Lecture8ChangesofStateAndColligativeProperties

“PHASE”(P)

Astateofmatterthatisuniformthroughout,notonlyinchemicalcompositionbutalsoinphysicalstate.

“NUMBEROFCOMPONENTS”(C)

Theminimumnumberofindependentspeciesnecessarytodefinethecompositionofallphasespresentinthesystem.

Thechemicalpotentialofasampleisuniformwhenitisatequilibrium,regardlessofthenumberofphases.

TTbTm

µ Solid

Liquid

Gas

Solidstable Liquidstable Gasstable

S(s)<S(l)<<S(g)

µs=µℓ

µℓ=µg

ONE-COMPONENTSYSTEMS

PHASEDIAGRAMSp,T-intensiveproperties

T

p

Liquidstable

Vapourstable

Vapourstable

Tc

Solidstable

Howdowedeterminetheboundariesbetweendifferentphases?

µα=µβ

Answer:from

WechangepandTinfinitesimallybydpanddT:

CLAPEYRONEQUATION

Slopeofthep(T)boundarycurvesT

p

s g

l

Solid-liquidboundary(melting)

>0

ifΔVm>0(common),dp/dT>0

Small:largeslope,steepcurve

ifΔVm<0(rare),dp/dT<0

T

p

sg

l

T

p

s g

l

Liquid-vapourboundary(evaporation)

large:theslopeissmallerthanforthesolid-liquidboundarywherethetwocurvesmeet.

T

p

sg

l

T1

T2>T1gp2>p1

ΔVm=Vm(g)-Vm(l)issmallerathigherp!

CLAUSIUS-CLAPEYRONEQUATION

(e) (d) (c) (b) (a)

CLAUSIUS-CLAPEYRONEQUATION,integralform

Solid-vapourboundary(sublimation)

T

p

s g

l

wheretheboundariesmeet

Themeetingpointofthethreeboundaries:THETRIPLEPOINT

T

p

s

g

l

THEPHASERULE

TheVARIANCE(i.e.thenumberofdegreesoffreedomofasystem)isgivenby:

F=C-P+2C-numberofcomponentsP-numberofphases2-pandT

Forasinglecomponent:F=1-P+2=3-P

T

p

sg

l

F=2F=1

F=0

F=2:thesinglephaseispreservedwhenbothTandparechangedindependently.F=1:Tandpcannotbechangedindependentlytopreservetheequilibriumbetweentwophases.

F = 0: the triple point is out of our control - it depends on thepropertiesofthesystemanditoccursatasingle,welldefined(p,T)coupleofvalues.

PhaseDiagramsCarbon dioxide

SupercriticalFluids

TheCriticalPoint

CriticalTemperaturesandPressures

Water

Water

Iodine

TWO-COMPONENTSSYSTEMS

(a)Twovolatilecomponents

ConsideramixtureoftwovolatileliquidsAandBAtequilibrium:

Wedenotepuresubstanceswith*.ForpureA:ForAinthemixture:

VapourPressureofpureA

VPofAinthemixture

Formixturesofcloselyrelatedliquids(“idealsolutions”):

Raoult’sLaw T=const.

ExampleofamixturecloselyobeyingRaoult’sLaw:

T=const.

DeviationsfromRaoult’sLaw

TheDILUTESOLUTEobeysHENRY’SLAW:

TheALMOSTPURESOLVENTobeysRAOULT’SLAW

T=const.

NegativeandpositivedeviationsfromRaoult’sLaw

Example1:negativedeviationsfromRaoult’sLaw

Example2:positivedeviationsfromRaoult’sLaw

Thevapourisricherinthemorevolatilecomponent

VapourPressureDiagrams

Thevapourisricherinthemorevolatilecomponent

T=const. T=const.

VapourPressureDiagrams:DistillationatT=const.

Lever’sRule:

Distillationatp=const.Temperature-CompositionDiagrams

ForIdealSolutions:FractionalDistillation

Vapour

Liquid

T=const

p=const

Distillationatp=const.Temperature-CompositionDiagramsForNon-IdealSolutions.Azeotropes.

Maximum-boilingazeotrope Minimum-boilingazeotrope

H2O HClMolefractionofHCl

108.58°C

-111°C

�HCl=0.111

100°C

MolefractionofH2O H2OEthanol

78.4°C

100°C

�H2O=0.096

78.17°C

Twoexamples

TWO-COMPONENTSSYSTEMS

(b)Anon-volatilesolute

COLLIGATIVEPROPERTIES

COLLIGATIVEPROPERTIESarethosepropertieswhichdependonlyontheNUMBERofsoluteparticlespresent,

notontheirIDENTITY.

- VapourPressureDecrease- BoilingPointElevation- FreezingPointDepression- OsmoticPressure

VAPOURPRESSUREDECREASE

non-volatilesolute,doesnotdissociate

p<p*

TherelativedecreaseofthesolventVPisequaltothesolutemolefraction

Whatifthesoluteisastrongelectrolite?

Whatifthesoluteisaweakelectrolite?

I

V

E

van’tHoffCoefficient

GENERALEQUATIONFORVAPOURPRESSUREDECREASE

van’tHoffCoefficient

χ solvent =

nsolvent

nsolvent + i × nsolute

= PP *

BOILINGPOINTELEVATIONANDFREEZINGPOINTDEPRESSION

m-molality[m]=mol/kg

Determinationofapproximatemolecularmasses

OSMOTICPRESSURE

Determinationofapproximatemolecularmasses

HighPforsmallconcentrationsÞ Verysensitive

Þ MMofmacromolecules

INVERSEOSMOSIS