Physical Transformations of Pure Substances

Phase – a region of system inside which we have uniformity of the chemical potential and physical properties.

Three Principal kinds of phases• Solid – long-range order

• Liquid – less long-range order

• Gas – random molecular distributions

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

Distinguish between • Thermodynamic stability – based on chemical

potential differences

• Metastable (kinetic stability) – slow conversion of one phase into another

The Criteria for Phase Stability

The driving force for phase stability is the chemical potential of the substance in a particular phase

For two phases to be in equilibrium, the chemical potential of the substance in both phases must be equivalent.

For a single component systemF=3-P

• F = degrees of freedom

• P = number of phases

For a single component system, with two phases in equilibrium

F = 3-2 = 1

The pressure of the vapour above the liquid is called the vapour pressure PJ.

Vapour pressures are temperature dependent.

PJ

Assume we apply an infinitesimal change in T or P to two phases in equilibrium

dd Applying the definition of the chemical

potential

dPVdTSd

dpVdTSd

When a pressure (or temperature) change is applied to an equilibrium system of two phases (point a), the equilibrium is disturbed.

It can be restored by changing the temperature (or pressure) along the boundary to point b.

Defining the transition

The slope of any phase boundary can be

obtained from the Clapeyron equation

V

SVVSS

dTdP

trs

trs

For the fusion transition

A(s)A(l) We can re-write the Clapeyron equation

to include the enthalpy of fusion

VTH

VS

dTdP

fusfus

fus

fus

fus

The dependence of the melting point on the applied pressure is given as follows

2

1

2

1

T

T fusfus

fusP

P TdT

VH

dP

*fus

fus*

TT

lnVH

PPP

From the Clapeyron equation, a typical solid-liquid phase boundary slopes steeply upwards.

Most substances increase their melting points behave in this way.

For the transition between a condensed phase and the vapour phase

A(c)A(g) We can re-write the Clapeyron equation

to include the enthalpy of the transition

cVgVTdT

HdPmm

T

T trm,tr

P

P

12

1

2

1

Using the ideal gas equation

2

1

2

1

2

T

T tr

m,trP

P TdT

R

H

PdP

*tr

* TTRH

PP

ln11

Note – tr represents vapourization or sublimation.

The boiling point is defined as the temperature at which PJ equals Pext.

• Normal Boiling Point – Pext = 1 atm.

• Standard Boiling Point – Pext = 1 bar.

Boiling points are pressure dependent (see later).

Critical temperature (Tc) - the temperature above which a gas cannot be liquefied

Critical pressure (Pc) – the minimum pressure that needs to be applied at Tc to bring about liquefaction.

Supercritical fluid – fluid at or above the Tc value.

The phase boundary from the plot of the (T,P) equilibrium points.

The liquid vapour phase boundary terminates at the critical point (not shown).

The solid-vapour phase boundary is identical in shape.

The temperature dependence of the phase stability is related to the numerical value of the molar entropy!

mp

ST

The dependence of the chemical potential with pressure depends on the volume of the phase!

mT

VP

When we classify phase transitions, we must look at the first and second derivatives of the chemical potentials

mp

ST

Tm

T

VP

2

2

T

C

Tm,p

p

2

2

mT

VP

A first order transition• At least one of the first derivatives of the

chemical potential is discontinuous at the transition point.

• The second derivative of is a singularity!

A second order transition• Both of the first derivatives of the chemical

potential are continuous at the transition point.

• One of the second derivatives of is discontinuous!

The changes in thermodynamic properties for a schematic first-order transition.

T

Vm

T

Cp,m

T

Sm

The changes in thermodynamic properties for a schematic second-order transition.

T

Cp,m

T

Vm

The fluid-superfluid transition in helium (the transition).

The heat capacity appears to become infinite (first order).

It actually rises smoothly at the transition point, instead of exhibiting a singularity.

Melting Point – the temperature at which the solid and the liquid phases are in equilibrium.• Normal Melting Point – melting temperature at

1 atm pressure.

• Standard Melting Point – melting temperature at 1 bar pressure.

Melting Points are pressure dependent.

(P,T) regions where the phases are thermodynamically stable.

A phase boundary is a curve in (T,P) space where the values of the substance in the different phases are equivalent.

An invariant point where the solid, liquid, and vapour phases are in mutual equilibrium.

p1

Schematic Phase Diagrams

Water

The Molecular Origin of Surface Tension

Imbalance of intermolecular forces exists at the liquid-air interface

la= the surface tension that exists at the liquid-air interface

Surface Tensions of Pure Liquids at 293 K

Substance / (10-3 N/m)

Acetone 23.7

Benzene 28.8

CarbonTetrachloride 27.0

Methylene Iodide 50.8

Water 72.8

Methanol 22.6

n-Hexane 18.4

Capillary Action

The tendency of liquids to rise up in narrow tubes - capillary action.

Due to the phenomenon of surface tension.

The Complication of Contact Angles The balance of

forces that results in a contact angle, c.

The contact angle gives information on the ‘wettability’ of a surface.

Capillary Rise

The pressure exerted by a column of liquid is balanced by the hydrostatic pressure.

This gives us one of the best ways to measure the surface tension of pure liquids and solutions.

2

2

r gh

ghr

Meniscus Up or Down??

For a wetting liquid, a capillary rise is observed.

For a non-wetting liquid, capillary rise is observed capillary wets the

Pressure Differential Across Curved Interfaces

Pressure differential exists across curved interfaces.

Due to surface tension forces

2inside outsideP P P

r

Enhancement of Vapour Pressure

Vapour pressure enhancement above the surface of spherical droplets.

Due to surface tension forces.

2ln m

o

VPP RT r

P