Chap 4. Physical transformations of pure...
Transcript of Chap 4. Physical transformations of pure...
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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by M Lim
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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