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

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1 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 for the Coexistence of Mutipe hases ure substances ay exist in any soid phases but it can ony exist in one aseous state. Most substances have a sine iquid state with a few exceptions. he stabiity of the phase of a pure substance is deterined by the physica conditions, and. Fro the enery point of view the stabiity of a syste is hihest when the Gibbs free enery (cheica potentia, ) of it is at a iniu. he chanes in cheica potentia teperature and pressure of a pure substance is iven by; d S d V d

2 0 G ng n n,, d S d V d S Sopes S > S > S G V, as, iquid, soid At a iven teperature phase with the owest is the ost stabe With increase, s 0 S fus H s b vap H b vap s Effect of on the phases: (1) V V V a s iq u id s o id V increases with pressure and the anitude of chane foows the V of the phase; therefore the vs. at a hiher than std. woud ook ike (iht ines) (eft); a ower than std. woud ook ike (iht ines) (riht); Fast heatin and cooin eads to super heatin and super cooin. he f.p. and b.p. chanes (in opposite directions).

3 ( 2) V V V a s iq u id s o id increases with pressure and the anitude of chane foows the V of the phase; therefore the vs. at a hiher for (2) woud ook ike (iht ines); V soid V iquid vs. pot for a ases shifts on axis uch ore rapidy with than those pots for iquid and soid curves. As a resut, chanes in can chane the phase chanes with increasin fro the expected s to s subiation. ressure ay be such that the three ines ove and intersect at a sine point (tripe point, tp ) tripe point pressure. At the tripe point a three phases coexist in equiibriu. Subiation. s tp

4 ifviqu<idsoidressure-eperature hase Diara: - phase diara raphicay dispays the experienta pressures and teperatures of a syste (pure substance, here) that ay exist as a sine phase, two phases in equiibriu, or three phases in equiibriu. Vs ripe points.soid curves (two phases coexist at equiibriu) for ost substances, phase boundary, the soid curve, has a positive sope. Reions (sine-phase) bounded by ines. Use of phase diara to predict phase chanes with and if V iquid < V soid No phase boundary? phase chanes a b; b to a c d; d. Note: Aon the two-phase coexistence (equiibriu) curves in which one of the coexistin phases is a as, refers to the vapor pressure of the substance. In a other reions, refers to the externa pressure that woud be exerted on the pure substance if it were confined in a suitabe container.

5 Soid-iquid coexistence curve - etin point dependence on pressure, is a weak function of the pressure. If the soid > iquid, the sope of this curve is positive, and the etin teperature increases with pressure. his is the case for ost substances. If the soid > iquid, the sope is neative and the etin teperature decreases with pressure. he sope of the iquid-as coexistence curve is uch saer than that of the soid-iquid coexistence curve; the boiin point is uch stroner function of the pressure than the freezin point. he boiin point aways increases with pressure. Soid-as coexistence curve ends at the tripe point and the iquid-as curve ends at the critica point, where the iquid and as phases have the sae density, with no distinct phases (super critica fuid). Because the iquid and as phases are indistinuishabe at the critica point, H vap approaches zero as the critica point is reached. b a C, sd C, d C, d C C d,, s d

6 H b b = H b a a b :Hess Law. In it s iit with the rectane encopassin tp and iniizes to a point (tripe point); a H subiation H fusion Hvaporization b hase Rue (one substance coponent) he hase Rue describes the possibe nuber of derees of freedo (F) in a (cosed) syste at equiibriu, in ters of the nuber of separate phases (p) and the nuber of cheica coponents (c) in the syste. F = C p + 2 For a pure substance (one coponent syste) C = 1. F = 3 p F = # of independent intensive variabes that need to be define the state of the syste e.. teperature, pressure, or concentration. Cheica coponents are the distinct substances invoved in the equations of the syste. (If soe of the syste constituents reain in equiibriu with each other whatever the state (, s or ), they shoud be counted as a sine constituent. i.e. one coponent syste)

7 Exape hase diara of water Exape hase diara of CO 2 H O()() s H O 2 2 Soid curves (two phases coexist at equiibriu) ; C =1, p =2, F = 1 s, s, Reions (sine-phase) bounded by ines. C =1, p =1, F = 2 ripe points. C =1, p =3, F = 0 For the coexistence of two phases, and, for exape, it requires that their cheica potentias be equa. For s- ine; (,)(,) F = 1 V and V hase Diaras -V phase diara is aso iportant in studyin phase equiibria. But phase diaras that incudes ony two of the three state variabes does not contain inforation on the third variabe. Cobination of - and -V phase diara ives the -V- phase diara. For tripe point; (,)(,)(,) F = 0 No ore than three phases of a pure substance can be in equiibriu as F is never neative nuber. F can increase if a syste contains severa cheicay independent species (coponents), for exape in a syste consistin of ethano and water.

8 V hase Diaras V hase Diaras heoretica Basis - - hase Diara (,)(,) For infinitesia chanes in d and d; (,)(,) d d Movin aon ine and sti in equiibriu; d d S d V d S d V d S S d ( V V ) d d S d V :Capeyron Equation etin tep. = G H S S d S d V etin/fusion (,)(,) fus fus fus fus H fus G fus heoretica Basis - - hase Diara For infinitesia chanes in d and d; d d (,)(,) d d S d V d S d V d S S d () V V d S S d () V V d d S d V :Capeyron Equation vaporization vaporization tep. = G H S vap vap vap d S d V Hvap Gvap Svap 90 J / o K routons Rue routon s rue, states that S vaporization ~ 90 J/ o- K for iquids. he rue fais for iquids capabe of forin hydroen bonds.

9 Causius-Capeyron Equation: Vapor ressure vs. (etin) d d f i S V d f i S V fusion fusion d :Capeyron Equation :for fusion f f f H fusion d H fusion d d V V i i fusion fusion i H H f i n V V fusion f fusion fusion i fusion i n : f i i H fusion f i n 1 : for 1 V fusion i i H fusion :inear variation V fusion i Causius-Capeyron Equation: Vapor ressure vs. (vaporization) d S d V f i f i d S H H d V V R d, vap vap vap 2, vap, as H R vap 2 d :Capeyron Equation f f f d H vap d H vap d 2 2 R R i i i :for vaporization f H vap 1 1 n :non-inear variation i R f i H vap f i H vap R 2 i f R i (1) f i = i e e e f i H vap H vap R 2 2 i Ri e i e = : exponentia variation

10 Vapor ressure of a ure Substance Appied ressure (constant teperature) pure iquid () pure vapor () * p he vapor pressure p at a certain teperature is a? constant (p = *) and depends on the substance. = p + p Ar How woud p chane if appied pressure is chaned? (, )(,) p (, p) (,) p p (, ) p * = p+ p Ar d S d V d p p V V V (,)(,) p R 1 dp V d R dp ' V d ' * ' p R n( *) V * d V d p d V d V *