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

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. If you alter, transform, or build upon this work, you may distribute the r

esulting work only under a license identical to this one.

For any reuse or distribution, you must make clear to others the license terms of this work.

Any of these conditions can be waived if you get permission from the copyright holder.

Your fair use and other rights are in no way affected by the above.