Chapter 4. The Physical transformations of

pure substances

2011 Fall Semester Physical Chemistry 1

(CHM2201)

Contents

Phase Diagrams 4.1 The stabilities of phases 4.2 Phase boundaries 4.3 Three representative phase diagrams

Thermodynamic aspects of phase transitions

4.4 The dependence of stability on the conditions 4.5 The location of phase boundaries 4.6 The Ehrenfest classification of phase transitions

Phase diagrams

4.1 The stabilities of phases

Key points 1.  A phase is a form of matter that is uniform

throughout in chemical composition and physical state

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

3.  The thermodynamic analysis of phases is based on the fact that, at equilibrium, the chemical potential of a substance is the same throughout a sample

4.1 The stabilities of phases (a) The number of phases •  Phase : a form of matter that is

uniform throughout in chemical composition and physical state

1.  Solid, liquid, and gas phases •  The number of phases, P

1.  P = 1 : A gas, a crystal of a substance, two fully miscible liquids

2.  P = 2 : A slurry of ice and water

3.  There are two solid phases and one gaseous phase

CaCO3(s) → CaO(s) + CO2 (g)

A single phase solution

A dispersion

4.1 The stabilities of phases (b) Phase transitions •  Phase transition : the spontaneous

conversion of one phase into another phase

•  A phase transition occurs at a characteristic temperature for a given pressure

•  Below 0℃ the Gibbs energy decreases as liquid water change into ice

•  Above 0℃ the Gibbs energy decreases as ice changes into liquid water

•  Transition temperature, Ttrs : T at which two phases are in equilibrium and the Gibbs energy of the system is minimized for a given pressure

A cooling curve

4.1 The stabilities of phases (b) Phase transitions •  Thermal analysis: a technique that

takes advantage of the heat during any transition

•  The transition is detected by noting that T does not change even though heat is being supplied or removed

•  Differential scanning calorimetry (DSC)

•  X-ray diffraction (Chapter 19)

A cooling curve

4.1 The stabilities of phases (b) Phase transitions •  Distinguish between the thermodynamic description of a process

and the kinetics at which the process occurs •  Diamond ⟶ Graphite •  Metastable phases : thermodynamically unstable phase that

persist because the transition is kinetically hindered

Diamond Graphite

4.1 The stabilities of phases (c) Thermodynamic criteria of phase stability •  Chemical potential, µ (mu)

•  Molar Gibbs energy for a one-component system, µ=Gm

•  A measure of the potential that a substance has for undergoing (either physical or chemical) change in a system

•  At equilibrium, the chemical potential of a substance is the same throughout a sample, regardless of how many phases are present

•  When an infinitesimal amount dn of a substance is transferred from one location to another, dG=(µ2-µ1)dn

•  Only when µ2 = µ1 and dG = 0, the system is at equilibrium

4.2 Phase Boundaries

Key points 1.  A substance is characterized by a variety of

parameters that can be identified on its phase diagram

2.  The phase rule relates the number of variables that may be changed while the phases of a system remain in mutual equilibrium

4.2 Phase boundaries

•  The phase diagram of a pure substance shows the regions of p and T at which its various phases are thermodynamically stable

•  Phase boundaries shows the values of p and T at which two phases coexist in equilibrium

•  Vapor pressure : p of a vapor in equilibrium with the liquid ; the liquid-vapor phase boundary

•  Sublimation vapor pressure : the vapor pressure of the solid phase ; solid-vapor phase boundary

•  Boiling : the condition of free vaporization

•  Boiling temperature

(a) Characteristic properties related to phase transitions

(normal boiling point, standard boiling point)

4.2 Phase boundaries

•  Supercritical fluid •  Boiling does not occur when a

liquid is heated in a rigid, closed vessel

•  Critical temperature, Tc •  Critical pressure, pc

•  Melting temperature : the temperature at which the liquid and solid phases coexist in equilibrium

•  Freezing temperature : normal freezing point

•  Triple point : a point at which the three phase boundaries meet

•  The triple point of a pure substance is outside our control

(a) Characteristic properties related to phase transitions

T increases from (a) to (c)

4.2 Phase boundaries

•  Phase rule : the number of parameters that can be varied independently

•  C : the number of components •  Components : a chemically independent constituent of a system •  Constituent : a chemical species that is present

•  2 constituents : a mixture of ethanol and water •  3 constituents and 2 components : a solution of sodium

chloride •  P : the number of phases •  F : variance, the number of intensive variables that can be changed

independently without disturbing the number of phases in equilibrium

(b) The phase rule

F =C −P + 2

4.2 Phase boundaries

•  Phase rule

•  For C = 1 and P = 1, F = 2 ; bivariant •  For C = 1 and P = 2, F = 1 •  For a one-component system, F = 3 − P

•  For P = 2 and F = 1 with phases α and β, µ(α;p,T) = µ(β;p,T)

•  For P = 3 and F = 0 with phases α, β, and γ, µ(α;p,T) = µ(β;p,T) = µ(γ;p,T)

•  For P = 4 with phases α, β, γ, and δ, µ(α;p,T) = µ(β;p,T) = µ(γ;p,T) = µ(δ;p,T)

(b) The phase rule

F =C −P + 2

Typical regions of a one-component phase diagram

4.3 Three representative phase diagrams

Key points 1.  Carbon dioxide is a typical substance but shows

features that can be traced to its weak intermolecular forces

2.  Water shows anomalies that can be traced to its extensive hydrogen bonding

3.  Helium shows anomalies, including superfluidity, that can be traced to its low mass and weak interactions

4.3 Three representative phase diagrams

•  The positive slope of the solid-liquid boundary

•  The triple point lies above 1 atm : the liquid cannot exist at normal atmospheric pressures for any T (dry ice)

•  Carbon dioxide gas cannot be liquefied unless one applies high pressure, which implies the weakness of the intermolecular forces between the nonpolar carbon dioxide molecules

(a) Carbon dioxide

4.3 Three representative phase diagrams

•  The solid-liquid boundary has a steep negative slope due to the open structure of ice

•  Anomalously high boiling point for a molecule of its molar mass

•  High critical temperature and pressure

•  Polymorphism : the solid phases of ice differ in the arrangement of the water molecule

(b) Water

The structure of ice I

4.3 Three representative phase diagrams

•  The solid and gas phases are never in equilibrium : Solid helium can be obtained only by holding the atoms together by applying pressure

•  Pure helium-4 has two liquid phases •  He-I : normal liquid •  He-II : superfluid ; it flows

without viscosity •  Pure helium-3 is different

(c) Helium, 4He