Physical Chemistry Chapter 10 Nonideal Solutions
1 Chapter 10 Nonideal Solutions Physical Chemistry
Physical Chemistry Solutions Ideal solutions B at T,Cat T,B-B, C-C △U=0 P P △V=0 mLx △H=0 B+C B-B. C-C △S>0 mux atT. P B-C △G<0 If B-B. C-C and B-C interactions are all different
2 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 mixU = 0 mixV = 0 mixH = 0 mixS 0 mixG 0
Physical Chemistry Solutions Nonideal solutions If B-B, C-C and B-C interactions are all different B at T.C at T △U≠0 IB-B C-C △≠0 △mH≠0 The molecules of one B+C B-BC-C, type cluster together atT. p B-C △S≈0 Reorganization of the molecules: orderly mixture Separation is spontaneous △G>0 mIX Liquids become immiscible or partially miscible
3 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 mixH 0 mixS 0 mixG 0 mixU 0 mixV 0 Separation is spontaneous Liquids become immiscible or partially miscible
Physical Chemistry Nonideal Solutions e The Wide Significance of Chemical Potential The chemicalpotential (u) does more than show how G varies with composition G=U+PV-TS U=-PV+S+G A general infinitesimal change in U for a system of variable composition can be written du=-Pdv-Vdp+ sdT+tds+dG Pdv-VerP+SaT+ TdS +(dP -SaT+u,dn ,+u,dn,+.) =-Pd+7aS+(m1+2dm2+…) At constant v and s thn+2oh2+…=∑
4 The chemical potential () does more than show how G varies with composition. The Wide Significance of Chemical Potential Nonideal Solutions G =U + PV −TS A general infinitesimal change in U for a system of variable composition can be written ( ) ( ) 1 1 2 2 1 1 2 2 = − + + + + + − + + + = − − + + = − − + + + PdV TdS dn dn VdP SdT dn dn PdV VdP SdT TdS dU PdV VdP SdT TdS dG At constant V and S = + + = i dU 1 dn1 2 dn2 i dni U = −PV +TS +G Physical Chemistry
Physical Chemistry Nonideal Solutions e The Wide Significance of Chemical Potential ence U S,V,n1(j≠i) In the same way, it is easy to deduce H aA 1 1 O I/SP ,T,n1(j≠i) H aA 1 S,V,n1(j≠i) S,P,n1(j≠i) V,T,n1(j≠i) G 7,P,n1(j≠)
5 The Wide Significance of Chemical Potential Nonideal Solutions hence S,V ,n ( j i) i i j n U = In the same way, it is easy to deduce , , ( ) , , ( ) , V T n j i i i S P n j i i i j j n A n H = = , , ( ) , , ( ) , , ( ) , , ( ) T P n j i i V T n j i i S P n j i i S V n j i i i j j j j n G n A n H n U = = = = Physical Chemistry
Physical Chemistry Nonideal Solutions Activity and Activity Coefficients u=u,+RTIn x idealsolution (9.42) 1≡1(T,P) idealsolution (9.43) 从1=1(T,P)+RThx,mr≠ A ideally dilute solution99 H42=C+Rrhx1,=(,P)b(600 u;=u:+RTIn x idealor ideallydilute solution(10.1) RT RT idealor ideallydilute solution (10.2)
6 Activity and Activity Coefficients Nonideal Solutions ln , ( , ) * RT x A T P o A A o A = A + T P RT xi for i A o i = i ( , ) + ln ideally dilute solution (9.59)* ideally dilute solution (9.60)* i i RT ln xi ideal solution * = + (9.42)* ( , ) ideal solution * i T P o i (9.43)* i ideal or ideally dilute solution o i id i = + RT ln x (10.1)* − = RT x o i id i i ln − = RT x o i id i i exp ideal or ideally dilute solution (10.2) Physical Chemistry
Physical Chemistry Nonideal Solutions Activity and Activity Coefficients X =exp ideal or ided RT llydilute solution (10.2) When the solution is neither ideal nor ideally dilute solution, a;=exP RT every solution (10.3) a; is defined as activity, a kind of "effective mole fraction u, =u;+Rt In a The difference between u, and e very solution (10.4) u d=RT In a,-RTInx;=RTIn/a
7 Activity and Activity Coefficients Nonideal Solutions − = RT x o i id i i exp ideal or ideally dilute solution (10.2) When the solution is neither ideal nor ideally dilute solution, − = RT a o i i i exp every solution (10.3) ai is defined as activity, a kind of “effective” mole fraction. i every solution o i = i + RT ln a (10.4)* − = − = i i i i i d i i x a RT ln a RT ln x RT ln The difference between and i id i Physical Chemistry
Physical Chemistry Nonideal Solutions Activity and Activity Coefficients u-u=RTIn, - x;=RT In x The ratio is the measure of the departure from ideal behavior activity coefficient every solution (10.5) The activity coefficient yi measures the degree of departure of substance is behavior from ideal or ideally dilute e behavior The activity a; is obtained from the mole fraction x by correcting for nonideality
8 Activity and Activity Coefficients Nonideal Solutions − = − = i i i i i d i i x a RT ln a RT ln x RT ln The ratio is the measure of the departurefrom ideal behavior. i i x a i i i x a ai = i xi every solution (10.5)* activity coefficient The activity coefficient i measures the degree of departure of substance i’s behavior from ideal or ideally dilute behavior. The activity ai is obtained from the mole fraction xi by correcting for nonideality. Physical Chemistry
Physical Chemistry Nonideal Solutions Activity and Activity Coefficients u;=ui+RTnyix (10.6) Since u; depends on Tand P, and the mole fraction x;, the activity a; and the activity coefficient ri depend on these variables a1=a1(T,P2x1,x2,…)2=y(T,P2x1,x2…) Note from(10.3)and(10. 5 )that a, and yi are dimensionless and nonnegative The task ofthermodynamics: show how a; and ri can be e obtained from experimental data. The task of statistical mechanics: show how ai and rican e be found from the intermolecular interactions in the solution
9 Activity and Activity Coefficients Nonideal Solutions Note from (10.3) and (10.5) that ai and i are dimensionless and nonnegative. i i (10.6)* o i i = + RT ln x Since i depends on T and P, and the mole fraction xi , the activity ai and the activity coefficient i depend on these variables: ( , , , , ), ( , , , , ) ai = ai T P x1 x2 i = i T P x1 x2 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
Physical Chemistry Nonideal Solutions Activity and Activity Coefficients a =e 12=l1 exp RT every solution (10.3) The activity a; is a measure of the chemical potential u;in the solution 个.a.个 Like the chemical potential, ai is a measure of the escaping e tendency of i from the solution The activity a is more convenient to use in numerical calculations than u, 10
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. , . i i a The activity a i is more convenient to use in numerical calculations than i − = RT a o i i i exp every solution (10.3) Physical Chemistry
