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The properties of mixtures
Yongsik LeeMarch 2005
Thermodynamic description of mixtures
Yongsik Lee
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 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)
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
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 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 All gases mix spontaneously
Gibbs energy of mixing (ΔGmix) < 0
nA, p, T nB, p, T
nA+ nB, p, T
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
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 Chemical potential of
a solute Partial vapor pressure
(pJ) of each component in the mixture
Francois Raoult (1830-1901)
Raoult’s Law pJ = xJpJ* The partial vapor pressur
e 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
Ideal solution
Definition A hypothetical solution That obeys Raoult’s law throughout the compos
ition range from pure A to pure B No mixture is perfectly ideal! (deviations)
Real solution vs. ideal 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
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
Yongsik Lee
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
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
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
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 t
he membrane Osmotic pressure (Π)
Jacobus H. van 't Hoff (1852-1911) Nobel Prize 1901
The first nobel prize in chemistry
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 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
Yongsik Lee2005. 4. 7
Phase Diagram 물질의 상전이도 (phase diagram)
물질의 온도를 일정하게 하고 압력을 변화시키면 어떤 특정한 압력에서 물질의 두 상 사이의 전이 (p
hase transition) 가 일어나게 된다 . 이 과 정 을 많 은 다 른 온 도 에 서 되 풀 이 하 면
평형곡선이 완성된다 . 상전이도의 구성
가로축에 온도 , 세로축에 압력을 표시하고 주어진 온도와 압력에서 가장 안정된 상을 표시한다 .
Mixtures of volatile liquids Temp(T)-composition(xA) dia
gram Vapor in equilibrium is also
a mixture of two Composition is different (ti
e line) Tie line
A line joining two phases that are in equilibrium with each other
Fractional distillation
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 ( 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 , 감미
료 , 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
azeotrope
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
Iodine in heptane/water The two layers are then mi
xed 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
Do not mix together in all proportions
Consists of two liquid phases
Nitrobenzene/hexane Use lever rule
Lever rule Lever rule
Mixture of xA
(Amount of phase of a”)(l”) = (amount of phase of a’)(a’)
Critical solution temperature Upper critical solution temperatu
re (Tuc) Upper limit of temperature at w
hich 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 misc
ible because they form a weak complex
Water(A) & 2-methyl-1-propanol(B)
Liquid-solid phase diagrams A system of Two metals
(alloy) At xA = a1, molten liquid c
omposition Liquid + A (pure solid) B richer solution b3 + pure
solid A At xA = e, almost pure A +
almost pure B
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
Ultrapurity and controlled impurity
Nine nine pure = 99.9999999%
Wafer stepper for lithography
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
exercises
6-4, 6-5, 6-16, 6-18, 6-27
References http://www.whfreeman.com/ECHEM/INDEX.HTML http://www.schaft.org/eri/people.html http://cwx.prenhall.com/bookbind/pubbooks/hillchem3/medi
alib/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
http://fox.rollins.edu/~tlairson/ecom/ E-commerce lecture
http://www.fbh-berlin.de/english/pres/pres_3.html stepper
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