lecture n. 8 farmacia · 2019. 1. 17. · lecture n. 8_farmacia.pptx author: maurizio_retina...
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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