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

1(2015) Spring Physical Chemistry (I)

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


by M Lim

• 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


by M Lim

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


by M Lim

• 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


by M Lim

• 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)


by M Lim

( ) /* 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


by M Lim

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


by M Lim

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


by M Lim

• 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


by M Lim

• 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)


by M Lim

• l-transition: not 1st order yet Cp is infinite at Ttrs

4B.3 The Ehrenfest classification of phase transitions

4B.3(b) Molecular interpretation


by M Lim

chap 4. physical transformations of pure...

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