chapter 4 atkins pchem

8/13/2019 Chapter 4 atkins pchem

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Physical

Transformations ofPure Substances

Chapter 4


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Definitions

!A phase is a state of matter that is uniformthroughout, not only in composition but also in

physical state.

!A pure gas!A gaseous mixture!Two totally miscible liquids!A crystal


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Definitions

!A solution of sodium chloride! Ice!A slurry of ice and water


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Definitions

!An alloy of two metals?


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Definitions

!An alloy of two metals is a two phase system ifthe metals are immiscible, but a single phase

system if they are miscible.

! Dispersion can be uniform on a macroscopiclevel, but not on a microscopic scale.

! Dispersions are important in many advancedmaterials.


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Stabilities of Phase! A phase of a substance is a form of matter that is

uniform throughout in chemical composition and

physical state.

! A phase transition is the spontaneous conversion ofone phase into another.

! Phase transitions occur at a characteristictemperature and pressure.


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Stabilities of Phase! At 1 atm, < 0 C, ice is the stable phase of H2O,

but > 0 C, liquid water is the stable phase.

!The transition temperature, Ttrs, is the temperatureat which two phases are in equilibrium.

! So what happens to Gibbs energy?


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Stabilities of Phase! At 1 atm, < 0 C, ice is the stable phase of H2O,

but > 0 C, liquid water is the stable phase.

!The transition temperature, Ttrs, is the temperatureat which two phases are in equilibrium.

! So what happens to Gibbs energy?! < 0 C Gibbs energy decreases as liquid"solid.! > 0 C Gibbs energy decreases as solid"liquid.


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Stabilities of Phase


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Phase Diagrams


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Vapor Pressure


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Boiling Point


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Critical Point


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Critical Point


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Melting and Freezing


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Triple Point


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Carbon Dioxide


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Helium


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Definitions

!A constituent of a system is a chemical species(an ion or a molecule) that is present.

!A mixture of water and ethanol has twoconstituents.

!A solution of sodium chloride has threeconstituents: Na+, Cl-, H2O.


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Definitions

!A component is a chemically independentconstituent of a system.

!The number of components in a system is theminimum number of independent species

necessary to define the composition of all the

phases present in the system.


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Definitions

!When no reaction takes place and there are noother constraints, the number of components is

the equal to the number of constituents.

! Pure water is a one component system!A mixture of ethanol and water is two

component system.


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Definitions

!An aqueous solution of sodium chloride is a twocomponent system, because by charge balance,

the number of Na+ions must be the same as the

number of Cl-ions.

!A system that consists of hydrogen, oxygen andwater at room temperature has three

components.


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Definitions

!The number of phases, P.!The number of components, C.!The variance of the system, F is the number of

intensive variables (e.g. p and T) that can be

changed independently without disturbing the

number of phases in equilibrium.


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Phase Rule

! F = C P + 2!This is not an empirical rule based upon

observations, it can be derived from chemicalthermodynamics.

! For a one component system F = 3 P!When only one phase is present, F = 2 and both

p and T can be varied without changing the

number of phases.


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Experimental Procedures

!Thermal analysis a sample is allowed to cooland it temperature is monitored. When a phase

transition occurs, cooling may stop until the

phase transition is complete and is easily

observed on a thermogram.


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! Modern work on phase transitions often dealwith systems at very high pressures and more

sophisticated detection properties must be

adopted.

!A diamond anvil cell is capable of producingextremely high pressures.


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!A sample is placed in a cavity between to gem-quality diamonds and then pressure is exerted by

turning a screw. Pressures up to ~2 Mbar can be

achieved.

! One application is the study the transition ofcovalent solids to metallic solids.


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! Iodine, I2, becomes metallic at ~ 200 kbar andmakes a transition to a monatomic metallic solid

at around 210 kbar.

! Relevant to the structure of material deep insidethe Earth and in the interiors of giant planets,

where even hydrogen may be metallic.


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Thermodynamics of Phase

Transitions


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Transitions


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Transitions


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Temperature Dependence of

Phase Transitions

"Gm

"T

#

$%

&

'(p

=)Sm"

"T

#

$%

&

'(p

=)Sm


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Melting and Applied Pressure

"Gm

"p

#

$%

&

'(T

=Vm"

"p

#

$%

&

'(T

=Vm


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Melting and Applied Pressure

"Gm

"p

#

$%

&

'(T

=Vm"

"p

#

$%

&

'(T

=Vm


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Vapor Pressure and Applied

Pressure

p = p*eVm ( l )"P RT

p = vapor pressure

p

*=

vapor pressure of condensed phasein the absence of an additional pressure

"P = pressure applied


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Vapor Pressure and Applied

Pressure


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Location of Phase Boundaries

"(p,T) = #(p,T)


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dG =Vdp" SdT

d=Vmdp " SmdT

V#,mdp" S#,mdT=V$,mdp" S$,mdT

(S$,m " S#,m )dT=(V$,m "V#,m )dp

%trs

S

% trsV=

dp

dT "Clapeyron equation


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Solid-liquid boundary

" trsS

" trsV=

dp

dT#Clapeyron equation

" trsS= "trsHT

dp

dT

=

" fusH

T" fusV


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dpdT

= " fusHT" fusV

dp =" fusH

" fusV

dT

T

dp =" fusH

" fusV

dT

TT*

T

#p

*

p

#

dp$" fusH

" trsV

dT

TT

*

T

#p

*

p

#

p$ p* +" fusH

" fusVln

T

T*

%

&'

(

)*


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p" p* +# fusH

# fusVln

T

T*

$

%&

'

()

When T and T*

do not differ much

p" p* +# fusH

T*# fusV

(T* T*)


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Liquid-vapor boundary

" trsS

" trsV=

dp

dT#Clapeyron equation

" trsS= "trsHT

dp

dT

=

" vapH

T" vapV


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dp

dT

" "small"

dT

dp" "large"


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dp

dT=

" vapH

T" vapV" vapV # Vm (g)

dp

dT=

" vapH

T(RT p)

dlnp

dT

=

" vapH

RT2

- Clausius - Clapeyron equation


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Liquid-vapor boundarydlnp

dT=

" vapH

RT2

dlnp =" vapH

RT2

dT

dlnpln p *

ln p

# =" vapH

RT2

dTT*

T

#

dlnpln p *

ln p# = " vapHR

dTT

2T*

T# =$"vapHR

1

T$ 1

T*

%

&' (

)*

ln p p*( ) =$

"vapH

R

1

T$ 1

T*

%

&'

(

)*

p

p*=e

$+

+=

" vapH

R

1

T$

1

T*

%

&'

(

)*

p = p*e$+


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Liquid-vapor boundarydlnp

dT=

" vapH

RT2

dlnp =" vapH

RT2

dT

dlnpln p *

ln p

# =" vapH

RT2

dTT*

T

#

dlnpln p *

ln p# = " vapHR

dTT

2T*

T# =$"vapHR

1

T$ 1

T*

%

&' (

)*

ln p p*( ) =$

"vapH

R

1

T$ 1

T*

%

&'

(

)*

p

p*=e

$++=

" vapH

R

1

T$

1

T*

%

&'

(

)*

p = p*e$+


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Solid-gas boundary

p = p*e"#

#=$ subH

R

1

T" 1

T*

%

&'

(

)*

chapter 4 atkins pchem

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