNonideal SolutionsThe activity of a component of a nonideal gas mixtu

22、rebarafii1The fugacityfugacity fi of a component of any gas mixture RTaoiiiexp(10.94)ioiiaRTTln)(10.95)(10.96)barPwhereaPfoioi1(10.95)becomesoioiiPfRTTln)(10.97)*“effective P”Physical ChemistryPhysical ChemistryNonideal Gas MixturesNonideal Solutionsnonideal gas mixtureoioiiPfRTTln)(10.97)*oioiidiPP

23、RTTln)(6.4)*ideal gas mixture1)/(lim00iiPiiPforPasPf(10.98)The deviation of the fugacity fi of i from the partial pressure Pi in a gas mixture is measured by the fugacity coefficient i of gas i.PxPfiiiii(10.99)*For each component of an ideal gas mixture,1iiiandPfPhysical ChemistryPhysical ChemistryHomeworkNonideal SolutionsPhysical ChemistryPhysical ChemistryP317,Section 10.910.46,10.47P317,Section 10.1010.50,10.54,10.57P317-318,Section 10.1110.61,10.64P318,General10.70,10.71,10.74