廈大課件物化chapter

1、1Chapter 7 ponent Phase Equilibrium2The Phase RulePhase: a state of matter that is uniform throughout in chemical composition and physical state. (Gibbs)Number of phase (p): Gas or gaseous mixture single phaseLiquid one, two and three phasestwo tally miscible liquids single phasea slurry of ice and

2、water two phasesSolid a crystal is a single phasean alloy of two metals two phases (immiscible)- one phase (miscible)Physical ChemistryChapter 73The Phase Rule(a)(b)The difference between (a) a single-phase solution, in which the composition is uniform on a microscopic scale, and (b) a dispersion, i

3、n which regions of one component are embedded in a matrix of a second component.Physical ChemistryChapter 74The Phase RuleThe difference between (a) constituent and (b) componentconstituent: a chemical species (an ion or a molecule) that is present in a systemcomponent: a chemically independent cons

4、tituent of a systemnumber of components (c): the minimum number of independent species necessary to define the composition of all the phase present in the systemPhysical ChemistryChapter 75The Phase RuleWhen no reaction takes place,The number of constituent = the number of componentPure water:a pone

5、nt systemMixture of ethanol and water:a ponent systemwaterethanolwaterPhysical ChemistryChapter 76The Phase RuleWhen a reaction takes place,CaCO3(s) CaO(s) + CO2(g)Phase 1a ponent systemCaOCO2Phase 2Phase 3CaO + CO2 CaCO3Physical ChemistryChapter 7The number of constituent the number of component7Th

6、e Phase RuleCounting componentsNH4Cl(s) NH3(g) + HCl(g)Phase 1a ponent systemNH4ClPhase 2NH4Cl NH3 + HClHow many components are present in a system in which ammonium chloride undergoes thermal position?three constituentsadditional NH3 or HCl ponentPhysical ChemistryChapter 78The Phase RuleDegree of

7、freedom or Variance (f): the number of intensive variables that can be changed independently without disturbing the number of phases in equilibrium.The phase rule: a general relation among the variance f, the number of components c and the number of phases p at equilibrium for a system of any compos

8、ition.f = c p + 2(7.7)no reactionsPhysical ChemistryChapter 79The Phase RuleTwo assumptions:Counting the total number of intensive variables (properties that do not depend on the size of the system). The pressure P and temperature T count as 2.(1) no chemical reactions occur(2) every chemical specie

9、s is present in every phaseSpecify the composition of a phase by giving the mole fractions of c-1 components (because x1+x2+xc=1, and all mole fractions are known if all except one are specified.)There are p phases, the total number of composition variables is p(c-1). At this stage, the total number

10、 of intensive variables is p(c-1)+2. Physical ChemistryChapter 710The Phase RuleAt equilibrium, the chemical potential of a component j must be the same in every phase:That is, there are p-1 equations to be satisfied for each component j. as there are c components, the total number of equations is c

11、(p-1).j, = j, = for p phaseEach equation reduces the freedom to vary one of the p(c-1)+2 intensive variables. It follows that the total variance isf = p(c-1) + 2 - c(p-1) = c p + 2Physical ChemistryChapter 711f1p23p，(C1）f 0, p 1, 3p1p1，f2p2，f1p3，f0 ponent phase equilibriumFor a ponent system (pure w

12、ater)Physical ChemistryChapter 712The Phase RulePhase diagram: shows the regions of pressure and temperature at which its various phases are thermodynamically stable.Phase boundary: a boundary between regions, shows the values of P and T at which two phases coexist in equilibrium. Physical Chemistry

13、Chapter 713The Phase RuleSolid-liquid phase boundary: a plot of the freezing point at various P.T3TcPTGas stableLiquid stableSolid stableTfTbTTriple pointCritical pointvapor liquid solid Liquid-vapor phase boundary: a plot of the vapor P of liquid against T.Solid-vapor phase boundary: a plot of the

14、sublimation vapor P against T.Physical ChemistryChapter 714The Phase RuleTriple point: at which three different phases (s, l, g) all simultaneously coexist in equilibrium. It occurs at a single definite pressure and temperature characteristic of the substance (outside our control).T3TcPTTriple point

15、Critical pointvapor liquid solid Critical point: at which (critical P and critical T) the surface disappears.Physical ChemistryChapter 715t/ADC0.006110.01solidgasliquidOP / 10 5 Pa374.2218 atm H2O phase diagram: P T LinePointRegion99.9741 atm0.0024IRSYTfTbT3Physical ChemistryChapter 716H2O phase dia

