Phase Behavior and Equilibria

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Arleen Kerrie King
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1 hase Behavior and Equiibria E-1 he next portion of this course (minus kinetics) wi use the aws of thermodynamics to examine different physica and chemica processes (such as phase equiibria). hase Diarams of Benzene

2 hase transitions as function of Benzene E-2 1 atm 2 atm 3 atm At 1 atm the metin pt is 5.5 C. At 34 atm the metin point is 6.5 C. At 1 atm the boiin pt is 80.1 C. At 0.66 atm the boiin point is 67 C. M at 1 atm Norma metin point M at 1 bar Standard metin point B at 1 atm Norma boiin point B at 1 bar Standard boiin point

3 Some definitions E-3 Benzene Coexistence curve can be thouht of as the pressure dependence of a certain phase transition (metin). ripe point: S-L- a coexist. Benzene 5.5 C and 36.1 torr hase rue f 3 - p Derees of freedom (different than previous!) Number of phases in coexistence In sine phase reion both and must be specified to describe system. A coexistence curves ony one must be specified. At tripe point?

4 hase transitions for H 2 O E-4 How does this differ from benzene? M of H 2 O decreases with increasin pressure! his is because moar voume of ice is reater than that of water at same conditions.

5 Is ice aways cod? E-5

6 Critica oint E-6 CO 2 Remember critica points from as aws? If you foow bue arrow the as can be transformed into a iquid without every passin throuh a two-phase state. What happens to vap H? c

7 hase diarams and ibbs enery E-7 ibbs at a function of temperature See Side A&-20 Continuous function Discontinuity in sope at phase transition Sopes reated to entropies Dashed ines are metastabe states S phase

8 ibbs as a function of E-8 phase Aways positive (sopes +) Manitude of sopes depends on substance Imaine - phase diaram and Exampes near tripe point Benzene above t.p. Water beow t.p.

9 Can you ID ocation on phase diarams? E Identify the ine on phase diaram that corresponds to fiure on eft What is the difference between these ines?

10 E-10 Consider a two phase system + dn n dn n d + dn n n d he ibbs enery of two phases in equiibrium with each other is simpy the sum of the individua ibbs eneries. Now imaine dn moes are transferred from the iquid phase to the as phase with and hed constant. We can write the chane in ibbs enery as: WHY?

11 Chemica potentias he partia derivatives in the ast expression are caed chemica potentias d i μ i i n [ ] μ μ dn E-11 What happens at equiibrium? d 0 μ μ Out of equiibrium the transfer of matter occurs so d < 0. vacuum

12 E-12 Simpe form of the chemica potentia i i μ ) ( ) ( β μ μ d d d d + + β β μ μ μ μ d d d d + + β β d Sd d + For a pure substance the chemica potentia is simpy the moar ibbs enery an intensive quantity. At equiibrium Aso true that the tota derivatives are equa to each other Reca: What are &?

13 Capeyron Equation E-13 d S d β d S β d d d S β β S OR d d trs trs S d d trs trs H Capeyron Equation In words Reationship between the sope of the twophase boundary ine in a phase diaram with the chane in moar enthapy and moar voume. Impicit in equation 1. 2.

14 Causius-Capeyron Equation E-14 Capeyron Equation works we for fusion but not vaporization or subimation. Why?? Because moar voume of as is strony pressure dependent! d d ( vap H ) Away from critica point d d ( vap H ) vap H Assume idea as d d vap R 2 H 1 d d d n d vap R H 2 Causius-Capeyron Equation

15 Interated form of CC Equation: art 1 E-15 Indefinite intera 1 d vaph d 2 R apor pressure of iquid benzene from 313 K to 353 K vaph n + constant R But we know that the moar enthapy of vaporization does vary with temperature (dhc p d). We can mode this (statisticay) vaph A + B + C A B C n + n + + k +... R R R Interation constant

16 Interated form of the CC Equation: art 2 Definite intera d 2 1 vap R H 2 d E-16 n vap 1 R H 2 1 he above equation can be used to cacuate the vapor pressure at some temperature iven the moar enthapy of vaporization and vapor pressure at some other temperature. Exampe: Benzene What is vapor pressure at K for benzene (norma boiin point K vap H 30.8 kj mo -1 )? ive answer in torr. Experimenta 1360 torr Why the discrepancy?

17 E-17 μ from q N B Q k U 2 n Q k Q k S B N B n n + S U A Q k A B n n A n μ Reca: B N Q R n Q k n n μ

18 Summary E-18 hase diarams Chemica potentia: Matter fows from a hiher chemica potentia to a ower chemica potentia Capeyron and Causius-Capeyron Equations Connectin chemica potentia to stat mech!

Phase Diagrams. Chapter 8. Conditions for the Coexistence of Multiple Phases. d S dt V

Phase Diagrams. Chapter 8. Conditions for the Coexistence of Multiple Phases. d S dt V hase Diaras Chapter 8 hase - a for of atter that is unifor with respect to cheica coposition and the physica state of areation (soid, iquid, or aseous phases) icroscopicay and acroscopicay. Conditions