Chap 4. Physical transformations of pure substances
The phase transition of pure substances is among the simplest application of thermodynamics to chemistry
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Succinct way of presenting the physical changes
of state: in terms of its phase diagram
HomeworkChap 4. Physical transformations of pure
substances
(2015) Spring Physical Chemistry (I) by M Lim
2
• Problems: 4B.2, 4B.4, 4B.5, 4B.7, 4B.10,
4B.14, 4B.15, 4B.16, 4B.17, 4B.18
• Integrated activities: 4.1, 4.3, 4.5
4장-1 수업목표: Phase, phase rule
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• Phase diagrams
• The thermodynamic criterion of equilibrium: µ1 = µ2
• The phase rule: F = C − P + 2
Phase diagram
• Phase: a form of matter that is uniform throughout in chemical
composition and physical state (ex, s, g, l, black or white P)
• Phase transition: spontaneous conversion of one phase into another phase,
occurs at a characteristic T for a given p
• Transition T, Ttrs: T at which the two chemical potentials are equal and
two phases are in equilibrium
• Metastable phase: thermodynamically unstable phase but phases that
persist because the transition is kinetically hindered
• Vapor p: p of a vapor in equilibrium with the liquid
• Sublimation vapor p: pvap in equilibrium with the solid
: To show the regions of p and T at which its various phases are thermodynamically stable:a map of p & T at which at each phase of a substance is the most stable
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4A.1(b) Phase transitions
• Thermal analysis
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spontaneous conversion of one phase into another phase, occurs at a characteristic T for a given p
4A.1(c) The thermodynamic criteria of phase stability: chemical potential
• At equilibrium, µ of a substance is the same
throughout a sample, regardless of how many
phases are present.
mG
µ1
µ2
If µ1 > µ2,
ΔG = µ1 (‒dn) + µ2 (dn) = (µ2 ‒ µ1) dn < 0
spontaneous change.Only if µ1 = µ2 is there is no change in G, and only then is the system at equilibrium
molar Gibbs energy,
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‒dn
dn
4A.2 Phase boundaries
• Boiling: T at which its pvap = pext, vaporization can occur throughout the bulk of the liquid.
Normal boiling T (Tb): boiling T at 1 atm
Standard boiling T: boiling T at 1 bar (99.6 ℃)
• Tc, pc : supercritical fluid
• Melting (freezing) T (Tm, Tf)
normal (standard) Tm, Tf
• Triple point: three different phases of a substances all simultaneously coexist in equilibrium (characteristic of the substance, for water, T3 =273.16K, p3 =611 Pa).
the lines separating phases, show the values of p and T at which two phases coexist in equilibrium
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• Phase (P): number of phases at equilibrium
( ) ( ) ( 1, 2, # 3)NaCl solution Na aq Cl aq P C constituents
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• Degrees of freedom (F) : number of independent variables
• Component (C): chemically independent constituent of a system
– Constituent: chemical species that is present
– # of component: the minimum # of independent species necessary to define the composition of all the phases present in the system
• No reaction: C = # of constituentEx, pure water (P = 1, C = 1), a mixture of ethanol and water (P = 1, C = 2)
• Reaction:
4A.2(b) The phase rule (F = C − P + 2)
2, , ONa Cl H
4A.2(b) The phase rule (F = C − P + 2)• Degrees of freedom (F)
– (T, p): 2
– C components: C P
1i
ix
P
iii
P equations
(P − 1) C equations
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• For each phase:
• For each component:
★ ♠ ♥ ♣
★ ♠ ♥ ♣
★ ♠ ♥ ♣
★ 1
♠ 2
♥ 3
♣ 4
★♠♥♣
★ ♠ ♥ ♣★ ♠ ♥ ♣
★ ♠ ♥ ♣
31 2 4 1xx x x
2 2 2
3 3 3
4 4
1 1
4
1
(T, p)
1 1 1 1
,
F = C P + 2 − P − (P − 1) C
= C − P + 2
4A.2(b) The phase rule (F = C − P + 2)
• One-component system:
F = 3 − P
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• P = 1, F = 2: (T, p), area
• P = 2, F = 1: (T or p), line
• P = 3, F = 0: (invariant). point
4A.3 Three representative phase diagrams-1
• p3 > 1 atm: sublimation, dry ice
• Supercritical CO2: highly compressed CO2
• l is denser than s
• 5 more triple points
• polymorphs
• differ in the
arrangement of H2O
