phase diagrams and phase transitions of unary systems
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(Equilibrium) Phase Diagram H2O
Phase diagrams and phase transitions
of unary systems
•Phase transitions
•Phase boundaries
•Phase transition temperature
•Melting point
•Boiling point
•Triple point
•Critical point
•Polymorphic forms
•Thermodynamics vs kinetics
•Metastable phases
Solid
1
1 bar
2
Phase diagrams and phase transitions of unary systems
(Equilibrium) Phase Diagram H2O
Solid
Tfus = Tcryst = 273.15 K H-bonding
1 bar
3
Phase diagrams and phase transitions of unary systems
(Equilibrium) Phase Diagram H2O
Solid
1 bar
Tvap = 373.15 K
l
g
4
Phase diagrams and phase transitions of unary systems
(Equilibrium) Phase Diagram H2O
Solid
1 bar
Triple point
273.16 K
611 Pa
0.006 bar
5
Phase diagrams and phase transitions of unary systems
(Equilibrium) Phase Diagram H2O
Solid
Super critical sc 1 bar
Triple point
Critical point 220.6 bar
647.1 K
6
Phase diagrams and phase transitions of unary systems
(Equilibrium) Phase Diagram H2O
Solid
Critical point
T
7
Phase diagrams and phase transitions of unary systems
l l
g g
super
critical
l l
g g
super
critical
Critical point
T
T < Tc(ritical) T > Tc
Critical
point
220.6 bar
647.1 K H2O
8
Phase diagrams and phase transitions of unary systems
H-bonding
1 bar
Triple point
Critical point
9
Phase diagrams and phase transitions of unary systems
(Equilibrium) Phase Diagram H2O
Solid
1 bar
10
Polymorphic forms
for the solids
Phase diagrams and phase transitions of unary systems
(Equilibrium) Phase Diagram H2O
Solid
* OHO
H3C
N
CH3
H3C
c c c
b
T < 40 ºC T > 40 ºC T > 60 ºC (Tfus = 70 ºC) Venlafaxine
Polymorphic (solid state) phase transitions 11
Phase diagrams and phase transitions of unary systems
sub
CO2 4He
1 bar
1 bar
sublimation point
at 1 bar
ambient conditions “dry
ice”
12
Phase diagrams and phase transitions of unary systems
13
Phase boundary lines in diagrams of unary systems
1 bar
Tvap = 373.15 K
l
g
14 (Equilibrium) Phase Diagram H2O
Phase boundary lines in diagrams of unary systems
Solid
l
g
15
The chemical potential of phase i (i = l,g)
Equilibrium between phases gl OHOH 22
0idn
i
i
idnSdTVdPdG
ijnTPi
in
G
,,
lg nn
Note: we are dealing with a unary system
m,ii G (pure compound)
Phase boundary lines in diagrams of unary systems
(Study guide p.11-13)
l
g
16
Importance of the chemical potential:
ggll dndnSdTVdPdG
Equilibrium between phases gl OHOH 22
Equilibrium 0, PTdG
gl dndn
gl
Phase boundary lines in diagrams of unary systems
17 (Equilibrium) Phase Diagram H2O
Phase boundary lines in diagrams of unary systems
Triple point
gl
gs I
ls I
Solid
III ss
ls VII
18 (Equilibrium) Phase Diagram H2O
Phase boundary lines in diagrams of unary systems
Triple point
m,m, gl GG
m,m,I gs GG
m,m,I ls GG Solid
m,m, III ss GG
m,m,VII ls GG
pure compound: m,ii G
19 (Equilibrium) Phase Diagram H2O
Phase boundary lines in diagrams of unary systems
Triple point
m,m, gl GG
Solid
Along phase boundary line:
m,m, gl dGdG
dTSdPVdG iii m,m,m,
dTSdPVdTSdPV ggll m,m,m,m,
20 (Equilibrium) Phase Diagram H2O
Phase boundary lines in diagrams of unary systems
Triple point
m,m, gl GG
Solid
Along phase boundary line:
m,m, gl dGdG
m
m
V
S
dT
dP
gl
gl
0m Ggl
m
m
VT
H
dT
dP
glgl
gl
Clapeyron equation:
dTSdPVdG iii m,m,m,
dTSdPVdTSdPV ggll m,m,m,m,
21 (Equilibrium) Phase Diagram H2O
Phase boundary lines in diagrams of unary systems
Triple point
m,m, gl GG
Solid
Along phase boundary line:
m,m, gl dGdG
m
m
V
S
dT
dP
gl
gl
0m Ggl
m
m
VT
H
dT
dP
glgl
gl
Clapeyron equation:
dTSdPVdG iii m,m,m,
dTSdPVdTSdPV ggll m,m,m,m,
22
Phase boundary lines in diagrams of unary systems
Along phase boundary line:
dTVT
HdP
glgl
gl
m
m
Clapeyron equation:
Triple point
Solid
Perfect gas: RTPV m
P
RTVV ggl m,m
dTRT
H
P
dP
gl
gl
2
m
dT
RT
H
P
dP
gl
gl
2
m
23
Phase boundary lines in diagrams of unary systems
Along phase boundary line:
Triple point
Solid
T
T
glP
P
dTRT
H
P
dP
gl
2
m
T*
P*
P
T
mm )( HTH glgl
T
T
glP
PT
dT
R
H
P
dP2
m
TTR
H
P
P gl 11ln
m
24
Phase boundary lines in diagrams of unary systems
Along phase boundary line:
Triple point
Solid
T*
P*
P
T
TTR
H
P
P gl 11ln
m
