Matriks RPS (Silabus)

Physical Physical Transformations Transformations

of Pure of Pure SubstancesSubstances

Chapter 4Chapter 4

Stabilities of PhaseStabilities of Phase A phase of a substance is a form of A phase of a substance is a form of

matter that is uniform throughout in matter that is uniform throughout in chemical composition and physical chemical composition and physical state.state.

A phase transition is the spontaneous A phase transition is the spontaneous conversion of one phase into another.conversion of one phase into another.

Phase transitions occur at a Phase transitions occur at a characteristic temperature and characteristic temperature and pressure.pressure.

Stabilities of PhaseStabilities of Phase At 1 atm, < 0 °C, ice is the stable At 1 atm, < 0 °C, ice is the stable

phase of Hphase of H22O, but > 0 °C, liquid water O, but > 0 °C, liquid water is the stable phase. is the stable phase.

The transition temperature, TThe transition temperature, Ttrstrs, is the , is the temperature at which two phases are temperature at which two phases are in equilibrium.in equilibrium.

So what happens to Gibbs energy?So what happens to Gibbs energy?

Stabilities of PhaseStabilities of Phase At 1 atm, < 0 °C, ice is the stable phase of HAt 1 atm, < 0 °C, ice is the stable phase of H22O, O,

but > 0 °C, liquid water is the stable phase. but > 0 °C, liquid water is the stable phase. The transition temperature, TThe transition temperature, Ttrstrs, is the , is the

temperature at which two phases are in temperature at which two phases are in equilibrium.equilibrium.

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

Stabilities of PhaseStabilities of Phase Thermodynamics does not provide Thermodynamics does not provide

information regarding the rate of information regarding the rate of phase change.phase change.

Diamond Diamond graphite graphite Thermodynamically unstable phases Thermodynamically unstable phases

that persist due to slow kinetics are that persist due to slow kinetics are called metastable phases.called metastable phases.

Phase DiagramsPhase Diagrams Phase boundaries Phase boundaries

show the values of p show the values of p and T at which two and T at which two phases coexist in phases coexist in equilibrium.equilibrium.

Vapor PressureVapor Pressure The pressure of a The pressure of a

vapor in equilibrium vapor in equilibrium with a liquid is called with a liquid is called the vapor pressure.the vapor pressure.

The pressure of a The pressure of a vapor in equilibrium vapor in equilibrium with a solid is called with a solid is called the sublimation the sublimation vapor pressurevapor pressure..

Boiling PointBoiling Point Liquid can vaporize from a liquid surface Liquid can vaporize from a liquid surface

below it’s boiling point – as we learnt from below it’s boiling point – as we learnt from the Drinking Bird.the Drinking Bird.

In an open vessel, the temperature at In an open vessel, the temperature at which the vapor pressure equals the which the vapor pressure equals the external pressure, is called the boiling external pressure, is called the boiling temperature.temperature.

At 1 atm, it’s called the normal boiling At 1 atm, it’s called the normal boiling temperature, Ttemperature, Tbb..

At 1 bar, it’s called the standard boiling At 1 bar, it’s called the standard boiling point.point.

Normal point of HNormal point of H22O is 100.0 °C; it’s O is 100.0 °C; it’s standard boiling point is 99.6 °C.standard boiling point is 99.6 °C.

Critical PointCritical Point In a closed rigid vessel, boiling does not In a closed rigid vessel, boiling does not

occur.occur. As the temperature is raised the density As the temperature is raised the density

of vapor increases and the density of the of vapor increases and the density of the liquid decreases.liquid decreases.

When the density of the vapor and liquid When the density of the vapor and liquid phases are equal the surface between the phases are equal the surface between the two phases disappears.two phases disappears.

The temperature at which this occurs is The temperature at which this occurs is called the critical temperature, Tcalled the critical temperature, Tcc..

The vapor pressure at the critical The vapor pressure at the critical temperature is called the critical temperature is called the critical pressure, ppressure, pcc..

Critical PointCritical Point

Melting and FreezingMelting and Freezing The temperature at which, under a specified The temperature at which, under a specified

pressure, the liquid and solid phases of a pressure, the liquid and solid phases of a substance coexist in equilibrium is called them substance coexist in equilibrium is called them melting temperature.melting temperature.

The freezing temperature is the same as the The freezing temperature is the same as the melting point.melting point.

At 1 atm, the freezing temperature is called the At 1 atm, the freezing temperature is called the normal freezing point, Tnormal freezing point, Tff..

