Published on January 4, 2008
The properties of mixtures: The properties of mixtures Yongsik Lee March 2005 Thermodynamic description of mixtures: Thermodynamic description of mixtures Yongsik Lee Partial molar properties: Partial molar properties Definition Contribution (per mole) that a substance makes to an overall property of a mixture Example Partial molar volume (VJ) Partial molar Gibbs energy (GJ) Partial molar volume: Partial molar volume Example : VJ 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 cm3 1 mol of water + pure ethanol = ? Partial molar volume (VJ): Partial molar volume (VJ) Water/ethanol mixture VJ V = nAVA + nBVB 1 mol of water + pure water = 18 cm3 1 mol of water + pure EtOH = 14 cm3 2.77 mol water + 1.09 mol EtOH Mole fraction X EtOH = 0.282 Partial molar Gibbs energy: Partial molar Gibbs energy Contribution of J to the total Gibbs energy of a mixture G = nAGA + nBGB Chemical potential (μ) Partial molar Gibbs energy G = nAμ A + nBμ B Variation of chemical potential: Variation of chemical potential For a perfect gas, G(Pf)-G(Pi)=nRT ln(Pf/Pi) Gm(Pf) = Gm(Pi) + RT ln(Pf/Pi) Set Pf=P and Pi=P°(the standard pressure, 1 bar) Gm(P) = Gm(P°) + RT ln(P/P°) For a mixture of perfect gases, Gm(P) = Gm(P°) + RT ln(P/P°) μJ = μJ° + RT ln(PJ/P°) μJ = μJ° + RT lnPJ μJ° = Standard chemical potential of the gas J Spontaneous mixing: Spontaneous mixing All gases mix spontaneously Gibbs energy of mixing (ΔGmix) < 0 nA, p, T nB, p, T nA+ nB, p, T Gibbs energy of mixing: Gibbs energy of mixing ΔGmix = Gf - Gi Gi = nAμ A + nBμ B = nA(μA° + RT ln p) + nB(μB° + RT ln p) Gf= nA(μA° + RT ln xAp) + nB(μB° + RT ln xBp) consider partial pressure for A and B ΔGmix = nA(RT ln xA) + nB(RT ln xB) = nRT[xAln xA + xBln xB] (ΔGmix) < 0 Entropy of mixing: Entropy of mixing ΔGmix = nRT[xAln xA + xBln xB] With ΔG = ΔH - T ΔS ΔH =0 then ΔSmix = -nR[xAln xA + xBln xB] The increase in entropy of the system is the driving force of the mixing! Raoult’s law: Raoult’s law Chemical potential of a solute Partial vapor pressure(pJ) of each component in the mixture Francois Raoult (1830-1901) Raoult’s Law: Raoult’s Law pJ = xJpJ* The partial vapor pressure of a substance(pJ) in a mixture is proportional to its mole fraction(xJ) in the solution and its vapor pressure when pure(pJ*) Limiting law ([J]→0) Molecular origin of Raoult’s law: Molecular origin of Raoult’s law Ideal solution: 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) Real solution vs. ideal solution: Real solution vs. ideal solution Ideal dilute solution: Ideal dilute solution Henry’s law pB=xBKB KB= Henry’s law constant Only at low [B] Ideal-dilute solution Solute B obeys Henry’s Real solution: Real solution Activity(aJ) = effective concentration μJ = μJ° + RT ln aJ Always true at any concentration For ideal solution, aJ = xJ For ideal-dilute solution, aA = γAxA, aB = γB[B], Activity coefficient γA →1 as xA →1 ; γB →1 as [B] →0 For a pure liquid or solid, a=1 Colligative properties: Colligative properties Yongsik Lee Colligative properties: 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 Modification of bp and fp: Modification of bp and fp Condition of solute: Condition of solute 용질의 조건 Solute is not volatile No concentration to the vapor phase Solute does not dissolve in solid solvent ΔTb = Kb b(B) Ebullioscopic constant ΔTf = Kf b(B) Cryoscopic constant osmosis: osmosis Osmotic Pressure: 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 Osmotic pressure: Osmotic pressure osmosis: 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) Jacobus H. van 't Hoff (1852-1911) Nobel Prize 1901: Jacobus H. van 't Hoff (1852-1911) Nobel Prize 1901 The first nobel prize in chemistry Van’t Hoff equation: 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(xA solvent, p+Π) μ*(pure solvent, p)= μ*(p+Π) + RT ln xA μ*(pure solvent, p)= μ*(p) + VAΔp + RT ln xA 0 = VAΔp + RT ln xA VAΠ = RTxB Useful for Molecular weight determination Macromolecules – MALDI Van’t Hoff Coefficient: 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 Phase diagrams of mixtures: Phase diagrams of mixtures Yongsik Lee 2005. 