Chapter 10 Nonideal Solutions Physical Chemistry 1 Ideal Solutions Solutions B at T, P C at T, P B + C at T, P B-B, C-C B-B, C-C, B-C Physical Chemistry If B-B, C-C and B-C interactions are all different 2 Nonideal Solutions Solutions B at T, P C at T, P B + C at T, P B-B, C-C B-B, C-C, B-C Physical Chemistry If B-B, C-C and B-C interactions are all different The molecules of one type cluster together Reorganization of the molecules: orderly mixture Separation is spontaneous Liquids become immiscible or partially miscible 3 The chemical potential () does more than show how G varies with composition. The Wide Significance of Chemical Potential Nonideal Solutions A general infinitesimal change in U for a system of variable composition can be written At constant V and S Physical Chemistry 4 The Wide Significance of Chemical Potential Nonideal Solutions hence In the same way, it is easy to deduce Physical Chemistry 5 Activity and Activity Coefficients Nonideal Solutions (9.59)*ideally dilute solution (9.60)*ideally dilute solution ideal solution(9.42)* ideal solution(9.43)* ideal or ideally dilute solution(10.1)* ideal or ideally dilute solution(10.2) Physical Chemistry 6 Activity and Activity Coefficients Nonideal Solutions ideal or ideally 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 and Physical Chemistry 7 Activity and Activity Coefficients Nonideal Solutions The ratio is the measure of the departure from ideal behavior. every solution(10.5)* activity coefficient The 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 nonideality. Physical Chemistry 8 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 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 solution. Physical Chemistry 9 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 numerical calculations than i every solution(10.3) Physical Chemistry 10 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 numerical calculations than i. (b) Physical Chemistry 11 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 choice of standard state every solution(10.3) depends on the choice of standard state Physical Chemistry 12 Standard States for Nonideal-Solution Components Nonideal Solutions Convention I (10.7)*for all components depends on the choice of standard state every solution(10.3) depends on the choice of standard state depends on the choice of standard state Therefore, we denote as convention I activities, activity coefficients and standard chemical potentials. Physical Chemistry 13 Standard States for Nonideal-Solution Components Nonideal Solutions Convention I ideal or ideally dilute solution(10.1)* (10.6)*nonideal solution For 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 i Physical Chemistry 14 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 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 15 Standard States for Nonideal-Solution Components Nonideal Solutions Convention 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 standard