At 1 bar, it’s called the standard freezing point.At 1 bar, it’s called the standard freezing point. The difference is negligible in most cases.The difference is negligible in most cases. The normal freezing point is also called the The normal freezing point is also called the

normal melting point.normal melting point.

Triple PointTriple Point There is a set of conditions under which There is a set of conditions under which

three different phases of a substance three different phases of a substance (typically solid, liquid and vapor) all (typically solid, liquid and vapor) all simultaneously coexist in equilibrium.simultaneously coexist in equilibrium.

This point is called the triple point.This point is called the triple point. For any pure substance the triple point For any pure substance the triple point

occurs only at single definite pressure and occurs only at single definite pressure and temperature.temperature.

The triple point of water lies at 273.16 K The triple point of water lies at 273.16 K and 611 Pa.and 611 Pa.

Triple PointTriple Point The triple point The triple point

marks the lowest marks the lowest pressure at which a pressure at which a liquid phase can liquid phase can exist.exist.

Carbon DioxideCarbon Dioxide

WaterWater

HeliumHelium

Thermodynamics of Thermodynamics of Phase TransitionsPhase Transitions

The molar Gibbs energy, GThe molar Gibbs energy, Gmm, is also called , is also called chemical potential, chemical potential, . Phase transitions . Phase transitions will be investigated primarily considering will be investigated primarily considering the change in the change in

Thermodynamic definition of equilibrium: Thermodynamic definition of equilibrium: At equilibrium the chemical potential of a At equilibrium the chemical potential of a substance is the same throughout the substance is the same throughout the sample, regardless of how many phases sample, regardless of how many phases are present.are present.



At low temperatures, and provided the At low temperatures, and provided the pressure is not too low, the solid phase of pressure is not too low, the solid phase of a substance has the lowest chemical a substance has the lowest chemical potential and is therefore the most stable.potential and is therefore the most stable.

Chemical potentials change with Chemical potentials change with temperature: this explains why different temperature: this explains why different phases exist.phases exist.

Temperature Temperature Dependence of Phase Dependence of Phase

TransitionsTransitions

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∂Gm∂T

⎛ ⎝ ⎜

⎞ ⎠ ⎟p

= −Sm∂μ∂T ⎛ ⎝ ⎜

⎞ ⎠ ⎟p

= −Sm

As temperature As temperature increases, chemical increases, chemical potential decreases.potential decreases.

Melting and Applied Melting and Applied PressurePressure

€

∂Gm∂p

⎛ ⎝ ⎜

⎞ ⎠ ⎟T

=Vm∂μ∂p ⎛ ⎝ ⎜

⎞ ⎠ ⎟T

=Vm

Molar volume of Molar volume of solid is smaller than solid is smaller than that of the liquid.that of the liquid.


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∂Gm∂p

⎛ ⎝ ⎜

⎞ ⎠ ⎟T

=Vm∂μ∂p ⎛ ⎝ ⎜

⎞ ⎠ ⎟T

=Vm

Molar volume of Molar volume of solid is greater than solid is greater than that of the liquid.that of the liquid.


€

∂∂p ⎛ ⎝ ⎜

⎞ ⎠ ⎟T

=Vm

Δμ =VmΔp


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Vm = Mρ

Δμ = MΔpρ

M =18.02 g mol-1 = 0.01802 kg mol-1

p =1 bar = 105 Pa

ρ ice = 917 kg m-3 ρwater = 999 kg m-3

Calculate the effect on the chemical Calculate the effect on the chemical potentials of ice and water of potentials of ice and water of increasing pressure from 1.00 to increasing pressure from 1.00 to 2.00 bar at 0 °C. The density of ice is 2.00 bar at 0 °C. The density of ice is 0.917 g cm0.917 g cm-3-3 and that of liquid water and that of liquid water is 0.999 g cmis 0.999 g cm-3-3..


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Δu(ice) = (0.01802 kg mol-1) × (1.00 Pa) 917 kg m-3 = +1.97 J mol-1

Δu(liquid) = (0.01802 kg mol-1) × (1.00 Pa) 999 kg m-3 = +1.80 J mol-1

Calculate the effect on the chemical Calculate the effect on the chemical potentials of ice and water of potentials of ice and water of increasing pressure from 1.00 to increasing pressure from 1.00 to 2.00 bar at 0 °C. The density of ice is 2.00 bar at 0 °C. The density of ice is 0.917 g cm0.917 g cm-3-3 and that of liquid water and that of liquid water is 0.999 g cmis 0.999 g cm-3-3..

