결정화공정의상평형의 원리와이해 - cheric...결정화공정의상평형의...

결정화 공정의 상평형의원리와 이해

2007년 8월 20일

결정화 분리기술 사업단

고려대학교 화공생명공학과 강정원

3. 용해도 계산과 상도

Simple Solubility Correlation for Solutions

Influence of temperature on solubility

....2 +++= CtBtAc

TCBTAxCTBTAx

BTAxCTBTAx

BTAx

loglogloglogloglog

1

21

1

2

++=

++=

+=

++=

+=

−

−−

−

Solubility expression for inorganic salts(Electrolytes)

Ionic equilibrium relation (Or Reaction Equilibrium)a A + b B c C + d D

Example) NaCl (s) Na+ + Cl-

Condition for Equilibrium

DCBA dcba μμμμ +=+

Chemical Potential

iiii xRTTT γμμ ln)()( 0 +=

iiimi mRTTT γμμ ln)()( 0 +=Can be expressed in composition

Or molarity

Solubility expression for inorganic salts (Electrolytes)

bBB

aAA

dDD

cCC

DCBA mmmmRTdcba

)()()()(ln0000

γγγγμμμμ =−−+

DCBA dcba μμμμ +=+ iiimi mRTTT γμμ ln)()( 0 +=

)exp(0000

RTGdGcGbGa

K fDfCfBfAT

Δ−Δ−Δ+Δ=

bBB

aAA

dDD

cCC

T mmmmK

)()()()(

γγγγ

=

Standard free energy Change of reaction


For the case of salt in solution, M(s) a A (aq) + b B (aq)

)()()(

MM

dDD

cCC

sp xmmK

γγγ

=

)exp(000

RTGGbGa

K fMfBfAsp

Δ−Δ+Δ=

Basis : formation of hypotheticalIdeal solution of 1 molarity at standard condition

Basis : formation of 1 mol of solid at standard condition

This value becomes 1(Pure solid)


Solubility Product M(s) a A (aq) + b B (aq)

dDD

cCCsp mmK )()( γγ=

)exp(000

RTGGbGa

K fMfBfAsp

Δ−Δ+Δ=

Example) Al(OH)3 Al3+ + 3OH- Ksp = 1.1E-15153 101.1))(( 3

−×== −+ OHAlsp mmK

−+ = OHAl mm 33molgmm

AlOHAl /108 5)( 3

3

−×== +

Advanced Topics in Electrolyte Solutions

Effect of Ksp– Temperature – Pressure

Activity Coefficients – From thermodynamic models

• Debye-Huckel Model• Guggenheim Model • Pitzer Model • Bromley Model • Meissner Model

Difficulties in Electrolyte Solution

Existing activity model only applies to limited range – Applicable only for dilute solution – No model can effectively explain the behavior of dilute and

highly concentrated solution

For practical purposes, simple empirical correlations are normally used ….

TCBTAxCTBTAx

BTAxCTBTAx

BTAx

loglogloglogloglog

1

21

1

2

++=

++=

+=

++=

+=

−

−−

−

Data Source

Solubility of Electrolytes and Nonelectrolytes– J. M. Mullin, “Crystallization” , Butterworth-Heinemann

(1993)

Method for Electrolyte Solutions – J. F. Zemaitis, Jr., D. M. Clark, M. Rafal and N. C.

Scrivner , “Handbook of Aqueous Electrolyte Solution”, AIChE (1986)

Solubility Expression for Organic Compounds in Organic Solvents

Ideal Solubility – Solution (liquid phase) exhibit “ideal behavior”

• Fugacity of mixture is proportional to mole fraction (solubility)

Nonideal solubility – Solution exhibit non-ideal behavior

),(),,( ,22,2 PTfxxPTf pureliquidliquid =

),(),,( ,222,2 PTfxxPTf pureliquidliquid γ=


Ideal Solubility Calculation Method – Solution (liquid phase) exhibit “ideal behavior”– Solid (crystal) is in a pure state

),(),( ,22 ,2 PTfxPTf pureliquidsolidpure =

),(),(

,2

,22 PTf

PTfx

liquidsubcooledpure

solidpure=

Solid Liquid transition properties are importantSolid Liquid Transition can occur in any temperature


Solid-Liquid transition P

T

Solid Phase

Liquid Phase

VaporPhase

Pc

Tc

critical point

triple point

Gas

Super-critical (fluid) phase

This curve corresponds solid-liquid transition


Solid-Liquid transition– To calculate fugacity ratio of solid and liquid phase, two reference states are

normally used • Triple point : Tt

• Normal Melting Point : Tm

– Because heat of fusion (Hf) data are reported at those temperatures Thermodynamic Cycles for calculating fugacity ratio (or chemical potential changes)

a d

bcTemperature

Tf or Tt

Operating Temperature (T)

Solid Phase Liquid Phase


a d

bcTemperature

Tf or Tt

Operating Temperature (T)

