物理化學(xué)英文課件：chapter10-1 Nonideal Solutions

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 different2Nonideal SolutionsSolutionsB at T, PC at T, PB + C at T, PB-B, C-CB-B, C-C, B-CPhysical ChemistryIf B-B, C-C

2、 and B-C interactions are all differentThe molecules of one type cluster togetherReorganization of the molecules: orderly mixtureSeparation is spontaneousLiquids become immiscible or partially miscible3The chemical potential () does more than show how G varies with composition.The Wide Significance

3、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 easy to deducePhysical Chemistry5Activity and A

4、ctivity CoefficientsNonideal Solutions(9.59)*ideally dilute solution(9.60)*ideally dilute solutionideal solution(9.42)*ideal solution(9.43)*ideal or ideally dilute solution(10.1)*ideal or ideally dilute solution(10.2)Physical Chemistry6Activity and Activity CoefficientsNonideal Solutionsideal or ide

5、ally dilute solution(10.2)When the solution is neither ideal nor ideally dilute solution, every solution(10.3)ai is defined as activity, a kind of “effective” mole fraction.every solution(10.4)*The difference between andPhysical Chemistry7Activity and Activity CoefficientsNonideal SolutionsThe ratio

6、 is the measure of the departure 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 behavior. The activity ai is obtained from the mole fraction xi by correcting for nonidealit

7、y.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, the activity ai and the activity coefficient i depend on these variables:The task of therm

8、odynamics: 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 Chemistry9Activity and Activity CoefficientsNonideal SolutionsLike the chemical potential, ai is a meas

9、ure 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 ai is more convenient to use in numerical calculations than ievery solution(10.3)Physical Chemistry10Activity and Activity CoefficientsNonideal Solutions(c) ai c

10、an 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 values). The activity ai is more convenient to use in numerical calculations than i. (b)Physical Chemistry11Standard States for Nonideal-Solution ComponentsNonideal So

11、lutionsConvention I(10.7)*for all componentsConvention I is the same convention as that used for ideal solutions.is independent of the choice of standard statedepends on the choice of standard stateevery solution(10.3)depends on the choice of standard statePhysical Chemistry12Standard States for Non

12、ideal-Solution ComponentsNonideal SolutionsConvention I(10.7)*for all componentsdepends on the choice of standard stateevery solution(10.3)depends on the choice of standard statedepends on the choice of standard stateTherefore, we denote as convention I activities, activity coefficients and standard

13、 chemical potentials. Physical Chemistry13Standard States for Nonideal-Solution ComponentsNonideal SolutionsConvention Iideal 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-solut

14、ion behavior.(10.7)*for all components(10.8)*for each iPhysical Chemistry14Standard States for Nonideal-Solution ComponentsNonideal SolutionsConvention ISince the Convention I standard state of each solution is the pure substance, the Convention I standard state thermodynamic properties of i equal t

15、he corresponding properties of pure i.Convention I puts all the components on the same footing and does not single out one component as the solvent. Convention I is often called the symmetrical convention. Physical Chemistry15Standard States for Nonideal-Solution ComponentsNonideal SolutionsConventi

16、on IIConvention II is chosen when one wants to treat one solution component (the solvent A) differently 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 convention. The Convention II standard sta

17、te of the solvent A is pure liquid A at the T and P of the solution.(10.6)*nonideal 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

18、 to 1 in the limit of infinite dilution:(10.10)*Physical Chemistry17Standard 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 ,

19、get in the standard stateWe choose the standard state of each solute i as the 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. 9.20Th

20、e Convention II solute standard state is the same as that used for solutes in 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

21、)The thermodynamic properties of nonideal (real) solutions may be expressed in 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 functio

22、ns are found from mixing quantities.(9.44)ideal solution, const. T, P(9.46)Physical 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 soluti

23、on. or then A regular solution can be thought of as one in which 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 potenti

24、alIn a regular solution, lni is proportional to the inverse of 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 effe

25、ct (due to SE 0). Physical Chemistry24Athermal SolutionNonideal 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 measureme

26、ntsConvention I(10.13)*ideal vapor, P not very high(10.14)orPhysical 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 solutio

27、n, ideal vapor(10.15)for i A, ideal vapor(10.16)ideal vapor, 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 EquationNonidea

28、l Solutions(10.17)(10.18)const. T, PThe Gibbs-Duhem equationThe significance of Gibbs-Duhem equation 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 Che

29、mistry29Activity CoefficientsNonideal Solutions(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 iPhysical Chemistry31Activity CoefficientsNonideal Solutions-6-4-202Fig. 10.5-6-4-20Fig. 9.20Physical ChemistryextrapolationIdeally dilute solution32Standard States for Nonideal-Solution ComponentsNo