4. 7 Phase Diagram: 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 평형곡선이 완성된다. 상전이도의 구성 가로축에 온도, 세로축에 압력을 표시하고 주어진 온도와 압력에서 가장 안정된 상을 표시한다. Mixtures of volatile liquids: Mixtures of volatile liquids Temp(T)-composition(xA) 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 Fractional distillation: Fractional distillation Distiller: 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 쉬운 단점이 있으며, 원료 성분에서 오는 특유의 향기와 부드러운 맛이 있다. 막걸리, 과실주(포도주, 사과주 등), 맥주, 청주 증류주: 증류주 증류주(蒸溜酒) 양조주를 다시 증류하므로써 알코올분이 비교적 높으며 증류과정에서 불순물을 대부분 제거했다. 마시고 난후 양조주에 비해 숙취가 덜한 것도 이때문이다. 와인을 증류한 브랜디, 곡주를 증류한 소주, 보드카, 고량주, 맥주를 증류한 위스키, 사탕수수주를 증류한 럼 등이 증류주에 속하며 이밖에도 선인장주를 증류한 데킬라 따위를 들 수 있다. 증류주는 양조주와 달리 오래 묵으면 묵을수록 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 향기가 있는 것이 특징이다. 재제주류에 속하는 술로는 매실주, 인삼주, 오가피주 등을 들 수 있다. Oil refining: Oil refining azeotrope: azeotrope Slide38: 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℃ Liquid-liquid phase diagrams: Liquid-liquid phase diagrams Iodine in heptane/water: 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 I2 I2 is more soluble in heptane than water. http://www.sfu.ca/chemistry/students/courses/chem110-111/techniques/hept_iodine.htm Partially miscible liquids: Partially miscible liquids Partially miscible Do not mix together in all proportions Consists of two liquid phases Nitrobenzene/hexane Use lever rule Lever rule: Lever rule Lever rule Mixture of xA (Amount of phase of a”)(l”) = (amount of phase of a’)(a’) Critical solution temperature: Critical solution temperature Upper critical solution temperature (Tuc) Upper limit of temperature at which phase separation occurs Fully miscible when T> Tuc Because of thermal motion of molecules Gibbs energy of mixing is negative Lower c. s. Temperature(Tlc) Two components are more miscible because they form a weak complex Water(A) & 2-methyl-1-propanol(B): Water(A) & 2-methyl-1-propanol(B) Liquid-solid phase diagrams: Liquid-solid phase diagrams A system of Two metals (alloy) At xA = a1, molten liquid composition Liquid + A (pure solid) B richer solution b3 + pure solid A At xA = e, almost pure A + almost pure B Eutectic composition: 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℃) Thermal analysis for eutectic point: Thermal analysis for eutectic point Ultrapurity and controlled impurity: Ultrapurity and controlled impurity Nine nine pure = 99.9999999% Wafer stepper for lithography: Wafer stepper for lithography Ingot pulling: 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. Zone refining: Zone refining exercises: exercises 6-4, 6-5, 6-16, 6-18, 6-27 References: References http://www.whfreeman.com/ECHEM/INDEX.HTML http://www.schaft.org/eri/people.html http://cwx.prenhall.com/bookbind/pubbooks/hillchem3/medialib/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/index.s7.html Various elements http://www.ami.ac.uk/courses/ami4019_bim/u02/index.asp Wafer processing References: References http://fox.rollins.edu/~tlairson/ecom/ E-commerce lecture http://www.fbh-berlin.de/english/pres/pres_3.html stepper Creative Commons: Creative Commons Attribution-NonCommercial-ShareAlike 2.0 You are free: to copy, distribute, display, and perform the work to make derivative works Under the following conditions: Attribution. You must give the original author credit. Noncommercial. You may not use this work for commercial purposes. Share Alike. 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