Solid Phase Liquid Phase

dcbadcbadadadaS

L STHSTHGffRT →→→→→→→→→ Δ−Δ=Δ−Δ=Δ=ln

∫∫ +Δ+=Δ+Δ+Δ=Δ →→→→→→

T

T

Lpff

T

T

spdccbbabcba

f

f dTCTHdTCHHHH )(

∫∫ +Δ

+=Δ+Δ+Δ=Δ →→→→→→

T

T

Lp

f

fT

T

sp

dccbbabcbaf

f dTT

CTH

dTTC

SSSS


Ideal Solubility equation

You can use Tt or Tf depending on Hf data available

liquid

solid

liquidsolid

ff

x

fxf

,2

,22

,22,2

=

=

2121211

2ln →→→ Δ−Δ=Δ= STHGffRT

TT

RC

TT

RC

TT

RTH

xRT fPfPf

f

f ln111ln2

Δ+⎟⎟

⎠

⎞⎜⎜⎝

⎛−

Δ−⎟⎟

⎠

⎞⎜⎜⎝

⎛−

Δ=


Non-Ideal Solubility equation

How to calculate activity coefficient ?– Solution models in molecular thermodynamics

• Magules• Wilson • NRTL• UNIQUAC

liquid

solid

liquidsolid

ff

x

fxf

,2

,222

,222,2

=

=

γ

γ

TT

RC

TT

RC

TT

RTH

xRT fPfPf

f

f ln111ln22

Δ+⎟⎟

⎠

⎞⎜⎜⎝

⎛−

Δ−⎟⎟

⎠

⎞⎜⎜⎝

⎛−

Δ=

γ

SLE for Solid Solution

Two Types of Phase Behavior

Molecular structures are different Molecular structures are similar


Basic Thermodynamic Framework s

il

i ff =

si

sii

li

lii fzfx γγ =

isii

lii zx ψγγ = l

i

si

i ff

≡ψ Similar technique in 2.2 can be used

Required information - Melting points- Heat of fusion/melting- Heat capacity of solid and liquid

SLE for Solid Solution – Rigorous Derivation


If I and Heat capacity changes are negligible,

⎟⎠⎞

⎜⎝⎛ −Δ

=≡TTT

RTH

ff mi

im

sli

li

si

i,

expψ

isii

lii zx ψγγ =


Case I : Solid Solution i

sii

lii zx ψγγ =

111 ψzx =

222 ψzx =

11

21

21

=+=+

zzxx

21

22

21

211

)1(

)1(

ψψψ

ψψψψ

−−

=

−−

=

x

x

⎟⎠⎞

⎜⎝⎛ −Δ

=≡TTT

RTH

ff mi

im

sli

li

si

i,

expψ


Case II : Immiscible Solid (Eutectic Forming)i

sii

lii zx ψγγ =

11 ψ=x

22 ψ=x

⎟⎟⎠

⎞⎜⎜⎝

⎛ −Δ==

TTT

RTHx m

m

sl1,

1,

111 expψ

⎟⎟⎠

⎞⎜⎜⎝

⎛ −Δ==

TTT

RTHx m

m

sl2,

2,

222 expψ

Types of Phase Diagram… How to interpret ?

Two component system

Simple Behavior Complex Behavior


Lever Rule – Always applies to any kind of phase diagram – Two simple rules

• Three points those satisfies material balance equation must lie on a same line

• The amount of splits are proportional to the length of line in opposite direction


Example of Lever Rule : MgSO4 System Several structures can be produced for water-salt systems. – Example ) Solid magnesium sulfate

MgSO4 anhydrous magnesium sulfateMgSO4·H2O magnesium sulfate monohydrateMgSO4·6H2O magnesium sulfate hexahydrateMgSO4·7H2O magnesium sulfate heptahydrateMgSO4·12H2O magnesium sulfate dodecahydrate

Solution StateMgSO4 + H2O

cool down

Composition ofSolutions Composition of

Solid MgSO4·7H2O

Lever Rule

Solution (Cool down) Solid + Solution – Overall Material Balance Eqn.

F : FeedS : SolutionC : Crystal

– MgSO4 Balance

csF CxSxFx +=

CSF +=

csF CxSxxCS +=+ )(

FC

SF

xxxx

SC

−−

=

C

DECD

SC

=)solution kg(

)crystal kg(

D E

xs xF xc

Amount of crystal (C)

Amount of solution (S)

Lever Rule (지렛대원리)

C D E

xs xF xc



solution crystal



Three Component Systems

Construction of Ternary Diagram


How to read composition (M point)

A = 40 %B = 30 %C = 30 %


Lever RuleX + Y = Z

Or

Z = X + Y

XZ distanceYZ distance

Y mixture of massX mixture of mass

=

Three Component System - (1) Solid Solutions

System : o-, m-, p- nitrophenol– A, B, C : Eutectic Points

Three Component System – (2) Two Salts and Water

Different Types of Phase Behavior – No chemical reaction – Formation of a solvate (hydrate)– Formation of double salt – Formation of hydrate double salt

Two salt and water – No chemical reaction

KNO3 + NaNO3 + Water No chemical reaction No hydrateThey do not combine chemically

Isothermal evaporation T is fixed in this diagram

Two salt and water – Solvate formation

When one of solutes can form a compound (solvate, hydrate)NaCl + NaSO4 + Water System Legend : S(solution), H(hydrate, Na2SO4.10H2O), SO4 (Na2SO4), Cl (NaCl)

At 17.5 degree C At 25 degree C

Two salt and water – Double Compound Formation

When two dissolved solutes form double compound – C : double salt

Stable in Water Decomposed by Water

Hydrated Double Salt

H : HydrateC : Hydrated Double Salt

Two Salt and Water – Solid Solution Formation

Water + Two electrolyte with common ion

결정화공정의상평형의 원리와이해 - cheric...결정화공정의상평형의...

Documents