16、gram: P TRegion (s, l, g): f=2, one phaset/ADC0.006110.01solidgasliquidOP / 10 5 Pa374.2218 atm99.9741 atm0.0024IRSYTfTbT3Line (OA, AD, AC): f=1, two phases in equilibriumPoint (A): f=0, three phases in equilibriumTcPhysical ChemistryChapter 717Pure watervaporP=611Paicet=0.01Triple pointIn a sealed

17、vessel(a) Triple point of H2OAir and vaporP=101.325 kPa冰Air-saturated watert=0Freezing pointIn an open vessel(b) Freezing point of H2ODifference between triple point and freezing pointPhysical ChemistryChapter 718Difference between triple point and freezing pointThe higher pressure lowers the freezi

18、ng point compared with that of pure waterThe dissolved air (i.e. N2 and O2) lowers the freezing point compared with that of pure waterWhy the freezing point is lower than the triple point?Physical ChemistryChapter 719The Clapeyron EquationFig. 7.5 two neighboring points on a two-phase line of a pone

19、nt system.dTPT +Phase Phase Phase equilibrium: dP12For a pure substanceAt point 1,At point 2,(7.13)Physical ChemistryChapter 720The Clapeyron EquationFor a single phase(7.14)pure phase(7.15)one-phase, ponentPhysical ChemistryChapter 721The Clapeyron EquationFor any point on the - equilibrium line(7.

20、15)(7.13)(7.16)(7.17)*Physical ChemistryChapter 722The Clapeyron EquationFor a reversible (equilibrium) phase change(7.18)*(7.17)*Clapeyron Equation (Clausius-Clapeyron equation)one component two-phase equilibriumPhysical ChemistryChapter 723The Clapeyron EquationFig. 7.5: two neighboring points on

21、a two-phase line of a ponent system.dTPT +Phase Phase The slope of the phase boundariesdP12Any phase equilibrium of any pure substancePhysical ChemistryChapter 724The liquid-vapor boundary The solid-vapor boundarySolid-gas or liquid-gas equilibrium, not near Tc(7.19)*(7.20)Physical ChemistryChapter

22、725The liquid-vapor boundary The solid-vapor boundarySolid-gas or liquid-gas equilibrium, not near Tc(7.21)(7.22)liquid-gas equilibrium, not near TcPhysical ChemistryChapter 726The solid-liquid boundarySolid-liquid equilibrium, small temperature range(7.23)(7.24)Physical ChemistryChapter 727Construc

23、ting a solid-liquid phase boundaryExample: construct the ice-liquid phase boundary for water at temperature between 1oC and 0oC. What is the melting temperature of ice under a pressure of 1.5 kbar? fusH = +6.008 kJ/mol, fusV = -1.7 cm3/mol.Answer:(7.23)Physical ChemistryChapter 728The Phase RuleThe

24、formula gives the following values:T/oC-1.0-0.8-0.6-0.4-0.20.0P/bar1301057953271.0What is the melting temperature of ice under a pressure of 1.5 kbar?Rearrange the formula intoThen, with P=1.5 kbar, T=262 K or 11oC.Physical ChemistryChapter 729The Phase RuleP1=1.0 bar, T1=273 KP2=1.5 kbar, T2=262 KC

25、omment: notice the decrease in melting temperature with increasing pressure: water is denser than ice, so ice responds to pressure by tending to melt.Physical ChemistryChapter 730Solid-solid Phase TransitionsPolymorphism:Many substances have more than one solid form which has a different crystal str

26、ucture and is thermodynamically stable over certain ranges of T and P.Allotropy:Polymorphism in elements.Metastable:The rate of conversion of to is slow enough to allow to exist for a significant period of time.Physical ChemistryChapter 731Solid-solid Phase TransitionsFig. 7.9 (a)Phase diagram of S

27、(part)Et/80120160P / 10 5 Pa10210010-210-410-6104gasBCliquidmonoclinicorthorhombicsolid95119151Three triple points:B: 95 oCC: 119 oCE: 151 oCPhysical ChemistryChapter 732Solid-solid Phase TransitionsThere are many different types of Phase Transition.Fusion, vaporizationEhrenfest Classification:Chang

28、es of enthalpy and volume(7.15)Physical ChemistryChapter 733Solid-solid Phase TransitionsBecause trsV and trsS are non-zero for melting and vaporization for such transitions, the slopes of the chemical potential plotted against either pressure or temperature are different on either side of the trans

29、ition. The first derivatives of the chemical potentials with respect to pressure and temperature are discontinuous at the transition.First-order phase transitionTtHTtVTtSTtCPTtTPhysical ChemistryChapter 734Solid-solid Phase TransitionsCP is the slope of H-T. at Tt, the slope of H and Cp are infinite.F