Chapter 10 Nonideal Solutions (1)

1、1,Chapter 10,Nonideal Solutions,Physical Chemistry,2,Ideal Solutions,Solutions,B-B, C-C,B-B, C-C, B-C,Physical Chemistry,If B-B, C-C and B-C interactions are all different,3,Nonideal Solutions,Solutions,Physical Chemistry,If B-B, C-C and B-C interactions are all different,The molecules of one type c

2、luster together,Reorganization of the molecules: orderly mixture,Separation is spontaneous,Liquids become immiscible or partially miscible,4,The chemical potential () does more than show how G varies with composition.,The Wide Significance of Chemical Potential,Nonideal Solutions,A general infinites

3、imal change in U for a system of variable composition can be written,At constant V and S,Physical Chemistry,5,The Wide Significance of Chemical Potential,Nonideal Solutions,hence,In the same way, it is easy to deduce,Physical Chemistry,6,Activity and Activity Coefficients,Nonideal Solutions,ideal or

4、 ideally dilute solution,(10.1)*,ideal or ideally dilute solution,(10.2),Physical Chemistry,7,Activity and Activity Coefficients,Nonideal Solutions,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.,eve

5、ry solution,(10.4)*,The difference between and,Physical Chemistry,8,Activity and Activity Coefficients,Nonideal Solutions,The ratio is the measure of the departure from ideal behavior.,activity coefficient,The activity coefficient i measures the degree of departure of substance is behavior from idea

6、l or ideally dilute behavior. The activity ai is obtained from the mole fraction xi by correcting for nonideality.,Physical Chemistry,9,Activity and Activity Coefficients,Nonideal Solutions,Note from (10.3) and (10.5) that ai and i are dimensionless and nonnegative.,(10.6)*,Since i depends on T and

7、P, and the mole fraction xi, the 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 s

8、olution.,Physical Chemistry,10,Activity and Activity Coefficients,Nonideal Solutions,Like 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 ai is more convenient to use in nu

9、merical calculations than i,Physical Chemistry,11,Activity and Activity Coefficients,Nonideal 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 values).,The activity ai is more convenient to use in

10、numerical calculations than i.,(b),Physical Chemistry,12,Standard States for Nonideal-Solution Components,Nonideal Solutions,Convention I,(10.7)*,for all components,Convention I is the same convention as that used for ideal solutions.,is independent of the choice of standard state,depends on the cho

11、ice of standard state,depends on the choice of standard state,Physical Chemistry,13,Standard States for Nonideal-Solution Components,Nonideal Solutions,Convention I,(10.7)*,for all components,depends on the choice of standard state,depends on the choice of standard state,depends on the choice of sta

12、ndard state,Therefore, we denote as convention I activities, activity coefficients and standard chemical potentials.,Physical Chemistry,14,Standard States for Nonideal-Solution Components,Nonideal Solutions,Convention I,For a nonideal solution, the deviation of the from 1 measure the deviation of th

13、e solutions behavior from ideal-solution behavior.,Physical Chemistry,15,Standard States for Nonideal-Solution Components,Nonideal Solutions,Convention I,Since the Convention I standard state of each solution is the pure substance, the Convention I standard state thermodynamic properties of i equal

14、the 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 Chemistry,16,Standard States for Nonideal-Solution Components,Nonideal Solutions,Co

15、nvention II,Convention 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 stand

16、ard state of the solvent A is pure liquid A at the T and P of the solution.,Physical Chemistry,17,Standard States for Nonideal-Solution Components,Nonideal Solutions,Convention II,(10.9)*,For each solute iA, Convention II chooses the standard state so that II,i goes to 1 in the limit of infinite dil

17、ution:,(10.10)*,Physical Chemistry,18,Standard States for Nonideal-Solution Components,Nonideal Solutions,When 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 state,We choose the sta

18、ndard 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 Chemistry,19,Standard States for Nonideal-Solution Components,Nonideal Solutions,The Convention II solute standard state is the same as

19、 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 Chemistry,20,Excess Functions,Nonideal Solutions,(10.11),(10.12),The thermodynamic properties of nonideal

20、(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 Chemistry,21,Excess Functions,Nonideal Solutions,Excess functions are found from mixing quantities.,

21、(9.44),Physical Chemistry,22,Regular Solution,Nonideal Solutions,when,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 solution can be thought of as one in which

22、 the two kinds of molecules are distributed randomly (as in an ideal solution) but have different energies of interaction with each other.,Regular solution,Physical Chemistry,23,Regular Solution,Nonideal Solutions,note,excess chemical potential,In a regular solution, lni is proportional to the inver

23、se of T.,Physical Chemistry,24,Athermal Solution,Nonideal Solutions,when,or,then,The nonideality of regular solution is caused by the enthalpy effect (due to HE 0).,Athermal solution,The nonideality of athermal solution is caused by the entropy effect (due to SE 0).,Physical Chemistry,25,Athermal So

24、lution,Nonideal Solutions,then,In an athermal solution, lni is independent of T.,Physical Chemistry,26,Determination of activities and activity coefficients,Nonideal Solutions,From data on phase equilibriua,From vapor-pressure measurements,Convention I,Physical Chemistry,27,Determination of activiti

25、es and activity coefficients,Nonideal Solutions,nonideal solution,Convention II,and,ideally dilute solution,(10.15),for i A, ideal vapor,(10.16),ideal vapor, P not very high,Vapor measurements find Ki since II,i=1 in very dilute solution,Physical Chemistry,28,The Gibbs-Duhem Equation,Nonideal Soluti

26、ons,(4.73)*,(9.23),The use of,(10.17),Physical Chemistry,29,The Gibbs-Duhem Equation,Nonideal Solutions,(10.17),The Gibbs-Duhem equation,The 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

27、must decreases. The same applies to all partial molar quantities.,Physical Chemistry,30,Activity Coefficients,Nonideal Solutions,(10.23),On the Molality Scale,(9.3)*,The molality of solute i,mo 1 mol/kg,Physical Chemistry,31,Activity Coefficients,Nonideal Solutions,mo 1 mol/kg,dimensionless,define,(10.24),(10.25)*,(10.26),The molality-scale activity coefficient of solute i,The molality-scale standard state chemical potential of i,Physical Chemistry,32,Activity Coefficients,Nonideal Solutions,Physical Chemistry,extrapolation,Ideally di