1. The properties of mixtures Yongsik Lee March 2005

2. Thermodynamic description of mixtures Yongsik Lee

3. Partial molar properties  Definition Contribution (per mole) that a substance makes to an overall property of a mixture  Example Partial molar volume (V J ) Partial molar Gibbs energy (G J )

4. Partial molar volume  Example : V J Water/ethanol mixture What is the total volume of a mixture of 50.0 g of ethanol and 50.0 g of water at 25 ℃ ? 1 mol of water + pure water = 18 cm 3 1 mol of water + pure ethanol = ?

5. Partial molar volume (V J )  Water/ethanol mixture V J V = n A V A + n B V B 1 mol of water + pure water = 18 cm 3 1 mol of water + pure EtOH = 14 cm 3 2.77 mol water + 1.09 mol EtOH Mole fraction  X EtOH = 0.282

6. Partial molar Gibbs energy  Contribution of J to the total Gibbs energy of a mixture G = n A G A + n B G B  Chemical potential (μ) Partial molar Gibbs energy G = n A μ A + n B μ B

7. Variation of chemical potential  For a perfect gas, G(P f )-G(P i )=nRT ln(P f /P i ) G m (P f ) = G m (P i ) + RT ln(P f /P i )  Set P f =P and P i =P°(the standard pressure, 1 bar) G m (P) = G m (P°) + RT ln(P/P°)  For a mixture of perfect gases, G m (P) = G m (P°) + RT ln(P/P°) μ J = μ J ° + RT ln(P J /P°) μ J = μ J ° + RT lnP J  μ J ° = Standard chemical potential of the gas J

8. Spontaneous mixing  All gases mix spontaneously Gibbs energy of mixing (ΔG mix ) < 0 n A, p, Tn B, p, T n A + n B, p, T

9. Gibbs energy of mixing  ΔG mix = G f - G i G i = n A μ A + n B μ B = n A (μ A ° + RT ln p) + n B (μ B ° + RT ln p) G f = n A (μ A ° + RT ln x A p) + n B (μ B ° + RT ln x B p)  consider partial pressure for A and B  ΔG mix = n A (RT ln x A ) + n B (RT ln x B ) = nRT[x A ln x A + x B ln x B ]  (ΔG mix ) < 0

10. Entropy of mixing  ΔG mix = nRT[x A ln x A + x B ln x B ] With ΔG = ΔH - T ΔS  ΔH =0 then  ΔS mix = -nR[x A ln x A + x B ln x B ]  The increase in entropy of the system is the driving force of the mixing!

11. Raoult’s law  Chemical potential of a solute  Partial vapor pressure(p J ) of each component in the mixture  Francois Raoult (1830-1901)

12. Raoult’s Law  p J = x J p J *  The partial vapor pressure of a substance(p J ) in a mixture is proportional to its mole fraction(x J ) in the solution and its vapor pressure when pure(p J *)  Limiting law ([J]→0)

13. Molecular origin of Raoult’s law

14. Ideal solution  Definition A hypothetical solution That obeys Raoult’s law throughout the composition range from pure A to pure B No mixture is perfectly ideal! (deviations)

15. Real solution vs. ideal solution

16. Ideal dilute solution  Henry’s law p B =x B K B K B = Henry’s law constant Only at low [B]  Ideal-dilute solution Solute B obeys Henry’s

17. Real solution  Activity(a J ) = effective concentration  μ J = μ J ° + RT ln a J Always true at any concentration For ideal solution, a J = x J For ideal-dilute solution,  a A = γ A x A, a B = γ B [B],  Activity coefficient  γ A →1 as x A →1 ; γ B →1 as [B] →0 For a pure liquid or solid, a=1

18. Colligative properties Yongsik Lee

19. Colligative properties  Definition “Depending on the collection” Depending on the number  not the nature  Chemical potential equilibrium  Examples Boiling point, freezing point modification Osmosis, osmotic pressure

20. Modification of bp and fp

21. Condition of solute  용질의 조건 Solute is not volatile  No concentration to the vapor phase Solute does not dissolve in solid solvent  ΔT b = K b b(B) Ebullioscopic constant  ΔT f = K f b(B) Cryoscopic constant

22. osmosis

23.  Macromolecule is uncharged  Macromolecule can not pass through the membrane  Solvent flows from right to left, diluting the macromolecular sol’n  As the dilution takes place, the solutionn vol. increases and the level in the capillary rises Osmotic Pressure

24. Osmotic pressure

25. osmosis  movement of a solvent  through a semipermeable membran ( 반투막 )  into a solution of higher solute concentration  to equalize the concentrations of solute on the two sides of the membrane  Osmotic pressure (Π)

26. Jacobus H. van 't Hoff (1852-1911) Nobel Prize 1901 The first nobel prize in chemistry

27. Van’t Hoff equation  At Equilibrium μ(solvent in the solution, p+Π) = μ(pure solvent, p)  Van’t Hoff equation μ*(pure solvent, p)= μ(x A solvent, p+Π) μ*(pure solvent, p)= μ*(p+Π) + RT ln x A μ*(pure solvent, p)= μ*(p) + V A Δp + RT ln x A 0 = V A Δp + RT ln x A V A Π = RTx B  Useful for Molecular weight determination Macromolecules – MALDI

29. Van’t Hoff Coefficient  Van’t Hoff 계수 (i) 용액에 있는 입자의 몰 수와 용액에 녹아 있는 용질의 몰 수 비율  실제값과 이론값이 다른 이유 이온들이 이온쌍으로 행동 전하량이 큰 이온의 경우 두드러진다 ΔT = imK

30. Phase diagrams of mixtures Yongsik Lee 2005. 4. 7

31. Phase Diagram  물질의 상전이도 (phase diagram) 물질의 온도를 일정하게 하고 압력을 변화시키면 어떤 특정한 압력에서 물질의 두 상 사이의 전이 (phase transition) 가 일어나게 된다. 이 과정을 많은 다른 온도에서 되풀이하면 평형 곡선이 완성된다.  상전이도의 구성 가로축에 온도, 세로축에 압력을 표시하고 주어 진 온도와 압력에서 가장 안정된 상을 표시한다.