Vapor Pressure and Vapor Pressure and Applied PressureApplied Pressure

€

p = p*eVm ( l )ΔP RT

p = vapor pressure

p* = vapor pressure of condensed phase in the absence of an additional pressureΔP = pressure applied

When pressure is applied to a When pressure is applied to a condensed phase, its vapor pressure condensed phase, its vapor pressure rises.rises.

This is interpreted as molecules get This is interpreted as molecules get squeezed out of the condensed phase squeezed out of the condensed phase and escape as a gas.and escape as a gas.

Vapor Pressure and Vapor Pressure and Applied PressureApplied Pressure

Location of Phase Location of Phase BoundariesBoundaries

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α (p,T) = μβ (p,T)

Locations of phase boundaries – Locations of phase boundaries – pressures and temperatures - can be pressures and temperatures - can be located precisely by making use of located precisely by making use of the fact that at when two phases are the fact that at when two phases are in equilibrium, their chemical in equilibrium, their chemical potentials must be equalpotentials must be equal


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dG =Vdp− SdTdμ =Vmdp− SmdTVα ,mdp− Sα ,mdT =Vβ ,mdp− Sβ ,mdT

(Sβ ,m − Sα ,m )dT = (Vβ ,m −Vα ,m )dp

Δ trsSΔ trsV

= dpdT

− Clapeyron equation


Solid-liquid boundarySolid-liquid boundary

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Δ trsSΔ trsV

= dpdT


Δ trsS = Δ trsHT

dpdT

=Δ fusHTΔ trsV



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dpdT

=Δ fusHTΔ fusV

dp =Δ fusHΔ fusV

dTT

dp =Δ fusHΔ fusV

dTTT *

T∫p*

p∫

dp ≈Δ fusHΔ trsV

dTTT *

T∫p*

p∫

p ≈ p* +Δ fusHΔ fusV

ln TT*

⎛ ⎝ ⎜

⎞ ⎠ ⎟


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p ≈ p* +Δ fusHΔ fusV

ln TT*

⎛ ⎝ ⎜

⎞ ⎠ ⎟

When T and T* do not differ much

p ≈ p* +Δ fusHT*Δ fusV

(T −T*)

Liquid-vapor boundaryLiquid-vapor boundary

€

Δ trsSΔ trsV

= dpdT


Δ trsS = Δ trsHT

dpdT

=ΔvapHTΔvapV


€

dpdT

− "small"

dTdp

− "large"


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dpdT

=ΔvapHTΔvapV

ΔvapV ≈Vm (g)

dpdT

=ΔvapHT(RT p)

d ln pdT

=ΔvapHRT 2 - Clausius - Clapeyron equation


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d ln pdT

=ΔvapHRT 2

d ln p =ΔvapHRT 2 dT

d ln pln p*

ln p∫ =ΔvapHRT 2 dTT *

T∫

d ln pln p*

ln p∫ =ΔvapHR

dTT 2T *

T∫ = −ΔvapHR

1T

− 1T*

⎛ ⎝ ⎜

⎞ ⎠ ⎟

ln p p*( ) = −ΔvapHR

1T

− 1T*

⎛ ⎝ ⎜

⎞ ⎠ ⎟

pp* = e−χ χ =

ΔvapHR

1T

− 1T*

⎛ ⎝ ⎜

⎞ ⎠ ⎟

p = p*e−χ


€

d ln pdT

=ΔvapHRT 2

d ln p =ΔvapHRT 2 dT

d ln pln p*

ln p∫ =ΔvapHRT 2 dTT *

T∫

d ln pln p*

ln p∫ =ΔvapHR

dTT 2T *

T∫ = −ΔvapHR

1T

− 1T*

⎛ ⎝ ⎜

⎞ ⎠ ⎟

ln p p*( ) = −ΔvapHR

1T

− 1T*

⎛ ⎝ ⎜

⎞ ⎠ ⎟

pp* = e−χ χ =

ΔvapHR

1T

− 1T*

⎛ ⎝ ⎜

⎞ ⎠ ⎟

p = p*e−χ

Solid-gas boundarySolid-gas boundary

€

p = p*e−χ χ = ΔsubHR

1T

− 1T*

⎛ ⎝ ⎜

⎞ ⎠ ⎟

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Matriks RPS (Silabus)