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4.1. Partial molar quantity

Chapter 4 Simple mixture. 4.1. Partial molar quantity. V ， U ， H ， S ， A ， G. Multicomponent system Z ＝ f ( T ， p ， n A ， n B ， ……). Total differential. Z B   partial molar quantity. Partial molar volume. Z B =constant. if d T ＝ 0 ， d p ＝ 0. For example

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4.1. Partial molar quantity

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  1. Chapter 4 Simple mixture 4.1. Partial molar quantity V，U，H，S，A，G Multicomponent system Z＝ f (T，p，nA，nB，……) Total differential ZB partial molar quantity

  2. Partial molar volume

  3. ZB=constant if dT＝0，dp＝0 For example V ＝ nAVA＋nBVB＋……＋ nSVS

  4. (1) T=constant and p= constant n(C, C ≠ B)

  5. (2) ZB is intensive property (3) ZB = f (T，p，nA，nB，……) (4) pure substance ZB = ZM

  6. 4.2 Chemical potential of mixture 4.2.1 Chemical potential of pure ideal gas d=Vmdp

  7. 4.2.2. µB of component B in ideal gas mixture pB＝xBp pB＝pxB

  8. pure ideal gas pure real gas f: fugacity : fugacity coefficient 3.2.3. Chemical potential of pure real gas

  9. 3.2.4. µB of component B in real gas mixture fB＝xBfB* Lewis-Randall rule

  10. Raoult law Mixtures that obey Raoult’s law throughout the compositions range from pure A to pure A are called ideal solutions. 4.2.5 Ideal solutions

  11. A pictorial representation of the molecular basis of Raoult's law. The large spheres represent solvent molecules at the surface of a solution, and the small spheres are solute molecules. The latter hinder the escape of solvent molecules into the vapour, but do not hinder their return.

  12. (1) (2) (3) (4) 4.2.6. Partial molar properties of ideal solutions

  13. 4.2.7. Mixing properties of ideal solutions (1) mixV = 0 (2) mixH = 0 (3) mixS = -RnBlnxB>0 (4) mixG = RTnBlnxB<0

  14. 4.2.8. Gas-liquid equilibrium of ideal solutions (1) Composition of solution dependence of vapor pressure of solution xA＝1－xB

  15. T=constant {p} {pA*} p=f(xB) {pB*} pA p=f (y B) pB 0 1 xB (y B) A B

  16. (2)Relation between yB and xB pA＝yAp pB＝yBp

  17. T=constant {p} {pA*} p=f(xB) {pB*} pA p=f (y B) pB 0 1 xB (y B) A B (3) Vapor composition of solution dependence of vapor pressure of solution

  18. p B , pA T x ,xA B pB=kx,BxB 4.2.9 Ideal-dilute solutions (1). Henry law kx,Bhenry coefficient kx,B henry coefficient

  19. In a dilute solution, the solvent molecules (the green spheres) are in an environment that differs only slightly from that of the pure solvent. The solute particles, however, are in an environment totally unlike that of the pure solute. (2). Definition of ideal-dilute solutions Mixtures for which the solute obeys Henry’s law and the solvent obeys Raoult’s law are called ideal-solute solutions.

  20. 4.3 Dilute solution and real solution 4.3.1 dilute solution

  21. 1. The depression of vapor-pressure 2. The depression of freezing point kf freezing point lowering coefficient

  22. {p} pex pure solvent solution {Tb} 3. The elevation of boiling point The solute is involatile kb—boiling point elevation coefficient.

  23. 4. Osmotic pressure

  24. p {p} {p} p pB pA pA pB { kx,A} { kx,B} x B 0 1 x B 0 1 C3H6O(A) CS2(B) C3H6O(A) CHCl3(B) 4.3.2 Real solutions 1. Positive deviation and negative deviation

  25. ideal solution ideal solution real solution 2. Activity and activity coefficient ax,B: activity x,B: activity coefficient real solution

  26. Clapayron equation (ii) Perfect gas pVm*(g)=RT Clausius-Clapayron equation 4.4Clausius-Clapayron equation For liquid(or solid)-vapor boundary (i)[Vm*(g)－ Vm*( l)]≈ Vm*(g)

  27. T,p T,p liquid vapor ln{p} Solid vapor

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