32. Mixtures of volatile liquids  Temp(T)-composition(x A ) diagram  Vapor in equilibrium is also a mixture of two  Composition is different (tie line)  Tie line A line joining two phases that are in equilibrium with each other

33. Fractional distillation

34. Distiller  술은 보통 제조방법에 따라 세 가지로 분류된다. 양조주 증류주 재제주 ( 혼성주 )  양조주 ( 釀造酒 )- 발효주 과실이나 곡류 등에 함유된 당분이나 녹말을 효모의 작용에 의해 발효 알코올분이 비교적 낮아 변질되기 쉬 운 단점이 있으며, 원료 성분에서 오는 특유의 향기와 부 드러운 맛이 있다. 막걸리, 과실주 ( 포도주, 사과주 등 ), 맥주, 청주

35. 증류주  증류주 ( 蒸溜酒 ) 양조주를 다시 증류하므로써 알코올분이 비 교적 높으며 증류과정에서 불순물을 대부분 제거했다. 마시고 난후 양조주에 비해 숙취 가 덜한 것도 이때문이다. 와인을 증류한 브랜디, 곡주를 증류한 소주, 보드카, 고량주, 맥주를 증류한 위스키, 사탕 수수주를 증류한 럼 등이 증류주에 속하며 이밖에도 선인장주를 증류한 데킬라 따위를 들 수 있다. 증류주는 양조주와 달리 오래 묵으면 묵을 수록 주질이 좋아진다.  재제주 ( 再製酒 ) 양조주나 증류주 등에 과실, 향료, 감미료, 약초 따위를 첨가하여 침출 또는 증류하여 만든 술을 말한다. 혼성주 ( 混成酒 ) 라고도 하는 이 주류는 감미 ( 甘味 ) 및 혼입 재료에서 오는 독특한 향기 가 있는 것이 특징이다. 재제주류에 속하는 술로는 매실주, 인삼주, 오가피주 등을 들 수 있다.

36. Oil refining

37. azeotrope

38.  Azeotrope Greek words for “boiling without changing” No furthur separation by distillation  High-boiling azeotrope HCl/water mixture 80%wt, boils at 108.6 ℃  Low-boiling azeotrope EtOH/water 4%wt, boils at 78 ℃

39. Liquid-liquid phase diagrams

40. Iodine in heptane/water  The two layers are then mixed by "vigorously flicking" the test tube with the fingers of the right hand.  The purple color is the formation of I 2  I 2 is more soluble in heptane than water.  http://www.sfu.ca/chemistr y/students/courses/chem1 10- 111/techniques/hept_iodin e.htm

41. Partially miscible liquids  Partially miscible Do not mix together in all proportions Consists of two liquid phases Nitrobenzene/hexane Use lever rule

42. Lever rule  Lever rule Mixture of x A (Amount of phase of a”)(l”) = (amount of phase of a’)(a’)

43. Critical solution temperature  Upper critical solution temperature (T uc ) Upper limit of temperature at which phase separation occurs Fully miscible when T> T uc  Because of thermal motion of molecules  Gibbs energy of mixing is negative  Lower c. s. Temperature(T lc ) Two components are more miscible because they form a weak complex

44. Water(A) & 2-methyl-1-propanol(B)

45. Liquid-solid phase diagrams  A system of Two metals (alloy) At x A = a1, molten liquid composition Liquid + A (pure solid) B richer solution b3 + pure solid A At x A = e, almost pure A + almost pure B

46. Eutectic composition  Melting without change of composition  Melting at the lowest temperature  Solidifies at a single definite temperature Without gradually unloading one or other of the components from the liquid Microcrystal mixtures  Example Solder 67 wt% Sn + 33 wt% Pb (Te = 183 ℃ )

47. Thermal analysis for eutectic point

48. Ultrapurity and controlled impurity Nine nine pure = 99.9999999%

50. Wafer stepper for lithography

51. Ingot pulling  The base material for silicon is a sand. The sand is melted and refined to a high level of purity.  An ingot is drawn from molten pure silicon in a crucible. This ingot starts by dipping a seed crystal in the melt and pulling it back at a controlled speed and temperature profile.  The resulting cylindrical ingot has the single crystal structure required to manufacture active devices.

52. Zone refining

53. exercises  6-4, 6-5, 6-16, 6-18, 6-27

54. References  http://www.whfreeman.com/ECHEM/INDEX.HTML  http://www.schaft.org/eri/people.html  http://cwx.prenhall.com/bookbind/pubbooks/hillchem3/mediali b/media_portfolio/17.html Hill’s general chemistry  http://www.personal.psu.edu/ruc114/egee101.html Oil refining  http://www.theodoregray.com/PeriodicTable/Elements/Solid/in dex.s7.html Various elements  http://www.ami.ac.uk/courses/ami4019_bim/u02/index.asp Wafer processing

55. References  http://fox.rollins.edu/~tlairson/ecom/ E-commerce lecture  http://www.fbh- berlin.de/english/pres/pres_3.html stepper

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