《物理化学 Physical Chemistry》课程教学资源（英文版）Phase Equilibrium（Phase Diagrams）

Phase equilibrium Phase diagrams

Phase Equilibrium Phase Diagrams

Definitions F: the number of degrees of freedom, i.e the number of independent variables needed to describe the state of the system C the number of independent substances in the system P: the number of phases in the system where a phase is a form of matter that is uniform throughout in composition and state

Definitions • F: the number of degrees of freedom, i.e. the number of independent variables needed to describe the state of the system. • C: the number of independent substancesin the system. • P: the number of phases in the system, where a phase is a form of matter that is uniform throughout in composition and state

The phase rule Each phase needs C-1 composition variables plus t and p to describe its state Therefore the total number of state variables is P(C-1)+2 For each substance. there are p-1 equi constraints of the form u(a)=u(B) Therefore F=P(C-1)+2-C(P-1) or F=c-p+2

The Phase Rule • Each phase needs C-1 composition variables plus T and p to describe its state. Therefore, the total number of state variables is P(C-1) + 2 • For each substance, there are P-1 equil. constraints of the form () = () • Therefore F = P(C-1) + 2 - C(P-1) or F = C - P + 2

Phase diagram critical point qui I atm solid g as triple point

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

Cooling Curve: Pure Substance liquid cooling arrest solid cooling liquid freezing time

Cooling Curve: Pure Substance time T Tf arrest liquid cooling solid cooling liquid freezing

Boiling pt /Composition Diagram Tb个 * for the liquid vapor with composition x A boiling pt of pure B g boilins pt. of * B liquid pure A composition of the vapor that boils off A A at t XA→

Boiling Pt./Composition Diagram liquid xA Tb  vapor TA * TB * yA xA → Tb for the liquid with composition xA composition of the vapor that boils off at Tb boiling pt. of pure A boiling pt. of pure B

Lever rule let za be the total mole fraction of A. both phase a phases combined Let n and n be the phase p moles in phases a and阝 nza naXa t nByA noza+ nBZA AAA n 阝yA yA X

Lever Rule • Let z be the total mole fraction of A, both phases combined. • Let n and n be the moles in phases  and . • nz = nx + nyA = nz + nzA • n (z-x) = n (y-z) • n l = n l zA phase  phase  l l T yA xA

A zeotropes azeotropic boiling pi ot Ⅴapor liquid B A azeotropic composition

liquid vapor Tb  TA * TB * xA → Azeotropes azeotropic composition azeotropic boiling pt

Ideal Boiling Pt /Composition P p pB(pa -pB)a where from the Clausius-Clapeyron eq'n, AH(4)(1 PA=p exp R TT(A

Ideal Boiling Pt./Composition               − −  = + − = = ( ) ( ) 1 1 exp where from the Clausius -Clapeyron eq'n, ( ) * 0 * * * * R T T A H A p p p p p x x p p p y b vap A B A B A A A A A

Immiscible liquids T↑ I liquid phase upper critical temperature T 2 liquid phases x A → B composition of composition of phase a at T' phase Bat T

Immiscible Liquids xA → T  upper critical temperature T x x composition of phase  at T composition of phase  at T 2 liquid phases 1 liquid phase