《物理化学 Physical Chemistry》课程教学资源（英文版）Phase Transformations（Pure Substances）

Phase transformations Pure Substances Chemistry 331

Chemistry 331 Phase Transformations Pure Substances

Phase Change Chapters Phase Changes Chapter 6 Chapter 7 Chapter 8 Pure Substances Binary Mixtures Complex Systems Chemistry 331

Chemistry 331 Phase Change Chapters Chapter 6 Pure Substances Chapter 7 Binary Mixtures Chapter 8 Complex Systems Phase Changes

Phase diagram o critical point pe q 1 atm solid g as triple point Chemistry 331

Chemistry 331 Phase Diagram solid liquid gas p T critical point triple point 1 atm Tb

apor pressure the pressure of the vapor in equilibrium with the iqu id. depends on the temperature the only pressure(for a vapor given temperature)at which liquid and vapor coexist liquid Chemistry 331

Chemistry 331 Vapor Pressure the pressure of the vapor in equilibrium with the liquid. depends on the temperature. the only pressure (for a given temperature) at which liquid and vapor coexist. liquid vapor p

Phase equilibrium G OT solid liquid s>s,>S g gas Th Temperature Chemistry 331

Chemistry 331 Phase Equilibrium Temperature m gas liquid solid Tf Tb   G T S S S S p g l s       = −  

Pressure Effects on Phase equil > liquid gas Chemistry 331

Chemistry 331 Pressure Effects on Phase Equil. T m gas liquid solid Tf Tb   G p V V V V T g l s       =   Tf Tb

Clapeyron Equation solid(p+dp, T+dr)<> liquid(p+dp, T+dn) dμu solid(p, liquid dμu=dμ, if phase equilibrium is maintained herefore, V -ssdT= vdp-SdT dpT=△Sns△Vns Chemistry 331

Chemistry 331 Clapeyron Equation dms= dml , if phase equilibrium is maintained therefore, Vsdp -SsdT = Vldp -SldT dp/dT = DSfus/ DVfus solid(p,T)  liquid(p,T) solid(p+dp,T+dT)  liquid(p+dp,T+dT) dms dml

Clausius-Clapeyron equation qp△S△H for phase equilibrium cT△T △≈RT/ p if one phase is gaseous pdt rre or In p△H 1qp△H dT rT2 PP △E R(T Chemistry 331

Chemistry 331 dp dT S V H T V V RT p p dp dT H RT d p dT H RT p p H R T T = =  = =       = − −       D D D D D D D D for phase equilibrium if one phase is gaseous or / ln ln 1 1 1 2 2 0 0 Clausius-Clapeyron Equation

Nitric Acid Vapor Pressure m=-4565K △H=mR=3795kJ 0.0025 0.0027 0.0029 0.0031 0.0033 0.0035 0.0037 1/T Chemistry 331

Chemistry 331 Nitric Acid Vapor Pressure 0 2 4 6 8 0.0025 0.0027 0.0029 0.0031 0.0033 0.0035 0.0037 ln p 1/T m = - 4565 K DHvap= mR = 37.95 kJ

Vapor Pressure in Gas mixtures p+△P Vm(l)dp=m(g)dp liquid(p+4P)=gas(p) Vm()AP=R7φp/p *、D△P In(p/p)= m liquide) =gas(p) RT Chemistry 331

Chemistry 331 Vapor Pressure in Gas Mixtures d d V l dp V g dp V l P RT dp p p p V P RT l g m m p p p p P m p p m m = m = = =    + ( ) ( ) ( ) / ln( / ) * * * * * D D D liquid(p* ) = gas (p* ) liquid(p*+DP) = gas (p)