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• s and g are never in equilibrium
• 4He: 2 liquid phases
• He-I (a normal liquid)
• He-II (a superfluid: flows without viscosity)
• He is the only known substance with a l-l
boundary (l-line)
• Phase diagram of 3He differs from that of 4He
4He
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4A.3 Three representative phase diagrams-2
4장-2. 수업목표, Phase boundary
• p-dependence: T-dependence:
• The effect of applied p on pvap:
• Phase boundary:
• The location of phase boundary
m
p
ST
m
T
Vp
VT
H
V
S
dT
dp
trs
trs
trs
trs
(Clapeyron equation)
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( ) /* mV l RTP
p p e
* **
* *
*
*
*
ln 1fus fus
fus fus
fus
fus
H HT T T Tp p
V T V T
T Hp
T V
Tp
* *
* *
1 1ln
1 1ln
vap
sub
Hp
p R T T
p H
p R T T
2
ln vapd
dT T
p H
R
Clausius-Clapeyron eqn
4B.1 The dependence of stability on the conditions(a) T dependence of phase stability
ST
G
p
m
p
ST
Recall that
• Sm > 0: µ(T) has negative slope • Sm(g) > Sm(l) > Sm(s): µ(T) is the steepest for gases, and steeper for liquids than solids
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4B.1(b) The response of melting to applied p
Vm(s) < Vm(l) Vm(s) > Vm(l)
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water
m
T
Vp
positive slope
4B.1(c) The pvap of a liquid subjected to p
At constant T, as P↑, pvap ↑Molecules are squeezed out of the phase and escape as a gas
( ) /* mV l RTPp p e
(a) Mechanically(b) By an inert gas:
partial pvap
gas solvation
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Effect of applied pressure P on vapor pressure p
The effect of applied p (P) on pvap
*
* *
*
* *
* *
( ) for a perfect gas
( )
( )
( )
:
:
( )( ) ln ln
m
p P
m
m
p
p
mm
mp
RTdp
p
RTdp
V l dP
V l
p
p
d l
d g V g dp
g p
l p p
dP
V l dP
V
P P
PP
p
dpR
lV l RT
p p R
Tp
p
T
p
At equilibrium µ(l) = µ(g)
any change at equilibrium, dµ(l) = dµ(g)
( ) /* mV l RTP
p p e
when there is a small change in pvap
compare to ΔP
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at c onst.
m m
mV
d V dp S d
dp
T
T
Initial state Final state
*p
p P*p
p
P
VT
H
V
S
dT
dp
dTSSdpVV
dpVdTSdpVdTS
dpVdTSd
TpTp
trs
trs
trs
trs
mmmm
mmmm
mm
)()(
),(),(
,,,,
,,,,
Clapeyron equation
convenient to have dp/dT
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4B.2 The location of phase boundaries
trs
trs
VdT
dp S
To predicts Ttrs to the application of p
2
2
ln
ln
vap
vap
HdpdT
p RT
H
dT
d p
d
RT
p
(b) The solid-liquid boundary
* * *
2
2 2
* *
* *
( )
1
1 1ln
1 1ln
vap vap vap
vap m
vap
p T Tvap vap
p T T
vap
sub
H H Hdp p
dT T V TV g T RT
Hdp dT
p R T
H HdpdT dT
p RT R T
Hp
p R T T
p H
p R T T
* *
* **
* *
*
*
*
*
*
,
l
ln
n 1
fus
fus
fus
fus
fus
p Tfus
fus fus
fus fus
fus
fus
fus
fus
p T H T
Hdp
dT T V
H dTdp
V T
H dTdp
V T
H HT T T Tp p
V T V
Tp
T
T H
V T
T V
p
p
p
Clausius-Clapeyron equation
(c, d) The liquid(solid)-vapor boundary
small: large slope
large: small slope
2 31 1ln 1 for 1
2 6x x x x x x
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4B.2 The location of phase boundaries
T*
p*
T
p
4B.3 The Ehrenfest classification of phase transitions• Phase transitions:
m m trs
T T
trsm m trs
trsp p
V V Vp p
HS S S
T T T
• Many familiar phase transitions (ex, fusion , vaporization):
trsV or trsS is nonzero, the slope of against either p or T is
different on either side of the transition
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• Less familiar phase transitions (ex, s-s, conducting-superconducting, fluid-
superfluid transition): ??
Classify phase transitions using the behavior of the chemical potential,
4B.3 The Ehrenfest classification of phase transitions• First-order phase transition:
: discontinuous, infinite Cp at Ttrs,
p TT p
pT
pT
2
2
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• Second-order phase transitions
: continuous but : discontinuous
trs
trs
T
p
trs
p
T
H
TT
Vp
T
p
Ex, conducting-superconducting transition in metals at low T.
Ex, order-disorder transition in alloy, the onset of ferromagnetism, fluid-superfluid transition of He(l)
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• l-transition: not 1st order yet Cp is infinite at Ttrs
4B.3 The Ehrenfest classification of phase transitions
4B.3(b) Molecular interpretation
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