expPP
TTR
H 11mvap
Clausius-Clapeyron equation:
Clausius-Clapeyron equation
VT
H
V
S
T
P
trstrs
trs
trs
trs
d
d
Clapeyron
VT
H
T
P
fusfus
fus
d
d
*
fus
*
fus*
*
fus
fus* ln TTVT
HP
T
T
V
HPP
VT
H
T
P
subsub
sub
d
d
2
sub
RTd
lnd H
T
P
*
sub* 11
Rexp
TT
HPP
VT
H
T
P
vapvap
vap
d
d
2
vap
RTd
lnd H
T
P
Clausius-Clapeyron
*
vap* 11
Rexp
TT
HPP
25
Phase boundary lines in phase diagrams of unary systems
Exercise 5-8
Phase transitions in phase diagrams of unary systems
26
m
P
ST
m
T
VP
s
m
l
m VV
s
m
l
m VV
(H2O)
TSPVG mmm dddd
27
Phase transitions in phase diagrams of unary systems
s
m
l
m VV
(H2O)
(H2O)
28
TSPVG mmm dddd
m
P
ST
Phase transitions in phase diagrams of unary systems
3
m
T
VP
TSPVG mmm dddd
(H2O) 273.16 K 273.15 K
0.006 bar
1 bar
29
s
m
l
m VV
(H2O)
(H2O)
m
T
VP
Phase transitions in phase diagrams of unary systems
30
Ehrenfest classification of phase transitions transitions
T
T P
T
TP
2
2
First order Second order Exercise 9
* OHO
H3C
N
CH3
H3C
c c c
b
T < 40 ºC T > 40 ºC T > 60 ºC (Tfus = 70 ºC) Venlafaxine
Polymorphic (solid state) phase transitions
32
Polymorphic forms characterized using
X-Ray Powder Diffraction 33
Polymorphic solid state phase transitions
Characterized using Differential Scanning Calorimetry 34
Polymorphic solid state phase transitions
Kinetic roughening transition for naphthalene crystals in a toluene solution
35 ad: increasing driving force for crystallization
36
Gibbs phase rule: multicomponent phases
37
Triple point
m,m, gl GG
m,m,I gs GG
m,m,I ls GG Solid
m,m, III ss GG
m,m,VII ls GG
(pure compound)
What about mixtures of compounds in the phases?
Gibbs phase rule: multicomponent phases
38
Importance of the chemical potential:
Equilibrium between phases OHOH 22
in equilibrium:
Equilibrium between phases of component i in mixtures
,, ii in equilibrium:
phase α
phase β
Gibbs phase rule: multicomponent phases
phases α, β
components i
39
,, ii in equilibrium: phases α, β
components i
unary phase diagram
P phases in mutual equilibrium
1P
2P
3P
Gibbs phase rule: multicomponent phases
40
Equilibrium between phases of components i in mixtures
,, ii in equilibrium: phases α, β
components i
C components in the mixtures
# independent variables CxxTPF C 2,, 1
whole
system
for each
phase
Gibbs phase rule: multicomponent phases
P
j
ji
C
i
ji dnSdTVdPdG
,
1
,
j
j
ii
n
nx
mole fraction
41
Equilibrium between phases of components i in mixtures
,, ii in equilibrium: phases α, β
components i
C components in the mixtures
P phases in mutual equilibrium
# independent variables CxxTPF C 2,, 1
whole
system
for each
phase
Gibbs phase rule: multicomponent phases
P
j
ji
C
i
ji dnSdTVdPdG
,
1
,
42
Equilibrium between phases of components i in mixtures
,, ii in equilibrium: phases α, β
components i
# independent variables CxxTPF C 2,, 1
P phases PCF 2
for each
phase
Gibbs phase rule: multicomponent phases
P
j
ji
C
i
ji dnSdTVdPdG
,
1
,
43
Equilibrium between phases of components i in mixtures
,, ii in equilibrium: phases α, β
components i
C components in the mixtures
P phases
j
j
ii
n
nxfor each phase
mol fraction
1i
ix
PCF 2
# independent variables )1(2 CPF
Gibbs phase rule: multicomponent phases
44
Equilibrium between phases of components i in mixtures
,, ii in equilibrium: phases α, β
components i
PCCC
P
P
,,,
,2,2,2
,1,1,1
P phases in
mutual equilibrium
2)1()1(2 PCCPCPF
(P −1)C times
an “=” sign
Gibbs phase rule: multicomponent phases
45
Equilibrium between P phases of C components in mixtures
,, ii in equilibrium: phases α, β
components i
C components in the mixtures
P phases in mutual equilibrium 2 PCF
Gibbs phase rule: multicomponent phases
Gibbs phase rule
F = 2
F: # degrees of freedom
C: # components
P: # phases
46
Gibbs phase rule: unary phase diagrams
2 PCF
P = 1
unary phase diagram
C = 1
47
Gibbs phase rule
F = 1
2 PCF
P = 2 C = 1
unary phase diagram
Gibbs phase rule: unary phase diagrams
48
Gibbs phase rule
F = 0
2 PCF
P = 3 C = 1
unary phase diagram
Gibbs phase rule: unary phase diagrams
49
Gibbs phase rule
F = −1
2 PCF
P = 4 C = 1
unary phase diagram
Gibbs phase rule: unary phase diagrams
50
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