결정화공정의상평형의 원리와이해 - cheric...결정화공정의상평형의...
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결정화 공정의 상평형의원리와 이해
2007년 8월 20일
결정화 분리기술 사업단
고려대학교 화공생명공학과 강정원
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3. 용해도 계산과 상도
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Simple Solubility Correlation for Solutions
Influence of temperature on solubility
....2 +++= CtBtAc
TCBTAxCTBTAx
BTAxCTBTAx
BTAx
loglogloglogloglog
1
21
1
2
++=
++=
+=
++=
+=
−
−−
−
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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
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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
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Solubility expression for inorganic salts(Electrolytes)
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)
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Solubility expression for inorganic salts(Electrolytes)
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
−×== +
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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
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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
++=
++=
+=
++=
+=
−
−−
−
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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)
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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=
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Solubility Expression for Organic Compounds in Organic Solvents
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
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Solubility Expression for Organic Compounds in Organic Solvents
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
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Solubility Expression for Organic Compounds in Organic Solvents
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
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Solubility Expression for Organic Compounds in Organic Solvents
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
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Solubility Expression for Organic Compounds in Organic Solvents
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=
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Solubility Expression for Organic Compounds in Organic Solvents
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
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SLE for Solid Solution
Two Types of Phase Behavior
Molecular structures are different Molecular structures are similar
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SLE for Solid Solution
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
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SLE for Solid Solution – Rigorous Derivation
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SLE for Solid Solution
If I and Heat capacity changes are negligible,
⎟⎠⎞
⎜⎝⎛ −Δ
=≡TTT
RTH
ff mi
im
sli
li
si
i,
expψ
isii
lii zx ψγγ =
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SLE for Solid Solution
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
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SLE for Solid Solution
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
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Types of Phase Diagram… How to interpret ?
Two component system
Simple Behavior Complex Behavior
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Types of Phase Diagram… How to interpret ?
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
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Types of Phase Diagram… How to interpret ?
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
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Solution StateMgSO4 + H2O
cool down
Composition ofSolutions Composition of
Solid MgSO4·7H2O
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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)
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Lever Rule (지렛대원리)
C D E
xs xF xc
Amount of crystal (C)
Amount of solution (S)
solution crystal
Amount of crystal (C)
Amount of solution (S)
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Three Component Systems
Construction of Ternary Diagram
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Three Component Systems
How to read composition (M point)
A = 40 %B = 30 %C = 30 %
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Three Component Systems
Lever RuleX + Y = Z
Or
Z = X + Y
XZ distanceYZ distance
Y mixture of massX mixture of mass
=
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Three Component System - (1) Solid Solutions
System : o-, m-, p- nitrophenol– A, B, C : Eutectic Points
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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
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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
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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
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Two salt and water – Double Compound Formation
When two dissolved solutes form double compound – C : double salt
Stable in Water Decomposed by Water
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Hydrated Double Salt
H : HydrateC : Hydrated Double Salt
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Two Salt and Water – Solid Solution Formation
Water + Two electrolyte with common ion