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 CaCO 3 (s) CaO(s) + CO 2 (g) 3. There are two solid phases and one gaseous phase 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, T trs : 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 onecomponent system, µ=g m 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=(µ 2 -µ 1 )dn Only when µ 2 = µ 1 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 (a) Characteristic properties related to phase transitions 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 (normal boiling point, standard boiling point)
4.2 Phase boundaries (a) Characteristic properties related to phase transitions Supercritical fluid Boiling does not occur when a liquid is heated in a rigid, closed vessel Critical temperature, T c Critical pressure, p c 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 T increases from (a) to (c)
4.2 Phase boundaries (b) The phase rule Phase rule : the number of parameters that can be varied independently F = C P + 2 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
4.2 Phase boundaries (b) The phase rule Phase rule F = C P + 2 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) Typical regions of a onecomponent 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 (a) Carbon dioxide 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
4.3 Three representative phase diagrams (b) Water 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 The structure of ice I
4.3 Three representative phase diagrams (c) Helium, 4 He 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